Continuous transition with discrete energy spectrum.

[K^2]

This is in reply to a comment from another thread. I've figured it's worth a proper response for the sake of anyone who is likewise misinformed or just curious about quantum transitions, and it has taken me a bit longer to put this together than I anticipated, so I am posting this as a new thread. Hopefully, a discussion to follow will be worth a thread.

Discrete states, hmmm, sounds like what is said, super position implies simultaneity. If what you are saying is correct then flourescense and phophorescnce cannot exist, because the product photon could result from any state between its incident energy and dE of the excited state. But this is not the case, flourescence spectrum comes in a dsitribution completely separated from the excitation frequncy. If what you are saying true and there is a continuous sspectrum of eigenstates, a photon will spontaneously appear at any and thus the relaxation photn energies would not exhibit a discrete distrbution relative to the exciting photon. Show you explanation of dicrete flourescent states.

To keep things simple, let us consider a harmonic oscilaltor, rather than an atom, since oscillator can be described with just one dimension. The spectrum of a quantum harmonic oscillator is descrete, same as that of an atom, but unlike an atom, all of its energies are separated by an equal spacing of ћÉ between levels. Nonetheless, it serves as a simpler analog fo the purposes of this discussion.

What's going to follow is a bunch of math describing the system. If you don't care or end up giving up on following the math, skip to the pictures!

Dynamics of any quantum system is governed by Hamiltonian. In classical analog, it's the energy of the system. Given a Hamiltonian H, any physical state |È> of the system must satisfy H|È> = iћ∂_t|È>, which is known as time-dependent Shrodinger equation. Just like classical oscillator, the total energy is sum of kinetic and potential, which gives rise to the Hamiltonian.

H = p²/2m + kx²/2

There is a set of time-independent solutions to this equation that satisfies H|È_n> = (n+1/2)ћÉ |È_n>. Energy of each of these state is precisely (n+1/2)ћÉ, which is the eigen value of the Hamiltonian operator. Any other physical solution is a superposition of these states, and can be written as |È> = Σ b_n|È_n> for some set of complex numbers b_n that satisfy Σ |b_n|² = 1. In other words, any solution is a superposition of eigen states of the system, such that total probability of finding system in one of the eigen states is 1.

We wish to describe system in terms of these eigen states, for which there is a much more convenient formalism of rasing and lowering operators. (See Quantum Harmonic Oscillator for more details.)

H|È> = ћÉ(a†a + 1/2)|È>

We can also write down interaction with external field using these operators. Specifically, we wish to hit this oscillator with an electromagnetic field of frequency ν. I am going to demonstrate that so long as ν = É, the energy of incoming photon is absorbed. Otherwise, energy cannot be absorbed, and there is no transition to higher levels.

Because position is proportional to a† + a, we can describe the interaction with the electromagnetic field of incoming photon as follows.

H|È> = [ћÉ(a†a + 1/2) + (a† + a)qE cos(νt)]|È>

(There is a constant in there, dependent on ̉ۡ, which I absorbed into charge, q for simplicity.)

Finally, while there is no clean way to solve this algebraically, we have everything we need to solve it numerically.

∂/∂t |È> = -i/Ñ› H|È>

While one could solve this in coordinate space, it is far easier to use the fact that we have a convenient basis and re-write the equation in the following way.

∂b_i/∂t = H_ij b_j

Where b_i are the aforementioned complex numbers describing the system in term of its superposition of eigen states of the non-interacting Hamiltonain, and H_ij is the matrix representation of the interacting Hamiltonian. At this point, we might as well just plug these matrix representations into computer and make it do the hard work. The following are the results.

First, we hit the sytem with a resonant wave. ν = É

The top part of the image shows probability distribution for the charged particle. It's clear that under influence of the incoming energy, particle begins to oscillate. Which is what we expect. It's also clear that it does so in continuous fashion. Gradually building up the sing.

The bottom part shows corresponding energy levels in multiples of ћÉ. They are discrete. Energy is not a gradual distribution. Particle starts out at precisely (1/2) ћÉ and then starts gaining higher energy elevels with no states anywhere in between.

This leaves just one more things to consider. What happens if energies don't match? Here is the simulation with ν = 1.5 É

Note that while there is some effect, oscillations finally die down. (The electromagnetic wave keeps hitting the system, it does not go away.) Once oscillations die down, process repeats. There is slight and brief excitation of second energy level, but it quickly vanishes. The net transfer of energy from photon to the particle is zero. However, the fact that particle did move a little has an effect. And this happens with atomic excitations as well. The fact that glass has no transitions invisible light means that it does not absorb light. But there are transitions close to visible light, which is what gives glass an optical density. This interaction "slows down" the electromagnetic wave without ever absorbing it.

The conclusion is pretty straight forward. The description in Chemistry texts and some popular science articles about electrons "jumping" orbitals in atoms is a gross oversimplification. Electron never jumps. The electron cloud transitions gradually from one orbit to another over time. Likewise, probability of finding electron in ground or excited state transitions gradually. The only thing that "jumps" is the actual energy. It never matches an intermediate value between the two states.

The main difference between atom and simulations above is that in an atom, all energy levels are different. That's what allows a transition from one state to another, rather than to a distribution of states in the simulation. Otherwise, results are very similar, and the atomic orbital does look llike it's forced into rotation by the oscillating EM field. Maybe one day I'll actually have time to put together some animations for these as well.

[Mazon Del]

Thanks for that! This was a good read.

[KSK]

Agreed. Although I'm still trying to wrap my head around:

The conclusion is pretty straight forward. The description in Chemistry texts and some popular science articles about electrons "jumping" orbitals in atoms is a gross oversimplification. Electron never jumps. The electron cloud transitions gradually from one orbit to another over time. Likewise, probability of finding electron in ground or excited state transitions gradually. The only thing that "jumps" is the actual energy. It never matches an intermediate value between the two states.

Blame it on my chemistry background but I'm having trouble picturing that gradual transition. I'm familiar with orbitals of course and I imagine them as having a discrete shape (and yeah that is a simplification... but chemistry texts) for a given energy. Change the energy and you change the shape. So in that visualisation, if the energy jumps then the shape does too. Which is obviously wrong from what you're trying to tell us, so I guess I need to think about this some more.

Keeps the brain active anyway!

[K^2]

Blame it on my chemistry background but I'm having trouble picturing that gradual transition. I'm familiar with orbitals of course and I imagine them as having a discrete shape (and yeah that is a simplification... but chemistry texts) for a given energy. Change the energy and you change the shape. So in that visualisation, if the energy jumps then the shape does too. Which is obviously wrong from what you're trying to tell us, so I guess I need to think about this some more.

The jump is a jump only in a sense that energy never takes a value between the two levels. The transition still takes time, and in that time, energy state is a superposition of the two energy states. If you happen to measure it in the middle of transition, you'll only be able to measure the lower or higher energy. But it's going to be probabilistic, and probability will change gradually.

The probability distribution for the particle, in the same superposition state, has a much more interesting behavior. While orbitals themselves are static, time-independent solutions, their superpositions are dynamic. It's the same as the oscillator probability distribution starting to move above, while all of the eigen states, which are the analog of the orbitals for oscillator, are static.

[PB666]

The jump is a jump only in a sense that energy never takes a value between the two levels. The transition still takes time, and in that time, energy state is a superposition of the two energy states. If you happen to measure it in the middle of transition, you'll only be able to measure the lower or higher energy. But it's going to be probabilistic, and probability will change gradually.

The probability distribution for the particle, in the same superposition state, has a much more interesting behavior. While orbitals themselves are static, time-independent solutions, their superpositions are dynamic. It's the same as the oscillator probability distribution starting to move above, while all of the eigen states, which are the analog of the orbitals for oscillator, are static.

Just back from a rather exhausting 4 day trip, will examune and respond later (

after couple dozen NSAIDs and a muscle relaxant)

[PB666]

This is in reply to a comment from another thread. I've figured it's worth a proper response for the sake of anyone who is likewise misinformed or just curious about quantum transitions, and it has taken me a bit longer to put this together than I anticipated, so I am posting this as a new thread. Hopefully, a discussion to follow will be worth a thread.

To keep things simple, let us consider a harmonic oscilaltor, rather than an atom, since oscillator can be described with just one dimension. The spectrum of a quantum harmonic oscillator is descrete, same as that of an atom, but unlike an atom, all of its energies are separated by an equal spacing of ћÉ between levels. Nonetheless, it serves as a simpler analog fo the purposes of this discussion.

What's going to follow is a bunch of math describing the system. If you don't care or end up giving up on following the math, skip to the pictures!

Dynamics of any quantum system is governed by Hamiltonian. In classical analog, it's the energy of the system. Given a Hamiltonian H, any physical state |È> of the system must satisfy H|È> = iћ∂_t|È>, which is known as time-dependent Shrodinger equation. Just like classical oscillator, the total energy is sum of kinetic and potential, which gives rise to the Hamiltonian.

The lactic acid levels are low enough now, sooo

H = p²/2m + kx²/2

I don't mean too be nit-pickey but having to referee a particularly large share of pchem and predictive algorhythm manuscripts I have become very sensitive to defining variables in complex equations. So we have to stop and make sure everyone can understand

p = momentum

m = mass

k = ?

x = ?

some equivilant of hv?

i = (-1)^1/2

=Ñ› = reduced plancks constant

È = ?

note you can provide a link to any page that defines these.

Also quick note

one of the derivations below apoears to be in error and b

is not defined.

- - - Updated - - -

Agreed. Although I'm still trying to wrap my head around:

Blame it on my chemistry background but I'm having trouble picturing that gradual transition. I'm familiar with orbitals of course and I imagine them as having a discrete shape (and yeah that is a simplification... but chemistry texts) for a given energy. Change the energy and you change the shape. So in that visualisation, if the energy jumps then the shape does too. Which is obviously wrong from what you're trying to tell us, so I guess I need to think about this some more.

Keeps the brain active anyway!

It was actually A PBS Nova documentary that made the claim i made that the energy transfer is immediate and coupled to virtual pairs. i don't neccesarily believe them, but ...........

Edited September 16, 2015 by PB666

[KSK]

p = momentum

m = mass

k = ?

x = ?

some equivilant of hv?

i = (-1)^1/2

=Ñ› = reduced plancks constant

È = ?

È = wavefunction, ћ is h/2 pi, I presume k is just a constant of proportionality and x is the single co-ordinate needed to define the harmonic oscillator? The first two are standard notation and not unreasonable (IMO) to use without further explanation in a quantum mechanics thread. Likewise bra-ket notation ( | >) which (if I remember correctly) is an extremely condensed form of a page or so of algebra.

[K^2]

k is spring constant - standard physics notation. All that one needs to know about k and m is that ɲ = k/m. Same as in classical. p and x are, indeed, momentum and position, but they are operators. In coordinate notation, p = -iћ∂/∂x. Again standard notation.

All of this is consistent with any introductory text on QM.

[rtxoff]

Thanks, that was much work, appreciate it.

[KSK]

The jump is a jump only in a sense that energy never takes a value between the two levels. The transition still takes time, and in that time, energy state is a superposition of the two energy states. If you happen to measure it in the middle of transition, you'll only be able to measure the lower or higher energy. But it's going to be probabilistic, and probability will change gradually.

OK, that makes sense. Especially since my 'shapes' are just an arbitrary isosurface which denote a certain percentage probability that the electron will be found within the volume enclosed by the surface.

Thanks.

[Nuke]

hack a day had a good article about that the other day. did a really good job of explaining orbitals though the article was more about explaining the periodic table in quantum terms.

http://hackaday.com/2015/09/16/dont-know-much-about-the-periodic-table-2/

[PB666]

k is spring constant - standard physics notation. All that one needs to know about k and m is that ɲ = k/m. Same as in classical. p and x are, indeed, momentum and position, but they are operators. In coordinate notation, p = -iћ∂/∂x. Again standard notation.

All of this is consistent with any introductory text on QM.

Yes, however in journals that overlap several disciplines of science, definition of abbreviations and acronyms are best. The way I look at the problem is that if the average reader can not pick up your paper and interpret your math without going to an outside source . . . . . .I just had sent back a manuscript because the author used a six letter acronym in the title and did not defined it in the paper. Referees let us know, papers that are incomplete, we can't find referees for (they refuse) so its always better to complete the definitions.

The problem with the motive illistration is that the trasitional state is not complete at some point you would expect all energy to pour into the second state, it still does not have enough energy for its state, the outer most shell needs to lose while the inner most needs to gain.

But you are missing one thing, they claim, one of the so-called QM guys, that the transition was mediated by virtual pairs. So atsome point in your diagrm the virtual positron would annihilate the low energy orbit and a virtual elecrtron would appear in the second orbit to complete, the energy left in the two adjacent would relax into an unstable second orbital. Then the whole thing would spontaneously reverse.

Edited September 18, 2015 by PB666

[K^2]

The problem with the motive illistration is that the trasitional state is not complete at some point you would expect all energy to pour into the second state, it still does not have enough energy for its state, the outer most shell needs to lose while the inner most needs to gain.

Absolutely false. There is no such thing as "complete" or "incomplete" transition. There are situations where the quantum state of the incoming photon have to be considered also. A single photon might be interacting with multiple particles, resulting in a complex superposition. But there is absolutely no "backtracking" necessary if some other particle is found to have absorbed all the energy. All that tells you is that collapse has taken place.

But you are missing one thing, they claim, one of the so-called QM guys, that the transition was mediated by virtual pairs. So atsome point in your diagrm the virtual positron would annihilate the low energy orbit and a virtual elecrtron would appear in the second orbit to complete, the energy left in the two adjacent would relax into an unstable second orbital. Then the whole thing would spontaneously reverse.

When you start a statement with, "you are missing one thing," I am already prepared for a face-palm.

Creation/annihilation are inherently field-theoretical terms. You're seriously jumping the gun here. It's like trying to understand semiconductor physics without understanding what electrical current is. Learn basic Quantum Mechanics first. Understand what a superposition actually means. How the Hamiltonian describes the system. Why there are no jumps in QM, and then you can start learning about the field theory.

Yes, the whole thing can be described in terms of particles being created and destroyed. In that description, rather than having particle transition from state to state, you destroy and create particles in their state. Particles don't even propagate by any means other than being destroyed and re-created at new position. And in oscillator description, it's the a† and a that become creator and annihilator operators respectively. But it's crucial to understand basic Quantum Mechanics to understand why that description is equivalent. This doesn't make particles jump between orbitals any more than presence of creator/annihilator operators in propagator makes particles travel through space in jumps. These are fields. Quantized fields, which is why we have particle representations, but they are still fields. And until you know how to work with most basic cases, you shouldn't be making arguments from your own mis-understanding of an over-simplified explanation you've heard from second-hand sources. That's dumb.

Yes, however in journals that overlap several disciplines of science, definition of abbreviations and acronyms are best. The way I look at the problem is that if the average reader can not pick up your paper and interpret your math without going to an outside source . . . . . .I just had sent back a manuscript because the author used a six letter acronym in the title and did not defined it in the paper. Referees let us know, papers that are incomplete, we can't find referees for (they refuse) so its always better to complete the definitions.

You seem to have some very serious mis-understandings about how academia publishing works. I take it you've never published in a properly peer-reviewed journal. Each publication has a specific scope and audience in mind. The general audience for this particular piece was asked to skip to the pictures. The math was written for people who've actually taken some QM, and these people have been able to follow, based on responses I've gathered. For anyone who wants to follow this and can't, open up a QM text. This was never meant to be a lecture series.

[PB666]

Absolutely false. There is no such thing as "complete" or "incomplete" transition. There are situations where the quantum state of the incoming photon have to be considered also. A single photon might be interacting with multiple particles, resulting in a complex superposition. But there is absolutely no "backtracking" necessary if some other particle is found to have absorbed all the energy. All that tells you is that collapse has taken place.

yes, collapse has taken place, but in the diagram at most that collapse appears to have been 60% complete, we don't see a higher energy flourescence spectrum, which could certianly be one possibikty from that diagram. What you are saying is this model suffices to explain transitions, Rhodamine absorbs with green light and emits in the red spectrum. Show me these higher energy absorption lines and thier represative emmision lines for the basal flourescent absorption/emmision spectrum.

When you start a statement with, "you are missing one thing," I am already prepared for a face-......

Yes, the whole thing can be described in terms of particles being created and destroyed. In that description, rather than having particle transition from state to state, you destroy and create particles in their state. Particles don't even propagate by any means other than being destroyed and re-created at new position. And in oscillator description, it's the a† and a that become creator and annihilator operators respectively. But it's crucial to understand basic Quantum Mechanics to understand why that description is equivalent. This doesn't make particles jump between orbitals any more than presence of creator/annihilator operators in propagator makes particles travel through space in jumps.

Edited September 18, 2015 by PB666

[KSK]

I'm not going to get into a discussion about the content but I really don't think PB666s comments about abbreviations and acronyms are relevant here. The tone and intended comment of the thread was clearly pointed out at the start - this was not a post that was intended to overlap several disciplines of science and in the one discipline under discussion, K^2's notation was entirely standard. The last time I studied any QM (and that at the most superficial level) was nearly twenty years ago and the last time I studied maths was a couple of years before that, but even then the notation just wasn't that difficult to follow.

Putting in definitions for those symbols would have been akin to starting a thread on chemistry and beginning with definitions of C, H, N or O. At some point it is (or should be) acceptable to assume that your readers have some background knowledge, and as mentioned above, the required background knowledge for this thread was made clear from the outset.

[PB666]

I'm not going to get into a discussion about the content but I really don't think PB666s comments about abbreviations and acronyms are relevant here. The tone and intended comment of the thread was clearly pointed out at the start - this was not a post that was intended to overlap several disciplines of science and in the one discipline under discussion, K^2's notation was entirely standard. The last time I studied any QM (and that at the most superficial level) was nearly twenty years ago and the last time I studied maths was a couple of years before that, but even then the notation just wasn't that difficult to follow.

Putting in definitions for those symbols would have been akin to starting a thread on chemistry and beginning with definitions of C, H, N or O. At some point it is (or should be) acceptable to assume that your readers have some background knowledge, and as mentioned above, the required background knowledge for this thread was made clear from the outset.

I was corrected for using three letter amino acid code without defining it in one journal, you can use single letter code in a figure or table as long as its defined as a protein or nucleotide sequence, but dont use it text or it could get very confusing. Another one I was critcized is using Genbank code for a gene without giving the name of the protein that it encodes or vice versa, or not disclosing the locus from which it came. People are goimg to spend about 10 seconds googling something and if they cant find it, its finished. It depends on the scope really, if the audiance is large a multidisciplinary, then its best to define the variables. If you really want to get into the argument I can give examples, I have been assisting one international journal since 1995. For whatever reason it is particularly popular in developing countries, I was basically told by the editor if you pick up a manuscript, say Ph.D. (its a type of learning algorythm) and you cannot figure out the math in a few minutes, do not send it for referees send it back to the authors for a rewrite. And so I tested this out on a number of occasions. Predictive algorythms, in silico analysis, etc. Its one thing to say this is what I saw in college, its another thing to say this is whats happens in the real world, or this is what is happening right now, be ause for me right now is every weekday morning I have a small stack of manuscripts with little jewels from all over the world hoping to shine.

The result is this, I wont say 100% of the time, but nearly 100%, you can find the best referees that you want, no-one will referee the paper. When this happens, and I have to send the manuscript back to the corresponding author and get him to flesh out his math, i don't have any suitable referees left and then guess who has to referee the paper. Yes, the editirial board and their suurigates get stuck withbthe task. Lesson learned, send the manuscript back to the authors, make sure they fill in the gaps in the equations, then pick referees and send it. Even doing this, i have gotten papers back from the referees with glaring oversights in a peper missed requireing an editorial rejection. I take alot of pride in keeping the editorial process open scientifically to expert review, msny journals say they do this, but judjing by the results i suspect many repeatedly farm the same referees. I have never had a paper in my oversight workflow retracted, knock on wood, but I have been close to a couple that have and peering into the process I susoect i know why. I don't work in a specifically math feild, computer science, chemistry feild, physics, or biology; the feild I work in covers all of these so you could consider them a good reference audiance for this group. I stand behind the claim, define the variables and abbreviations, in the long run it will pay off, trust me.

I can simplify this, if K decided to pubish a paper in any number of feild specific peer reviewed organic chemistry, bio chemistry, biophysics, or molecular biology journals, lets say a paper on the quantum mechanisms of radiogenic mutations there is a pretty good chance the paper would cross they eyes of someone like me or a like minded editor. Either might pull that submission abstract aside, read it for intelligebility, as frequently happens, ask the journal assistent for a printout of the haul it off to a dark quite room with a sigle light and see if he/she could make sense of the M&M and results section. After pouring through abbreviated math, go back to the assistent and ask for a technical rewrite. It wouldn't matter how tough, complicated or long-winded that math is, that person would still have to go through it and try to make sure it made logical sense, that process would repeat itself until the submitter withdrew or complied. The reason is that no feild specific journal wants to sit on a Science/Nature like retraction rate, and the thought they dread and that referees dread is that someone tried to BS a paper by them.

Edited September 19, 2015 by PB666

[KSK]

I was corrected for using three letter amino acid code without defining it in one journal, you can use single letter code in a figure or table as long as its defined as a protein or nucleotide sequence, but dont use it text or it could get very confusing. Another one I was critcized is using Genbank code for a gene without giving the name of the protein that it encodes or vice versa, or not disclosing the locus from which it came. People are goimg to spend about 10 seconds googling something and if they cant find it, its finished. It depends on the scope really, if the audiance is large a multidisciplinary, then its best to define the variables. If you really want to get into the argument I can give examples, I have been assisting one international journal since 1995. For whatever reason it is particularly popular in developing countries, I was basically told by the editor if you pick up a manuscript, say Ph.D. (its a type of learning algorythm) and you cannot figure out the math in a few minutes, do not send it for referees send it back to the authors for a rewrite.

Well I believe you and parts of it sound perfectly reasonable, such as not using Genbank codes alone without also defining the gene. I would have thought three letter amino acid codes are standard enough not to need explicit definition though. And likewise, I'm a bit puzzled about the last part. Where do you fit into this process? What is your particular role? Naively, I would have thought it was the referee's job to review the maths and check whether it makes sense or whether it needs to be bounced back to the author. I'm genuinely curious here because what you're telling me seems an odd way to do things - but I have no reason to doubt you either.

And so I tested this out on a number of occasions. Predictive algorythms, in silico analysis, etc. Its one thing to say this is what I saw in college, its another thing to say this is whats happens in the real world, or this is what is happening right now, be ause for me right now is every weekday morning I have a small stack of manuscripts with little jewels from all over the world hoping to shine.

The result is this, I wont say 100% of the time, but nearly 100%, you can find the best referees that you want, no-one will referee the paper. When this happens, and I have to send the manuscript back to the corresponding author and get him to flesh out his math, i don't have any suitable referees left and then guess who has to referee the paper. Yes, the editirial board and their suurigates get stuck withbthe task. Lesson learned, send the manuscript back to the authors, make sure they fill in the gaps in the equations, then pick referees and send it. Even doing this, i have gotten papers back from the referees with glaring oversights in a peper missed requireing an editorial rejection. I take alot of pride in keeping the editorial process open scientifically to expert review, msny journals say they do this, but judjing by the results i suspect many repeatedly farm the same referees. I have never had a paper in my oversight workflow retracted, knock on wood, but I have been close to a couple that have and peering into the process I susoect i know why. I don't work in a specifically math feild, computer science, chemistry feild, physics, or biology; the feild I work in covers all of these so you could consider them a good reference audiance for this group. I stand behind the claim, define the variables and abbreviations, in the long run it will pay off, trust me.

Again, genuinely curious, but when can you assume an abbreviation is just part of the common parlance in the field (or outside it for that matter) and doesn't need to be defined. Something like DNA for example - surely you don't send that back to the author for failing to define it as deoxyribonucleic acid?

[PB666]

Well I believe you and parts of it sound perfectly reasonable, such as not using Genbank codes alone without also defining the gene.

.

and in most cases you would be right; however in some places its just silly. For example 16ORF168 might mean putative open reading frame 168 on chromosome 16. Some of the putative genes are actually QTL, quantitative trait loci, located up 500,000 base pairs from the gene they regulate. The problem is logical, once you define the gene for most loci, the referees or the reader becomes curious about the rest. The quantum mechanic equivilent of genetics is linkage disequilibrium, it is a logical nightmare because any specific inheritance group can have its own favored recombianation site. Almost any broad based gene searches done now are representative testing based on population standards and the cosequence is that if you have a particular representative setting on a inherited identity-by-descent locus. That particular site may be the only good representative on a haplotype up to 10 mbps in length. So that it looks real, until you realize that the hap-map surveys are not representative of very minor things. Its like a wormhole except in a genome, the effect is caused here, but the linkage shows up a light very far a way. When tested ODDGENE shows up significant, but its not the gene and its way far away.

I would have thought three letter amino acid codes are standard enough not to need explicit definition though. And likewise, I'm a bit puzzled about the last part. Where do you fit into this process? What is your particular role? Naively, I would have thought it was the referee's job to review the maths and check whether it makes sense or whether it needs to be bounced back to the author. I'm genuinely curious here because what you're telling me seems an odd way to do things - but I have no reason to doubt you either.

There are instances when the triple code means something else, surprisingly because of the mass of manuscripts from asia you have an assistent in some offices using scanning software or mannually looking for abbreviations because the editor tells her no undefined abbreviations. Thursday i heard this exact phrase 'No abbreviations in the title' paper went back to the author for a technical rewrite just like that. Its even worse than that, we are constantly sending back papers for plagerism of 25%, at 40% summary rejections begin, we have seen plagerism up to 95% - cookie cutter publications based on their own or colleagues work. From certain universities of certain countries a majority of manuscipt are return for plagerism scrubbing or outright rejected. 20 years ago this was unheard of, they would have been rejected.

Where i fit in was 20 years ago i was refereeing alot of papers really bad manuscript, so the editor sending me this stuff says yes, the rejection rate was too low but when they sent the papers out the referees were not paying attention. One reason was the papers were written like crap and hard to read and referees were making mistakes. Referees themselves were getting tired, and it became very hard to find them and more junks were ending up at my doorstep, at which it was difficult to refuse. the problem is that bad papers lower the impact factor. Impact factors show up. The the asian flood hits publication, the number of manuscripts quadrupeled in a manner of few years.

You are correct, don't look it from my point of view, every author should hope he gets the best and most critcal referees as possible. That seems like a automatic process, but potential referees will simply refuse. I have found MS were the invited referee is the most knowledgable person and no daylight between his work and the MS and they refuse. When do they refuse, when they see the abstract; that's it and its rejection by refusal to referee. But the assistent doesn't know why. So i become the potential referee, if i read an abstract and say I wouldn't mind being a referee, the paper goes to referees and in generally there is no problem, maybe 1 in 10 get hung up and i end up having to help find referees. But those that don't pass the initial those papers get inspected and they often go back for a technical, some papers don't even belong in that journal they belong in another feild. Some of them need major language rewrite. IOW i have to get the quality high enough so that I don't end up refering it. If everyone refuses to referee the MS, then someone on the editorial board gets it and well, it seems im it. The most common papers stalled are on theory, literally and emphatically, no one wants to referee these. In silico are the biggest hot potatoes, they fair much better if they offer one emperical test or new experiment. You would think a referee would ask for experiments in the revision; nope, they all just refuse to referee. Its peer review via austricizing the manuscript. Now you see why i don't do math, i've had migranous afternoons trying to figure out the logic of some of these monsters, and you have to look up 5 papers with 2% differences that use similarly migranous formulations. If its not related to my own work or something i enjoy, the math is too much like work. IOW, those formula should be as fluid or they are going directlty back to the authors. You just cannot imagine the difference between the first submission and a published paper.

Again, genuinely curious, but when can you assume an abbreviation is just part of the common parlance in the field (or outside it for that matter) and doesn't need to be defined. Something like DNA for example - surely you don't send that back to the author for failing to define it as deoxyribonucleic acid?

The problem is two fold, in different feilds we use the same abbreviation to describe two different things. So for instance the symbol use for differentiation in physics is a subunit in biochemistry. The second problem is that two feilds use different symbols for the same thing. In physics they use little greek d which is they same letter used for the 4th subunit of a protein. In math the symbol if f(x) and in some cases d/dx ...

DNA i have seen defined, DNA might be situationally defined if there is a specific instance, such a z, b or other structural isoforms of DNA.

Again you have an assistent in some office trying to force compliance and she does not know what is a good versus bad abbreviation while BTW she is scanning your MS for plagerism anyway and you are dropping abbreviations. If you have a filled abbreviation page, including deoxyribonucleic acid, chances are shes is going to love you. If you expect her to search the MS for first uses of 15 abbreviation then you might be asked to define it. It has happenned. Its actually not the referee who does alot of this, its an assistent. Its a referee if its written up in the report, and its an editor or an associate editor if they have picked through your math and asked for a technical. The assistent may ask the editor if the abbreviation is acceptable.

[KSK]

Interesting - thanks.

So there are two main problems - the sheer volume of papers submitted, some of which are of less than stellar quality anyway, and the fact that sometimes you just can't get a paper peer reviewed because scientists are people too and may refuse to referee a paper for many reasons. As a result, whilst it might be nice to use a 'common sense' approach to abbreviations and such, there is simply not enough time for the journal to do this and a lot of the review process is done 'by the book' because that's the only way to get it done a) in a reasonable timeframe and whilst maintaining a reasonable level of quality.

Net result - it's best for authors to err on the side of caution. Even if it seems incredibly pedantic and unnceccesary to define a particular abbreviation, it's a good idea to do it because it makes it easier for your paper to get through the review.

Does that sound about right? Please feel free to correct me if not!

[Jouni]

In most fields, there's no standard terminology or notation beyond the trivial cases. Things have alternate names and definitions, the notation varies from article to article, and many things are discovered multiple times independently without anyone noticing it for a long time.

For example, a graph may have nodes or vertices and edges, lines, or links. The one-dimensional construct may be an array, a vector, a list, a sequence, or a table, it's indexing may start from 0 or 1, and the notation can be A, A_i, or even a_i.

When a computer scientist or a mathematician says 'subsequence', they're implying that the subsequence is not a substring, except by accident. When a bioinformatician uses the word, they're probably meaning a substring. As many people working in bioinformatics are really computer scientists and mathematicians, this is a common source of confusion. To further confuse things, some mathematicians may talk about factors or subwords instead of substrings, and the original object may be a sequence, a string, or a word.

In computer science articles, log x usually means ceil(log₂ (ceil(x)+1)) and x/2 means floor(x/2). This is so obvious to everyone that it's rarely mentioned explicitly. In reality, it's actually not so obvious, as many computer scientists work in other fields, and people from other fields use results from computer science.

[PB666]

Interesting - thanks.

So there are two main problems - the sheer volume of papers submitted, some of which are of less than stellar quality anyway, and the fact that sometimes you just can't get a paper peer reviewed because scientists are people too and may refuse to referee a paper for many reasons. As a result, whilst it might be nice to use a 'common sense' approach to abbreviations and such, there is simply not enough time for the journal to do this and a lot of the review process is done 'by the book' because that's the only way to get it done a) in a reasonable timeframe and whilst maintaining a reasonable level of quality.

Net result - it's best for authors to err on the side of caution. Even if it seems incredibly pedantic and unnceccesary to define a particular abbreviation, it's a good idea to do it because it makes it easier for your paper to get through the review.

Does that sound about right? Please feel free to correct me if not!

prepublished submission is called a manuscript, a paper is what is published.

Mostly, think of the alternative, suppose you submitted a manuscript that is borderline for a journal, this happens alot, unbeknownst to you the secretary has gone through 50 potential referees for 8 months, you think your paper is being refereed then finally shes finds a referee or two and after a few more months your ms is rejected. So what an associate can do is raise the red flag right away, this is premature for our journal and here's why (generally it will be lack of experimentation along the feilds line, it might simply be a matter of emphasis), so now, four days later you know, you've got your paper back, rejected but with some guidance, and you can repair. iWhen you get it back it takes six days to find the referees and you will likely be accepted. You had to do more work, but for a couple of experiments you got fast-track through what would otherwise be a yearlong process. You will be able to publish more, and because you know what we want you will submit more tonour journal, win-win.

The other is ..... write a good abstract. ..For me any more than 2 obvious faults and its going back for a technical.

This is for my sake cause I don't want to referee 300 papers a year. The author more than anything else wants the referees to read cleanly and understand. If they have trouble reading then they will spend less time on the most abstract and constructive techniques. i personally have never been rejected, but I learned alot from the referees comments. Farm them by explaining you work nicely.

The publishing house wants us, as in long agonizing meetings, to publish more papers. So we really do want to help the authors, but I can't ask the secretary to hunt down 100 potential referees for each manuscript and even if we split them up between the board thats around 100 papers each per year. IOW they are refereeing about 10 times as many papers as they themselves publish, the board will disappear quickly. So the technicals are ways in which we can get the authors to improve their papers so that they have the greatest chance of being published with minimal interferance in the reveiw process.

And it does work, last year was the peak of the 'In silico only' wave, those papers were marked premature, now the papers are coming back with experiments and they are moving onto referees, maybe this year we will have 20% more publications and everyone is happy. If you get a paper that is returned for a technicalaities like abbreviations, style, tone you have to think of it like this, that critique has likely saved it from being rejected and also saved you several months of not knowing what the status of the manuscript is.

So the question is what can authors do to help us publish more, one thing, before submiiting your ms always let a generally well educated technical English familiar read your paper. If you are in genetics let a protein chemist see it, if you are in biophysics let a biologist read it or vice versa. Give them a big nice and juicy red marker, lol. If that person is asking what does this variable mean, you need to define them.

[PB666]

On 9/13/2015, 11:10:40, K^2 said:

This is in reply to a comment from another thread. I've figured it's worth a proper response for the sake of anyone who is likewise misinformed or just curious about quantum transitions, and it has taken me a bit longer to put this together than I anticipated, so I am posting this as a new thread. Hopefully, a discussion to follow will be worth a thread.

To keep things simple, let us consider a harmonic oscilaltor, rather than an atom, since oscillator can be described with just one dimension. The spectrum of a quantum harmonic oscillator is descrete, same as that of an atom, but unlike an atom, all of its energies are separated by an equal spacing of ћÉ between levels. Nonetheless, it serves as a simpler analog fo the purposes of this discussion.

What's going to follow is a bunch of math describing the system. If you don't care or end up giving up on following the math, skip to the pictures!

Dynamics of any quantum system is governed by Hamiltonian. In classical analog, it's the energy of the system. Given a Hamiltonian H, any physical state |È> of the system must satisfy H|È> = iћ∂_t|È>, which is known as time-dependent Shrodinger equation. Just like classical oscillator, the total energy is sum of kinetic and potential, which gives rise to the Hamiltonian.

H = p²/2m + kx²/2

There is a set of time-independent solutions to this equation that satisfies H|È_n> = (n+1/2)ћÉ |È_n>. Energy of each of these state is precisely (n+1/2)ћÉ, which is the eigen value of the Hamiltonian operator. Any other physical solution is a superposition of these states, and can be written as |È> = Σ b_n|È_n> for some set of complex numbers b_n that satisfy Σ |b_n|² = 1. In other words, any solution is a superposition of eigen states of the system, such that total probability of finding system in one of the eigen states is 1.

We wish to describe system in terms of these eigen states, for which there is a much more convenient formalism of rasing and lowering operators. (See Quantum Harmonic Oscillator for more details.)

H|È> = ћÉ(a†a + 1/2)|È>

We can also write down interaction with external field using these operators. Specifically, we wish to hit this oscillator with an electromagnetic field of frequency ν. I am going to demonstrate that so long as ν = É, the energy of incoming photon is absorbed. Otherwise, energy cannot be absorbed, and there is no transition to higher levels.

Because position is proportional to a† + a, we can describe the interaction with the electromagnetic field of incoming photon as follows.

H|È> = [ћÉ(a†a + 1/2) + (a† + a)qE cos(νt)]|È>

(There is a constant in there, dependent on ̉ۡ, which I absorbed into charge, q for simplicity.)

Finally, while there is no clean way to solve this algebraically, we have everything we need to solve it numerically.

∂/∂t |È> = -i/Ñ› H|È>

While one could solve this in coordinate space, it is far easier to use the fact that we have a convenient basis and re-write the equation in the following way.

∂b_i/∂t = H_ij b_j

Where b_i are the aforementioned complex numbers describing the system in term of its superposition of eigen states of the non-interacting Hamiltonain, and H_ij is the matrix representation of the interacting Hamiltonian. At this point, we might as well just plug these matrix representations into computer and make it do the hard work. The following are the results.

First, we hit the sytem with a resonant wave. ν = É

The top part of the image shows probability distribution for the charged particle. It's clear that under influence of the incoming energy, particle begins to oscillate. Which is what we expect. It's also clear that it does so in continuous fashion. Gradually building up the sing.

The bottom part shows corresponding energy levels in multiples of ћÉ. They are discrete. Energy is not a gradual distribution. Particle starts out at precisely (1/2) ћÉ and then starts gaining higher energy elevels with no states anywhere in between.

This leaves just one more things to consider. What happens if energies don't match? Here is the simulation with ν = 1.5 É

Note that while there is some effect, oscillations finally die down. (The electromagnetic wave keeps hitting the system, it does not go away.) Once oscillations die down, process repeats. There is slight and brief excitation of second energy level, but it quickly vanishes. The net transfer of energy from photon to the particle is zero. However, the fact that particle did move a little has an effect. And this happens with atomic excitations as well. The fact that glass has no transitions invisible light means that it does not absorb light. But there are transitions close to visible light, which is what gives glass an optical density. This interaction "slows down" the electromagnetic wave without ever absorbing it.

The conclusion is pretty straight forward. The description in Chemistry texts and some popular science articles about electrons "jumping" orbitals in atoms is a gross oversimplification. Electron never jumps. The electron cloud transitions gradually from one orbit to another over time. Likewise, probability of finding electron in ground or excited state transitions gradually. The only thing that "jumps" is the actual energy. It never matches an intermediate value between the two states.

The main difference between atom and simulations above is that in an atom, all energy levels are different. That's what allows a transition from one state to another, rather than to a distribution of states in the simulation. Otherwise, results are very similar, and the atomic orbital does look llike it's forced into rotation by the oscillating EM field. Maybe one day I'll actually have time to put together some animations for these as well.

Another reason for defining variables in plain English, someone may upgrade the forum and this results in unintelligible variables.

I found this:

Which reiterates what I said:

See minutes 26:18-30:17