Often when I write a post commenter's suggest some useful references. Answers to any of the following questions would be appreciated. The questions relate to things I am curious about, working on or subjects of possible blog posts.
1. Quasi-particles are a key concept in quantum many-body theory. Is there an analogous concept in classical many-body systems, e.g., dense liquids or plasmas?
2. Is there a simple physical argument, possibly accessible to non-experts, of why decreased dimensionality leads to increased fluctuations?
(An example is the Mermin-Wagner theorem). I understand how to mathematically show that fluctuations increase due to decreased phase space, but I am skeptical that I could make this argument comprehensible to a non-expert?
3. Why does increased CO2 in the atmosphere lead to an increased frequency of extreme weather events (cyclones, droughts, floods, ...)? What is the basic physics involved?
This is the scientific aspect of climate change that I understand the least. It also seems to be the aspect of climate change that could be the worst. I write this in the context of the current bushfires in Australia.
4. Who was the first person to write down the Landau theory for a superfluid transition, suggesting that the order parameter was a complex number?
Was it Ginzburg and Pitaevskii in 1958?
5. Who was the first person to fully appreciate that at a critical point the correlation length of the order parameter diverges and fluctuations in the order parameter become large?
[In 1914 Ornstein and Zernike solved this problem for a liquid-gas transition].
6. Are there philosophical problems or paradoxes associated with the principle of least action in quantum mechanics?
Consider a particle that moves from x at time t to x' at time t'. The path taken is that which is an extrema of the action (time integral of the Lagrangian) along that path relative to others. Superficially, that sounds like the particle ''considers" all the possible paths and then "chooses" the right one. Spooky action at a distance? This makes it sound like to understand classical mechanics you have to consider it as a limit of quantum mechanics and just perhaps embrace the many-worlds interpretation....
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Regarding (1), the standard classical normal mode analysis of small fluctuations about a lattice state identifies the relevant low energy fluctuations out of a ground state and these are not particle-like but collective excitations. When quantized, they are phonons. To me this seems a bit like terminology. For particles moving in classical fluids, the entrainment of the fluid leads to an effective mass in some limits which is not the "bare" mass; I guess I would call this analogous to a quasiparticle
ReplyDeleteThe screening of the interactions between charged colloids in the presence of counter-ions and salt is fairly complex, but can be thought of as an effective renormalization of the bare charge. This would also qualify as a "classical quasiparticle"?
ReplyDeleteRegarding (4), not sure, but maybe London had the original idea regarding the order parameter?
ReplyDeleteConcerning 2, I tend to see it the other way around: increasing the dimension increases the mean-field nature of the surroundings. It is some kind of central limit theorem, the more neighbors you have, the less each individual neighbor matters, and only the "average neighbor" is important.
ReplyDeleteConcerning 6, while I somewhat disagree with your phrasing, I want to focus on another aspect.
ReplyDeleteWhile classically, the least action principle is indeed framed with a fixed initial position and time (x,t) and final position and time (x',t'), we never look for solutions of the equations of motion of the boundary problem that go from (x,t) to (x',t'). Instead, we change the problem to an initial value problem (x,v,t), with v the initial velocity. In fact, classically, you can have 0, 1, or multiple solutions for the same (x,t) and (x',t'), while there is only one solution starting from (x,v,t). Classically, this is rarely discussed, and in fact, the least action principle is interpreted as just a way to find the correct EOM in an elegant manner.
However, at the quantum level, we do look for solutions that start at (x,t) and finish at (x',t'), since we cannot both impose x and v at time t. This allows to recover the classical limit when there is only one path, but allows for more quantum like behavior at the semi-classical level (tunnel effect and interferences) when there are 0 or more than 1 classical solutions.
Regarding (1) can we think of a soliton wave as a classical quasiparticle?
ReplyDelete(1) How about monopoles in spin ice materials (as in Nature 451, pp. 42–45 (2008)) as classical quasiparticles? Or in artificial spin ice arrays if you want a more obviously classical system?
ReplyDelete(2) The Peierls argument for why there is no phase transition for the 1D Ising model, but there is for the 2D Ising model makes a relatively intuitive case in terms of how the internal energy and entropy scale with the size of fluctuations. Perhaps you could use this to motivate a relationship between dimensionality and fluctuations in a way that a non-expert could follow?
3) Because of the fluctuation-disipation theorem!
ReplyDeleteprediction - https://doi.org/10.1175/1520-0469(1975)032%3C2022:CRAFD%3E2.0.CO;2
recent comparison to date = https://www.nature.com/articles/nature25450
data not date
Delete2. Probably easiest to understand with brownian motion in increasing dimensions.
ReplyDelete4. more CO2 -> more IR absorption -> higher T -> more "local "fluctuations possible? Overly simplified view, my apologies
Thanks for all of these helpful answers. I am following up on them.
ReplyDelete