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I've only just started looking into many-body localization, so this question may come off as a little vague. But my understanding is that it relates to how some quantum systems do not thermalize, as in equilibrium statistical mechanics, because of how information is stored within local degrees of freedom or in subsystems. Is there a similar concept in classical physics, where classical systems fail to thermalize due to this kind of memory in certain degrees of freedom? Or is the general idea behind many-body localization somehow irreducibly quantum mechanical?

Thanks.

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  • $\begingroup$ All quantum systems thermalize, it just may be that the equilibrium is a non-trivial state. Is there such an example in classical physics? Of course. Take at look at your mirror. There is one in there. :-) $\endgroup$
    – CuriousOne
    Commented May 5, 2016 at 19:24
  • $\begingroup$ @CuriousOne unless you are using some definition of 'thermalize' that only you know, that statement is not true. A trivial example: non-interacting systems. $\endgroup$
    – Rococo
    Commented May 5, 2016 at 20:07
  • $\begingroup$ @Rococo: I am an experimentalist. To me a "non-interacting system" is a concept similar to the spherical cow that is homogeneously covered in milk. That only question I am asking is "How fast does it thermalize?". Thermalization is far from boring, by the way. It's the very thing that makes life in this universe interesting and it is the effect that leads to localization in the first place. $\endgroup$
    – CuriousOne
    Commented May 5, 2016 at 20:11

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Probably the best place to start classically is with integrable systems. A crude physicist definition is that these are systems that have, in the words of Nandkishore et al, "an infinite set of extensive conserved quantities that are sums of local operators" (1). Roughly speaking, such systems will never approach an equilibrium because none of these conserved quantities can change. A trivial example is a system in which particles are (classically or otherwise) confined to particular sites. Then the number of particles on each site is a locally conserved quantity, and will never reach a thermal distribution unless it was initialized that way.

MBL states are similar- one can construct an extensive set of locally conserved operators for them (2). The difference is that integrable models are generally 'fine-tuned,' in the sense that they lose their integrability if small non-idealities are turned on, while MBL seems to be a robust phase.

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  • $\begingroup$ There are about a dozen different integrable systems in total and none of them actually exists in the real world. $\endgroup$
    – CuriousOne
    Commented May 5, 2016 at 20:51
  • $\begingroup$ There is also no such thing as conservation of energy, a phase transition, a particle (or wave) prepared in an eigenstate of anything, ... $\endgroup$
    – Rococo
    Commented May 5, 2016 at 23:30
  • $\begingroup$ However, we often find these things to be useful approximations to reality, and integrability can be as well: nature.com/nature/journal/v440/n7086/full/nature04693.html $\endgroup$
    – Rococo
    Commented May 5, 2016 at 23:30
  • $\begingroup$ Already Newton was picking his brains out why the solar system did not behave as it "should have" based on the two-body problem and he seems to have been unhappy that he couldn't solve the three body problem, at all. Nature is not interesting where we can calculate it with high school algebra and calculus. It's interesting where we can't calculate it, at all. If you don't feel comfortable beyond the spherical cow, that's OK, but that's not where physics ends. It's where real physics begins. $\endgroup$
    – CuriousOne
    Commented May 5, 2016 at 23:34
  • $\begingroup$ Can you name the dozen examples of integrable systems you mentioned ? $\endgroup$
    – YoussefMabrouk
    Commented Aug 7, 2023 at 18:14

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