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Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

56 votes
6 answers
15k views

(How) is category theory actually useful in actual physics?

An answer to a recent question motivated the following question: (how) is category theory actually useful in actual physics? By "actual physics" I mean to refer to areas where the underlying t …
Steve Huntsman's user avatar
16 votes
3 answers
2k views

Are there any known quantum algorithms that clearly fall outside a few narrow classes?

I'm trying to refresh myself on quantum algorithms and have been skimming Childs and van Dam's 2008 RMP paper among other things. From my preliminary surfing it looks like the known quantum algorithms …
Steve Huntsman's user avatar
20 votes
2 answers
3k views

Why don't existence and uniqueness for the Boltzmann equation imply the same for Navier-Stokes?

As I understand it, Lions and DiPerna demonstrated existence and uniqueness for the Boltzmann equation. Moreover, this paper claims that Appropriately scaled families of DiPerna–Lions renormaliz …
Steve Huntsman's user avatar
4 votes
1 answer
267 views

What is known about first return times to Markov partitions for Anosov diffeomorphisms?

Consider an Anosov diffeomorphism $T: M \rightarrow M$ and a corresponding Markov partition $\mathcal{R}$ of $M$. For $x \in M$, let $\mathcal{R}(x)$ denote the element of $\mathcal{R}$ containing $x$ …
Steve Huntsman's user avatar