Timeline for Rigorous statistical mechanics: difficulty of realistic models
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Sep 13 at 2:32 | comment | added | Abdelmalek Abdesselam | Was thinking of something related to hard core, e.g., $V(r)=\infty$ for $r<r_1$ then $V(r)=-\epsilon$ for $r_1<r<r_2$, and then zero for $r>r_2$. I am not an expert though. A better source would be, e.g., arxiv.org/abs/1504.01153 | |
| Sep 13 at 1:32 | comment | added | Plemath | Thanks for answering! Can you give an example of such a simpler potential? | |
| Sep 13 at 1:17 | comment | added | Abdelmalek Abdesselam | As far as I know the transition has not been proved for other simpler potentials. The difficulty is not the form of the potential but going from the lattice to the continuum, and in particular showing the breaking of translational symmetry, i.e., the spontaneous formation of a crystal. | |
| Sep 12 at 13:49 | comment | added | Jules Lamers | There's often a tension between "realistic" and "rigorous" in modern theoretical physics. A well known example is QFT. I presume this is just another example. | |
| Sep 12 at 11:32 | answer | added | Carlo Beenakker | timeline score: 1 | |
| Sep 12 at 4:54 | comment | added | Tom Copeland | @MichaelEngelhardt, the apostophes mean that the word is being used in a nonstandard way, so indeed has more than one meaning. Anyone who has a sincere interest has sufficient words to Google the topic (covered in any book on the history of Q.M.) to understand the correct statistical analysis and relation to Q.M. in detail and how it differed from the nonviable classical analysis. | |
| Sep 12 at 2:02 | comment | added | Michael Engelhardt | @TomCopeland - hmm, but that statement sounds to me like it's conflating two different meanings of 'classical'. | |
| Sep 12 at 1:59 | comment | added | Tom Copeland | In addition, quantum mechanics has origins in understanding 'classical' blackbody radiation. | |
| Sep 12 at 1:55 | comment | added | Michael Engelhardt | The Ising model would usually be considered a quantum system, so you've studied quantum statistical mechanics already! | |
| Sep 12 at 1:22 | comment | added | Plemath | I have not studied quantum mechanics yet. But quantum makes models even more complicated. Let's focus on classical statistical mechanics. | |
| Sep 12 at 1:19 | history | edited | Plemath | CC BY-SA 4.0 |
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| Sep 12 at 1:14 | comment | added | Tom Copeland | Elementary excitations of a Bose liquid is an interesting realistic application of quantum statistical physics. See. e.g., Ch. III Superfluidity (beginning on p. 85) of "Statistical Physics, Part 2, Theory of condensed states" by Lifshitz and Pitaevskii, Volume 9 of Course of Theoretical Physics (haidinh89.wordpress.com/wp-content/uploads/2015/08/…). | |
| Sep 12 at 0:37 | history | asked | Plemath | CC BY-SA 4.0 |