BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Anatoli Polkovnikov (Boston U.) DTSTART:20210208T190000Z DTEND:20210208T200000Z DTSTAMP:20260423T023009Z UID:UKYhepth/26 DESCRIPTION:Title: Quantum eigenstates from classical Gibbs distributions\nby Anatoli P olkovnikov (Boston U.) as part of Theoretical Physics Seminars (Kentucky)\ n\n\nAbstract\nI will discuss how the language of wave functions (state ve ctors) and associated non-commuting Hermitian operators naturally emerges from classical mechanics by applying the inverse Wigner-Weyl transform to the phase space probability distribution and observables. In this language \, the Schrödinger equation follows from the Liouville equation\, with ℏ now a free parameter. Classical stationary distributions can be repres ented as sums over stationary states with discrete (quantized) energies\, where these states directly correspond to quantum eigenstates. Interesting ly\, it is now classical mechanics which allows for apparent negative prob abilities to occupy eigenstates. This correspondence is particularly prono unced for canonical Gibbs ensembles\, where classical eigenstates satisfy an integral eigenvalue equation that reduces to the Schrödinger equation in a saddle-point approximation controlled by the inverse temperature. Thi s correspondence by showing that some paradigmatic examples such as tunnel ing\, band structures\, Berry phases\, Landau levels\, level statistics an d quantum eigenstates in chaotic potentials can be reproduced to a surpris ing precision from a classical Gibbs ensemble\, without any reference to q uantum mechanics. At the end I will mention some unpublished results on em ergence of negative probabilities and associated doubling of the Hilbert s pace\, which is similar to emergence of spin degrees of freedom.\n LOCATION:https://researchseminars.org/talk/UKYhepth/26/ END:VEVENT END:VCALENDAR