Status Confirmed Seminar Series IPHT-STA Subjects cond-mat Date Monday 8 October 2018 Time 14:00 Institute IPHT Seminar Room Salle Claude Itzykson, Bât. 774 Speaker's Last Name Satya Majumdar Speaker's First Name Speaker's Email Address Speaker's Institution LPTMS Orsay Title Kinetic energy of a trapped Fermi gas at finite temperature Abstract We study the statistics of the kinetic (or equivalently potential) energy for $N$ non-interacting fermions in a 1d harmonic trap of frequency $\omega$, at finite temperature $T$. Remarkably, we find an exact solution for the full distribution of the kinetic energy, at any temperature $T$ and for any $N$. As a function of temperature $T$, and for large $N$, we identify: (i) a quantum regime, for $T \sim \hbar\omega$, where quantum fluctuations dominate and (ii) a thermal regime, for $T \sim N \hbar \omega$, governed by thermal fluctuations. We show how the mean, the variance, as well as the large deviation function associated with the distribution of the kinetic energy cross over from the quantum to the thermal regime as $T$ increases. \\ \\ J. Grela, S.N. Majumdar, G. Schehr, Phys. Rev. Lett., 119, 130601 (2017) \\ A. Grabsch, S.N. Majumdar, G. Schehr, C. Texier, SciPost Phys. 4, 014 (2018) arXiv Preprint Number Comments Attachments

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