Status  Confirmed 
Seminar Series  IPHTSTA 
Subjects  condmat 
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 $N$ noninteracting 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) 
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