Lectures on Quantum Statistics: With Applications to Dilute Gases and Plasmas

Jakob Yngvason

In these notes of six lectures on selected topics in the theory of cold, dilute Bose gases, presented at the 5th Warsaw School of Statistical Physics in June 2013, the following topics are discussed: 1) The concept of BEC, 2) the ground state energy of a dilute Bose gas with short range interactions, 3) Gross-Pitaevskii theory and BEC in trapped gases, 4) Bose gases in rotating traps and quantized vortices, and 5) strongly correlated phases in the lowest Landau level generated by rapid rotation.

W. Ebeling, Thorsten Pöschel

N. N. Bogolyubov

A. J. Leggett

These lectures address Bose and Fermi ultracold dilute alkali gases. For Bose gases I discuss general BEC concepts, superfluidity, the Josephson effect, and issues related to the establishment of a "phase standard". For Fermi gases I discuss prospects for Cooper pairing and its detection. The four lectures on alkali Bose gases which I actually gave at the School were based on a review paper in preparation for Reviews of Modern Physics. In order to avoid extensive duplication of the contents of that review, what I present here, condensed into three lectures, is a melange of informal commentary on the results presented there and some material which for space and other reasons had to be omitted. This material is ideally read in conjunction with the review. The fourth lecture, on the Fermi alkali gases, is presented here in (nearly) the form in which it was actually given.

Keith S. Stowe

F Baldovin, Alberto Cappellaro, Enzo Orlandini +1 more

Abstract We study cold dilute gases made of bosonic atoms, showing that in the mean-field one-dimensional regime they support stable out-of-equilibrium states. Starting from the 3D Boltzmann–Vlasov equation with contact interaction, we derive an effective 1D Landau–Vlasov equation under the condition of a strong transverse harmonic confinement. We investigate the existence of out-of-equilibrium states, obtaining stability criteria similar to those of classical plasmas.