Quantum Lunch: Bogoliubov theory at positive temperature – University of Copenhagen

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Quantum Lunch: Bogoliubov theory at positive temperature

Speaker: Robin Reuvers

Abstract: I will discuss Bogoliubov theory in the translation invariant case of a Bose gas. The theory arises by restriction to translation invariant quasi-free states. I will introduce the positive temperature pressure functional and the corresponding ground state energy functional. I will then describe several properties of the model: the existence of minimizers, the phase diagram, and an expression for the critical temperature in the dilute limit. The latter contains the predicted first-order correction C(\rho a^3)^{1/3} to the free critical temperature, where \rho is the density of the gas and a the scattering length of the interaction potential. Moreover, the constant C is in good agreement with values obtained via other methods. At the end of talk, I will discuss to what extent the model can be said to be a good approximation to the many-body quantum theory.