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Superfluidity without Symmetry-Breaking: The Time-Dependent Hartree-Fock Approximation for Bose-Condensed Systems

C. -H. Zhang·H. A. Fertig
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Abstract

We develop a time-dependent Hartree-Fock approximation that is appropriate for Bose-condensed systems. Defining a {\it depletion Green's function} allows the construction of condensate and depletion particle densities from eigenstates of a single time-dependent Hamiltonian, guaranteeing that our approach is a conserving approximation. The poles of this Green's function yield the energies of number-changing excitations for which the condensate particle number is held fixed, which we show has a gapped spectrum in the superfluid state. The linearized time-dependent version of this has poles at the collective frequencies of the system, yielding the expected zero sound mode for a uniform infinite system. We show how the approximations may be expressed in a general linear response formalism.

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C. -H. Zhang, H. A. Fertig. 2006-04-27. Superfluidity without Symmetry-Breaking: The Time-Dependent Hartree-Fock Approximation for Bose-Condensed Systems. https://doi.org/10.1103/physreva.74.023613

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