Variational Approach to Many-Body Problems Incorporating Many-Body Effects at Finite Temperature

Abstract

We develop a variational approach at finite temperature that incorporates many-body correlation self-consistently. The grand potential is constructed in terms of Green's function expressed by the variational parameters. We apply this formalism to weakly interacting Bose-Einstein condensates to incorporate the dynamical 3/2-body processes, which are considered important in the dynamical properties. The processes lower the free energy below the mean-field Hartree--Fock--Bogoliubov's value in the same way as a previous zero-temperature formalism. From our numerical results, the pair creation or annihilation processes neglected in the Popov--Shohno approximation are enhanced, particularly in the long wavelength region, owing to the many-body effects. Because the 3/2-body correlations give a finite contribution to the self-energy of quasiparticles, they may change the microscopic properties qualitatively, even in the weak-coupling region.

arXiv comment7 pages, 4 figures

References in corpus (8)

• Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures
• Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
• Atomic Bose and Anderson glasses in optical lattices
• Microscopic Treatment of Binary Interactions in the Non-Equilibrium Dynamics of Partially Bose-condensed Trapped Gases
• First-order superfluid-Mott insulator transition of spinor bosons in an optical lattice
• 3/2-Body Correlations and Coherence in Bose-Einstein Condensates
• Ground-State Wave Function with Interactions between Different Species in $M$-Component Miscible Bose-Einstein Condensates
• Variational Wave Function for Inhomogeneous Bose--Einstein Condensate with 3/2-Body Correlations