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      Renormalization Group Theory of the Three-Dimensional Dilute Bose Gas

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          Abstract

          We study the three-dimensional atomic Bose gas using renormalization group techniques. Using our knowledge of the microscopic details of the interatomic interaction, we determine the correct initial values of our renormalization group equations and thus obtain also information on nonuniversal properties. As a result, we can predict for instance the critical temperature of the gas and the superfluid and condensate density of the Bose-Einstein condensed phase in the regime \(na\Lambda_{th}^2\ll 1\).

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          Renormalization Group Approach to Interacting Fermions

          R. Shankar (1993)
          The stability of nonrelativistic fermionic systems to interactions is studied within the Renormalization Group framework. A brief introduction to \(\phi^4\) theory in four dimensions and the path integral formulation for fermions is given. The strategy is as follows. First, the modes on either side of the Fermi surface within a cut-off \(\Lambda\) are chosen and a path integral is written to describe them. An RG transformation which eliminates a part of these modes, but preserves the action of the noninteracting system is identified. Finally the possible perturbations of this free-field fixed point are classified as relevant, irrelevant or marginal. A \(d=1\) warmup calculation involving a system of fermions shows how, in contrast to mean-field theory, the RG correctly yields a scale invariant system (Luttinger liquid) In \(d=2\) and 3, for rotationally invariant Fermi surfaces, {\em automatically} leads to Landau's Fermi liquid theory, which appears as a fixed point characterized by an effective mass and a Landau function \(F\), with the only relevant perturbations being of the superconducting (BCS) type The functional flow equations for the BCS couplings are derived and separated into an infinite number of flows, one for each angular momentum. It is shown that similar results hold for rotationally non-invariant (but time-reversal invariant) Fermi surfaces also, A study of a nested Fermi surface shows an additional relevant flow leading to charge density wave formation. For small \(\Lambda / K_F\), a 1/N expansion emerges, with \(N = K_F/ \Lambda\), which explains why one is able to solve the narrow cut-off theory. The search for non-Fermi liquids in \(d=2\)
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            Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms

            P. A. Ruprecht, M. Holland, A K Burnett … (1995)
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              Moment of Inertia and Superfluidity of a Trapped Bose Gas

              S Stringari (1995)
              The temperature dependence of the moment of inertia of a dilute Bose gas confined in a harmonic trap is determined. Deviations from the rigid value, due to the occurrence of Bose-Einstein condensation, reveal the superfluid behaviour of the system. In the noninteracting gas these deviations become important at temperatures of the order of \(T_c N^{-1/12}\). The role of interactions is also discussed.
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                Author and article information

                Journal
                Publication date Created: 26 July 1996
                Article
                DOI: 10.1103/PhysRevA.54.5085
                ArXiV ID: cond-mat/9607188
                SO-VID: 931f616d-cfa0-454a-a1f4-7661103c8121
                History
                Custom metadata
                Report No THU-96/30
                Comments 48 pages of ReVTeX and 13 postscript figures. Submitted for publication in Physical Review A
                Categories cond-mat atom-ph

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