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Title: Thermodynamics of the BCS-BEC crossover

Abstract

We present a self-consistent theory for the thermodynamics of the BCS-BEC crossover in the normal and superfluid phase which is both conserving and gapless. It is based on the variational many-body formalism developed by Luttinger and Ward and by DeDominicis and Martin. Truncating the exact functional for the entropy to that obtained within a ladder approximation, the resulting self-consistent integral equations for the normal and anomalous Green functions are solved numerically for arbitrary coupling. The critical temperature, the equation of state, and the entropy are determined as a function of the dimensionless parameter 1/k{sub F}a, which controls the crossover from the BCS regime of extended pairs to the BEC regime of tightly bound molecules. The tightly bound pairs turn out to be described by a Popov-type approximation for a dilute, repulsive Bose gas. Even though our approximation does not capture the critical behavior near the continuous superfluid transition, our results provide a consistent picture for the complete crossover thermodynamics which compares well with recent numerical and field-theoretic approaches at the unitarity point.

Authors:
 [1];  [2];  [3];  [4];  [3]
  1. Fachbereich Physik, Universitaet Konstanz, D-78457 Konstanz (Germany)
  2. Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria)
  3. Technische Universitaet Muenchen, James-Franck-Strasse, D-85748 Garching (Germany)
  4. (Austria)
Publication Date:
OSTI Identifier:
20982161
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.023610; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BCS THEORY; BOSE-EINSTEIN CONDENSATION; BOSE-EINSTEIN GAS; CAPTURE; COMPARATIVE EVALUATIONS; COUPLING; CRITICAL TEMPERATURE; ENTROPY; EQUATIONS OF STATE; GREEN FUNCTION; INTEGRAL EQUATIONS; LADDER APPROXIMATION; MANY-BODY PROBLEM; MOLECULES; SUPERFLUIDITY; THERMODYNAMICS; VARIATIONAL METHODS

Citation Formats

Haussmann, R., Rantner, W., Cerrito, S., Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, and Zwerger, W.. Thermodynamics of the BCS-BEC crossover. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.023610.
Haussmann, R., Rantner, W., Cerrito, S., Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, & Zwerger, W.. Thermodynamics of the BCS-BEC crossover. United States. doi:10.1103/PHYSREVA.75.023610.
Haussmann, R., Rantner, W., Cerrito, S., Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, and Zwerger, W.. Thu . "Thermodynamics of the BCS-BEC crossover". United States. doi:10.1103/PHYSREVA.75.023610.
@article{osti_20982161,
title = {Thermodynamics of the BCS-BEC crossover},
author = {Haussmann, R. and Rantner, W. and Cerrito, S. and Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck and Zwerger, W.},
abstractNote = {We present a self-consistent theory for the thermodynamics of the BCS-BEC crossover in the normal and superfluid phase which is both conserving and gapless. It is based on the variational many-body formalism developed by Luttinger and Ward and by DeDominicis and Martin. Truncating the exact functional for the entropy to that obtained within a ladder approximation, the resulting self-consistent integral equations for the normal and anomalous Green functions are solved numerically for arbitrary coupling. The critical temperature, the equation of state, and the entropy are determined as a function of the dimensionless parameter 1/k{sub F}a, which controls the crossover from the BCS regime of extended pairs to the BEC regime of tightly bound molecules. The tightly bound pairs turn out to be described by a Popov-type approximation for a dilute, repulsive Bose gas. Even though our approximation does not capture the critical behavior near the continuous superfluid transition, our results provide a consistent picture for the complete crossover thermodynamics which compares well with recent numerical and field-theoretic approaches at the unitarity point.},
doi = {10.1103/PHYSREVA.75.023610},
journal = {Physical Review. A},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
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