Thermodynamics of the BCS-BEC crossover

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2007
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Rantner, Walter
Cerrito, Stefano
Zwerger, Willhelm
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Physical Review A ; 75 (2007), 2. - ISSN 1050-2947. - eISSN 1094-1622
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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 $1/k_Fa$, 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 behaviour near the continuous superfluid transition, our results provide a consistent picture for the complete crossover thermodynamics which compare well with recent numerical and field-theoretic approaches at the unitarity point.
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ISO 690HAUSSMANN, Rudolf, Walter RANTNER, Stefano CERRITO, Willhelm ZWERGER, 2007. Thermodynamics of the BCS-BEC crossover. In: Physical Review A. 75(2). ISSN 1050-2947. eISSN 1094-1622. Available under: doi: 10.1103/PhysRevA.75.023610
BibTex
@article{Haussmann2007Therm-22014,
  year={2007},
  doi={10.1103/PhysRevA.75.023610},
  title={Thermodynamics of the BCS-BEC crossover},
  number={2},
  volume={75},
  issn={1050-2947},
  journal={Physical Review A},
  author={Haussmann, Rudolf and Rantner, Walter and Cerrito, Stefano and Zwerger, Willhelm}
}
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