# 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:

- Fachbereich Physik, Universitaet Konstanz, D-78457 Konstanz (Germany)
- Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria)
- Technische Universitaet Muenchen, James-Franck-Strasse, D-85748 Garching (Germany)
- (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}

}