# New Bardeen-Cooper-Schrieffer-type theory at finite temperature with particle-number conservation

## Abstract

We formulate a new Bardeen-Cooper-Schrieffer (BCS)-type theory at finite temperature, by deriving a set of variational equations of the free energy after the particle-number projection. With its broad applicability, this theory can be a useful tool for investigating the pairing phase transition in finite systems with the particle-number conservation. This theory provides effects of the symmetry-restoring fluctuation (SRF) for the pairing phenomena in finite fermionic systems, distinctively from those of additional quantum fluctuations. It is shown by numerical calculations that the phase transition is compatible with the conservation in this theory, and that the SRF shifts up the critical temperature (T{sup cr}). This shift of T{sup cr} occurs due to reduction of degrees-of-freedom in canonical ensembles, and decreases only slowly as the particle-number increases (or as the level spacing narrows), in contrast to the conventional BCS theory.

- Authors:

- Department of Physics, Faculty of Science, Chiba University, Inage, Chiba 263-8522 (Japan)
- (Japan)

- Publication Date:

- OSTI Identifier:
- 20864177

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 74; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevC.74.061301; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BCS THEORY; CRITICAL TEMPERATURE; DEGREES OF FREEDOM; FERMI GAS; FERMI GAS MODEL; FERMIONS; FLUCTUATIONS; FREE ENERGY; PHASE TRANSFORMATIONS; SYMMETRY; VARIATIONAL METHODS

### Citation Formats

```
Nakada, H., Tanabe, K., and Department of Physics, Faculty of Science, Saitama University, Sakura, Saitama 338-8570.
```*New Bardeen-Cooper-Schrieffer-type theory at finite temperature with particle-number conservation*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVC.74.061301.

```
Nakada, H., Tanabe, K., & Department of Physics, Faculty of Science, Saitama University, Sakura, Saitama 338-8570.
```*New Bardeen-Cooper-Schrieffer-type theory at finite temperature with particle-number conservation*. United States. doi:10.1103/PHYSREVC.74.061301.

```
Nakada, H., Tanabe, K., and Department of Physics, Faculty of Science, Saitama University, Sakura, Saitama 338-8570. Fri .
"New Bardeen-Cooper-Schrieffer-type theory at finite temperature with particle-number conservation". United States.
doi:10.1103/PHYSREVC.74.061301.
```

```
@article{osti_20864177,
```

title = {New Bardeen-Cooper-Schrieffer-type theory at finite temperature with particle-number conservation},

author = {Nakada, H. and Tanabe, K. and Department of Physics, Faculty of Science, Saitama University, Sakura, Saitama 338-8570},

abstractNote = {We formulate a new Bardeen-Cooper-Schrieffer (BCS)-type theory at finite temperature, by deriving a set of variational equations of the free energy after the particle-number projection. With its broad applicability, this theory can be a useful tool for investigating the pairing phase transition in finite systems with the particle-number conservation. This theory provides effects of the symmetry-restoring fluctuation (SRF) for the pairing phenomena in finite fermionic systems, distinctively from those of additional quantum fluctuations. It is shown by numerical calculations that the phase transition is compatible with the conservation in this theory, and that the SRF shifts up the critical temperature (T{sup cr}). This shift of T{sup cr} occurs due to reduction of degrees-of-freedom in canonical ensembles, and decreases only slowly as the particle-number increases (or as the level spacing narrows), in contrast to the conventional BCS theory.},

doi = {10.1103/PHYSREVC.74.061301},

journal = {Physical Review. C, Nuclear Physics},

number = 6,

volume = 74,

place = {United States},

year = {Fri Dec 15 00:00:00 EST 2006},

month = {Fri Dec 15 00:00:00 EST 2006}

}