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 ($T^{\mathrm{cr}}$). This shift of $T^{\mathrm{cr}}$ 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.

10 pages including 3 figures, to be published in Phys. Rev. C

References in corpus (7)

• Spectroscopy of discrete energy levels in ultrasmall metallic grains
• Monte Carlo evaluation of path integrals for the nuclear shell model
• Total and Parity-Projected Level Densities of Iron-Region Nuclei in the Auxiliary Fields Monte Carlo Shell Model
• Critical temperature for quenching of pair correlations
• Signature of a Pairing Transition in the Heat Capacity of Finite Nuclei
• Quantum number projection at finite temperature via thermofield dynamics
• Effects of particle-number conservation on heat capacity of nuclei

Cited by in corpus (10)

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• Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems
• Particle-number conservation in static-path approximation for thermal superfluid systems
• Calculations of canonical averages from the grand canonical ensemble
• Thermodynamic properties of hot nuclei within the self-consistent quasiparticle random-phase approximation
• Thermodynamics of small superconductors with fixed particle number
• Confirming the role of nuclear tunnelling in aqueous ferrous-ferric electron transfer
• Projected shell model description of nuclear level density: Collective, pair-breaking, and multiquasiparticle regimes in even-even nuclei
• Shell model study of the pairing correlations
• Excitations of Quantum Many-Body Systems via Purified Ensembles: A Unitary-Coupled-Cluster-based Approach