The BCS functional for general pair interactions

C. Hainzl, E. Hamza, R. Seiringer, J. Solovej, Communications in Mathematical Physics 281 (2008) 349–367.


Journal Article | Published
Author
Hainzl, Christian; Hamza, Eman; Seiringer, RobertIST Austria ; Solovej, Jan P
Abstract
The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.
Publishing Year
Date Published
2008-07-01
Journal Title
Communications in Mathematical Physics
Volume
281
Issue
2
Page
349 - 367
IST-REx-ID

Cite this

Hainzl C, Hamza E, Seiringer R, Solovej J. The BCS functional for general pair interactions. Communications in Mathematical Physics. 2008;281(2):349-367. doi:10.1007/s00220-008-0489-2
Hainzl, C., Hamza, E., Seiringer, R., & Solovej, J. (2008). The BCS functional for general pair interactions. Communications in Mathematical Physics, 281(2), 349–367. https://doi.org/10.1007/s00220-008-0489-2
Hainzl, Christian, Eman Hamza, Robert Seiringer, and Jan Solovej. “The BCS Functional for General Pair Interactions.” Communications in Mathematical Physics 281, no. 2 (2008): 349–67. https://doi.org/10.1007/s00220-008-0489-2.
C. Hainzl, E. Hamza, R. Seiringer, and J. Solovej, “The BCS functional for general pair interactions,” Communications in Mathematical Physics, vol. 281, no. 2, pp. 349–367, 2008.
Hainzl C, Hamza E, Seiringer R, Solovej J. 2008. The BCS functional for general pair interactions. Communications in Mathematical Physics. 281(2), 349–367.
Hainzl, Christian, et al. “The BCS Functional for General Pair Interactions.” Communications in Mathematical Physics, vol. 281, no. 2, Springer, 2008, pp. 349–67, doi:10.1007/s00220-008-0489-2.
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