# The gap equation for spin-polarized fermions

Freiji A, Hainzl C, Seiringer R. 2012. The gap equation for spin-polarized fermions. Journal of Mathematical Physics. 53(1).

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Author

Freiji, Abraham;
Hainzl, Christian;
Seiringer, Robert

^{IST Austria}^{}Abstract

We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For cosh (δ μ/T) ≤ 2, with T the temperature and δμ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in [Frank, R. L., Hainzl, C., Naboko, S., and Seiringer, R., J., Geom. Anal.17, 559-567 (2007)10.1007/BF02937429; Hainzl, C., Hamza, E., Seiringer, R., and Solovej, J. P., Commun., Math. Phys.281, 349-367 (2008)10.1007/s00220-008-0489-2; and Hainzl, C. and Seiringer, R., Phys. Rev. B77, 184517-110 435 (2008)]10.1103/PhysRevB.77.184517. For cosh (δ μ/T) > 2 the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit.

Publishing Year

Date Published

2012-01-01

Journal Title

Journal of Mathematical Physics

Volume

53

Issue

1

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### Cite this

Freiji A, Hainzl C, Seiringer R. The gap equation for spin-polarized fermions.

*Journal of Mathematical Physics*. 2012;53(1). doi:10.1063/1.3670747Freiji, A., Hainzl, C., & Seiringer, R. (2012). The gap equation for spin-polarized fermions.

*Journal of Mathematical Physics*. American Institute of Physics. https://doi.org/10.1063/1.3670747Freiji, Abraham, Christian Hainzl, and Robert Seiringer. “The Gap Equation for Spin-Polarized Fermions.”

*Journal of Mathematical Physics*. American Institute of Physics, 2012. https://doi.org/10.1063/1.3670747.A. Freiji, C. Hainzl, and R. Seiringer, “The gap equation for spin-polarized fermions,”

*Journal of Mathematical Physics*, vol. 53, no. 1. American Institute of Physics, 2012.Freiji, Abraham, et al. “The Gap Equation for Spin-Polarized Fermions.”

*Journal of Mathematical Physics*, vol. 53, no. 1, American Institute of Physics, 2012, doi:10.1063/1.3670747.