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Frank, Rupert L.; Hainzl, Christian and Langmann, Edwin (2019): The BCS critical temperature in a weak homogeneous magnetic field. In: Journal of Spectral Theory, Vol. 9, No. 3: pp. 1005-1062

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We show that, within a linear approximation of BCS theory, a weak homogeneous magnetic field lowers the critical temperature by an explicit constant times the field strength, up to higher order terms. This provides a rigorous derivation and generalization of results obtained in the physics literature from WHH theory of the upper critical magnetic field. A new ingredient in our proof is a rigorous phase approximation to control the effects of the magnetic field.

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