Communications in Mathematical Physics

, Volume 342, Issue 1, pp 189–216 | Cite as

The External Field Dependence of the BCS Critical Temperature

  • Rupert L. FrankEmail author
  • Christian Hainzl
  • Robert Seiringer
  • Jan Philip Solovej


We consider the Bardeen–Cooper–Schrieffer free energy functional for particles interacting via a two-body potential on a microscopic scale and in the presence of weak external fields varying on a macroscopic scale. We study the influence of the external fields on the critical temperature. We show that in the limit where the ratio between the microscopic and macroscopic scale tends to zero, the next to leading order of the critical temperature is determined by the lowest eigenvalue of the linearization of the Ginzburg–Landau equation.


Critical Temperature Macroscopic Scale Integral Kernel Landau Equation Admissible State 
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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Rupert L. Frank
    • 1
    Email author
  • Christian Hainzl
    • 2
  • Robert Seiringer
    • 3
  • Jan Philip Solovej
    • 4
  1. 1.Mathematics 253-37CaltechPasadenaUSA
  2. 2.Mathematisches InstitutUniversität TübingenTübingenGermany
  3. 3.Institute of Science and Technology Austria (IST Austria)KlosterneuburgAustria
  4. 4.Department of MathematicsUniversity of CopenhagenCopenhagenDenmark

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