The external field dependence of the BCS critical temperature

TY - JOUR

T1 - The external field dependence of the BCS critical temperature

AU - Frank, Rupert L.

AU - Hainzl, Christian

AU - Seiringer, Robert

AU - Solovej, Jan Philip

N1 - 28 pages

PY - 2016/2/1

Y1 - 2016/2/1

N2 - 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.

AB - 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.

KW - math-ph

KW - cond-mat.quant-gas

KW - cond-mat.supr-con

KW - math.AP

KW - math.MP

U2 - 10.1007/s00220-015-2526-2

DO - 10.1007/s00220-015-2526-2

M3 - Journal article

SN - 0010-3616

VL - 342

SP - 189

EP - 216

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -