The BCS Model for General Pair Interaction
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The BCS Model for General Pair Interaction. / Hainzl, Christian; Hamza, Eman; Seiringer, Robert; Solovej, Jan Philip.
I: Communications in Mathematical Physics, Bind 281, Nr. 2, 02.06.2008, s. 349-367.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - The BCS Model for General Pair Interaction
AU - Hainzl, Christian
AU - Hamza, Eman
AU - Seiringer, Robert
AU - Solovej, Jan Philip
PY - 2008/6/2
Y1 - 2008/6/2
N2 - 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.
AB - 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.
M3 - Journal article
VL - 281
SP - 349
EP - 367
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 2
ER -
ID: 9223038