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The BCS Model for General Pair Interaction

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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.
OriginalsprogEngelsk
TidsskriftCommunications in Mathematical Physics
Vol/bind281
Udgave nummer2
Sider (fra-til)349-367
ISSN0010-3616
StatusUdgivet - 2 jun. 2008

ID: 9223038