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Excitons and Cooper PairsTwo Composite Bosons in Many-Body Physics$
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Monique Combescot and Shiue-Yuan Shiau

Print publication date: 2015

Print ISBN-13: 9780198753735

Published to Oxford Scholarship Online: March 2016

DOI: 10.1093/acprof:oso/9780198753735.001.0001

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The Bardeen-Cooper-Schrieffer Approach

The Bardeen-Cooper-Schrieffer Approach

Chapter:
(p.202) 7 The Bardeen-Cooper-Schrieffer Approach
Source:
Excitons and Cooper Pairs
Author(s):

Monique Combescot

Shiue-Yuan Shiau

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198753735.003.0007

Chapter 7 describes the Bardeen-Cooper-Schrieffer approach to Cooper pairing in two limiting cases: a single Cooper pair (the Cooper problem) and a dense regime of Cooper pairs (the BCS problem). To avoid the difficulties induced by the Pauli exclusion principle with a fixed number of fermions, Bardeen, Cooper, and Schrieffer reformulated the BCS problem in the grand canonical ensemble. They solved the problem through a variational procedure using a trial wave function called the “BCS ansatz,” which corresponds to having all Cooper pairs condensed into the same state. The BCS ground-state energy is obtained by minimizing the BCS Hamiltonian mean value. To elucidate the “moth-eaten effect” in the Cooper pair context, the average pair energy in the BCS configuration is shown to exactly equal half the single pair binding energy, rather than the much larger gap energy as commonly thought.

Keywords:   Cooper problem, BCS problem, BCS ansatz, gap energy, ground-state energy, average pair energy, moth-eaten effect

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