A study of the Bardeen-Cooper-Schrieffer distribution

Rudolf Haag

Геннадий Васильевич Коваль, Виктор Павлович Маслов

Vanessa Sulaiman, Götz Silvester Uhrig

Motivated by the generation by optical pulses of nonthermal distributions of nuclear spins in quantum dots we investigate the effect of optical pulses applied to Bardeen-Cooper-Schrieffer (BCS) superconductors. Using time-dependent mean-field theory formulated with Anderson pseudospins, we study the electronic configurations and the energy deposited in the system by optical pulses. The pulses are included by Peierls substitution and we study short rectangular pulses as well as idealized $\ensuremath{\delta}$ pulses. Already a few and even a single pulse generates highly nontrivial distributions of electron expectation values which we simulate numerically and explain analytically based on the linearization of the equations of motion. These results suggest so far unexplored experimental possibilities for the optical control of superconducting states.

Chun Kit Chung, C. K. Law

We analyze the momentum entanglement of homogeneous Bardeen--Cooper--Schrieffer (BCS) states between spin-up and spin-down particles at finite temperature. This is achieved by studying the structure of the partial transposition of the two-particle density matrix (denoted by ${\ensuremath{\rho}}_{2}^{{T}_{A}}$) in momentum space, as well as the corresponding negativity. We show that ${\ensuremath{\rho}}_{2}^{{T}_{A}}$ consists of infinitely many decoupled $2\ifmmode\times\else\texttimes\fi{}2$ submatrices, and momentum entanglement is a necessary and sufficient condition for a nonzero order parameter $\ensuremath{\Delta}$. From the distribution of eigenvalues of ${\ensuremath{\rho}}_{2}^{{T}_{A}}$, we discover that momentum entanglement is most significantly contributed by pairs with momenta slightly above a surface related to the Fermi energy. In addition, we propose an entanglement witness operator for detecting momentum entanglement in BCS states.

John W. Wilkins

MI Umo

We present a detailed diagonalization calculation of the Bardeen-Cooper-Schrieffer (BCS) Hamiltonian via the unitary transformation method which allows for the Bogolyubov-Valatin transformation to be arrived at naturally. The energy gap equation is derived and solved, and averages of some representative thermodynamic quantities are obtained.KEYWORDS: Hamiltonian, unitary matrix, superconductivity, interaction, ground state.