3,232 research outputs found
Multi-condensate states in BCS superconductors
A BCS (Bardeen-Cooper-Schrieffer) superconductor, which is placed out of
equilibrium, can develop quantum instabilities, which manifest themselves in
oscillations of the superconductor's order parameter (pairing amplitude
). These instabilities are a manifestations of the Cooper instability.
Inelastic collisions are essential in resolving those instabilities.
Incorporating the quantum instabilities and collisions in a unified approach
based on Richardson's exact solution of the pairing Hamiltonian, we find that a
BCS superconductor may end up in a state in which the spectrum has more than
one gap.Comment: Text expanded, figures added, Journal Ref and DOI adde
Fermi Edge Resonances in Non-equilibrium States of Fermi Gases
We formulate the problem of the Fermi Edge Singularity in non-equilibrium
states of a Fermi gas as a matrix Riemann-Hilbert problem with an integrable
kernel. This formulation is the most suitable for studying the singular
behavior at each edge of non-equilibrium Fermi states by means of the method of
steepest descent, and also reveals the integrable structure of the problem. We
supplement this result by extending the familiar approach to the problem of the
Fermi Edge Singularity via the bosonic representation of the electronic
operators to non-equilibrium settings. It provides a compact way to extract the
leading asymptotes.Comment: Accepted for publication, J. Phys.
Microscopic Simulation of Reaction-Diffusion Processes and Applications to Population Biology and Product Marketing
We simulate reaction-diffusion processes with discrete fields. We use a novel
algorithm to simulate different autocatalytic processes with trace densities.
Anderson localization with a diffusive potential is studied. A
reaction-diffusion process with dynamic localization is discussed in a
marketing context.Comment: To appear in Annual Reviews of Computational physic
Semi-classical analysis of the inner product of Bethe states
We study the inner product of two Bethe states, one of which is taken
on-shell, in an inhomogeneous XXX chain in the Sutherland limit, where the
number of magnons is comparable with the length L of the chain and the magnon
rapidities arrange in a small number of macroscopically large Bethe strings.
The leading order in the large L limit is known to be expressed through a
contour integral of a dilogarithm. Here we derive the subleading term. Our
analysis is based on a new contour-integral representation of the inner product
in terms of a Fredholm determinant. We give two derivations of the sub-leading
term. Besides a direct derivation by solving a Riemann-Hilbert problem, we give
a less rigorous, but more intuitive derivation by field-theoretical methods.
For that we represent the Fredholm determinant as an expectation value in a
Fock space of chiral fermions and then bosonize. We construct a collective
field for the bosonized theory, the short wave-length part of which may be
evaluated exactly, while the long wave-length part is amenable to a
expansion. Our treatment thus results in a systematic 1/L expansion of
structure factors within the Sutherland limit.Comment: 22 pages, 0 figure
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