36 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
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
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