2,300 research outputs found
The Cumulant Expansion for the Anderson Lattice with Finite U: The Completeness Problem
``Completeness'' (i.e. probability conservation) is not usually satisfied in
the cumulant expansion of the Anderson lattice when a reduced state space is
employed for . To understand this result, the well known
``Chain'' approximation is first calculated for finite , followed by taking
. Completeness is recovered by this procedure, but this result
hides a serious inconsistency that causes completeness failure in the reduced
space calculation. Completeness is satisfied and the inconsistency is removed
by choosing an adequate family of diagrams. The main result of this work is
that using a reduced space of relevant states is as good as using the whole
space.Comment: Latex 22 pages, 6 figures with postscript files attached, accepted
for publication in the Int. J. of Mod. Phys. B (1998). Subject field :
Strongly Correlated System
Convergence of numerical schemes for short wave long wave interaction equations
We consider the numerical approximation of a system of partial differential
equations involving a nonlinear Schr\"odinger equation coupled with a
hyperbolic conservation law. This system arises in models for the interaction
of short and long waves. Using the compensated compactness method, we prove
convergence of approximate solutions generated by semi-discrete finite volume
type methods towards the unique entropy solution of the Cauchy problem. Some
numerical examples are presented.Comment: 31 pages, 7 figure
Existence criteria for stabilization from the scaling behaviour of ionization probabilities
We provide a systematic derivation of the scaling behaviour of various
quantities and establish in particular the scale invariance of the ionization
probability. We discuss the gauge invariance of the scaling properties and the
manner in which they can be exploited as consistency check in explicit
analytical expressions, in perturbation theory, in the Kramers-Henneberger and
Floquet approximation, in upper and lower bound estimates and fully numerical
solutions of the time dependent Schroedinger equation. The scaling invariance
leads to a differential equation which has to be satisfied by the ionization
probability and which yields an alternative criterium for the existence of
atomic bound state stabilization.Comment: 12 pages of Latex, one figur
The quantum brachistochrone problem for non-Hermitian Hamiltonians
Recently Bender, Brody, Jones and Meister found that in the quantum brachistochrone problem the passage time needed for the evolution of certain initial states into specified final states can be made arbitrarily small, when the time-evolution operator is taken to be non-Hermitian but PT-symmetric. Here we demonstrate that such phenomena can also be obtained for non-Hermitian Hamiltonians for which PT-symmetry is completely broken, i.e. dissipative systems. We observe that the effect of a tunable passage time can be achieved by projecting between orthogonal eigenstates by means of a time-evolution operator associated with a non-Hermitian Hamiltonian. It is not essential that this Hamiltonian is PT-symmetric
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