94,298 research outputs found
Smilansky's model of irreversible quantum graphs, II: the point spectrum
In the model suggested by Smilansky one studies an operator describing the
interaction between a quantum graph and a system of K one-dimensional
oscillators attached at different points of the graph. This paper is a
continuation of our investigation of the case K>1. For the sake of simplicity
we consider K=2, but our argument applies to the general situation. In this
second paper we apply the variational approach to the study of the point
spectrum.Comment: 18 page
Selfadjoint and sectorial extensions of Sturm-Liouville operators
The self-adjoint and -sectorial extensions of coercive Sturm-Liouville
operators are characterised, under minimal smoothness conditions on the
coefficients of the differential expression.Comment: accepted by IEOT, in IEOT 201
Slow Coarsening in a Class of Driven Systems
The coarsening process in a class of driven systems is studied. These systems
have previously been shown to exhibit phase separation and slow coarsening in
one dimension. We consider generalizations of this class of models to higher
dimensions. In particular we study a system of three types of particles that
diffuse under local conserving dynamics in two dimensions. Arguments and
numerical studies are presented indicating that the coarsening process in any
number of dimensions is logarithmically slow in time. A key feature of this
behavior is that the interfaces separating the various growing domains are
smooth (well approximated by a Fermi function). This implies that the
coarsening mechanism in one dimension is readily extendible to higher
dimensions.Comment: submitted to EPJB, 13 page
Knudsen Effect in a Nonequilibrium Gas
From the molecular dynamics simulation of a system of hard-core disks in
which an equilibrium cell is connected with a nonequilibrium cell, it is
confirmed that the pressure difference between two cells depends on the
direction of the heat flux. From the boundary layer analysis, the velocity
distribution function in the boundary layer is obtained. The agreement between
the theoretical result and the numerical result is fairly good.Comment: 4pages, 4figure
Smilansky's model of irreversible quantum graphs, I: the absolutely continuous spectrum
In the model suggested by Smilansky one studies an operator describing the
interaction between a quantum graph and a system of one-dimensional
oscillators attached at several different points in the graph. The present
paper is the first one in which the case is investigated. For the sake of
simplicity we consider K=2, but our argument is of a general character. In this
first of two papers on the problem, we describe the absolutely continuous
spectrum. Our approach is based upon scattering theory
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