819,039 research outputs found
Nonlinear Discrete Systems with Nonanalytic Dispersion Relations
A discrete system of coupled waves (with nonanalytic dispersion relation) is
derived in the context of the spectral transform theory for the Ablowitz Ladik
spectral problem (discrete version of the Zakharov-Shabat system). This 3-wave
evolution problem is a discrete version of the stimulated Raman scattering
equations, and it is shown to be solvable for arbitrary boundary value of the
two radiation fields and initial value of the medium state. The spectral
transform is constructed on the basis of the D-bar approach.Comment: RevTex file, to appear in Journ. Math. Phy
Inverse problem and Darboux transformations for two-dimensional finite-difference Schredinger equation
A discrete version of the two-dimensional inverse scattering problem is
considered. On this basis, algebraic transformations for the two-dimensional
finite-difference Schredinger equation are elaborated.Comment: 12 pages, 1 figure (s_fig.eps), Late
The basis problem in many-worlds theories
It is emphasized that a many-worlds interpretation of quantum theory exists
only to the extent that the associated basis problem is solved. The core basis
problem is that the robust enduring states specified by environmental
decoherence effects are essentially Gaussian wave packets that form continua of
non-orthogonal states. Hence they are not a discrete set of orthogonal basis
states to which finite probabilities can be assigned by the usual rules. The
natural way to get an orthogonal basis without going outside the Schroedinger
dynamics is to use the eigenstates of the reduced density matrix, and this idea
is the basis of some recent attempts by many-worlds proponents to solve the
basis problem. But these eigenstates do not enjoy the locality and
quasi-classicality properties of the states defined by environmental
decoherence effects, and hence are not satisfactory preferred basis states. The
basis problem needs to be addressed and resolved before a many-worlds-type
interpretation can be said to exist.Comment: This extended version is to be published in The Canadian Journal of
Physic
Fluctuations in the Site Disordered Traveling Salesman Problem
We extend a previous statistical mechanical treatment of the traveling
salesman problem by defining a discrete "site disordered'' problem in which
fluctuations about saddle points can be computed. The results clarify the basis
of our original treatment, and illuminate but do not resolve the difficulties
of taking the zero temperature limit to obtain minimal path lengths.Comment: 17 pages, 3 eps figures, revte
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