46,345 research outputs found
Semi-classical States for Non-self-adjoint Schrodinger Operators
We prove that the spectrum of certain non-self-adjoint Schrodinger operators
is unstable in the semi-classical limit. Similar results hold for a fixed
operator in the high energy limit. The method involves the construction of
approximate semi-classical modes of the operator by the JWKB method for
energies far from the spectrum
Triviality of the Peripheral Point Spectrum
If T_t=\rme^{Zt} is a positive one-parameter contraction semigroup acting
on where is a countable set and , then the
peripheral point spectrum of cannot contain any non-zero elements. The
same holds for Feller semigroups acting on if is locally compact
Embeddable Markov Matrices
We give an account of some results, both old and new, about any
Markov matrix that is embeddable in a one-parameter Markov semigroup. These
include the fact that its eigenvalues must lie in a certain region in the unit
ball. We prove that a well-known procedure for approximating a non-embeddable
Markov matrix by an embeddable one is optimal in a certain sense.Comment: 15 page
Decomposing the Essential Spectrum
We use C*-algebra theory to provide a new method of decomposing the eseential
spectra of self-adjoint and non-self-adjoint Schrodinger operators in one or
more space dimensions
Spectral Properties of Random Non-self-adjoint Matrices and Operators
We describe some numerical experiments which determine the degree of spectral
instability of medium size randomly generated matrices which are far from
self-adjoint. The conclusion is that the eigenvalues are likely to be
intrinsically uncomputable for similar matrices of a larger size. We also
describe a stochastic family of bounded operators in infinite dimensions for
almost all of which the eigenvectors generate a dense linear subspace, but the
eigenvalues do not determine the spectrum. Our results imply that the spectrum
of the non-self-adjoint Anderson model changes suddenly as one passes to the
infinite volume limit.Comment: keywords: eigenvalues, spectral instability, matrices, computability,
pseudospectrum, Schroedinger operator, Anderson mode
Semi-classical Analysis and Pseudospectra
We prove an approximate spectral theorem for non-self-adjoint operators and
investigate its applications to second order differential operators in the
semi-classical limit. This leads to the construction of a twisted FBI
transform. We also investigate the connections between pseudospectra and
boundary conditions in the semi-classical limit
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