45,366 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
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
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
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