44,807 research outputs found

    Semi-classical States for Non-self-adjoint Schrodinger Operators

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    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

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    If T_t=\rme^{Zt} is a positive one-parameter contraction semigroup acting on lp(X)l^p(X) where XX is a countable set and 1≀p<∞1\leq p <\infty, then the peripheral point spectrum PP of ZZ cannot contain any non-zero elements. The same holds for Feller semigroups acting on Lp(X)L^p(X) if XX is locally compact

    Decomposing the Essential Spectrum

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    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

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    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

    Embeddable Markov Matrices

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    We give an account of some results, both old and new, about any nΓ—nn\times n 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

    Semi-classical Analysis and Pseudospectra

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    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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