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Resolutions of identity for some non-Hermitian Hamiltonians I: exceptional point in continuous spectrum
non-Hermitian quantum mechanics exceptional points resolution of identity
2011/9/23
Abstract: Resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated functions are given for the spectral problem defined on entir...
Absolutely continuous spectrum of a one-paramentric family of Schrodinger operators
one-paramentric family Schrodinger operators Spectral Theory
2011/7/27
Abstract: We consider a family of operators $-\Delta+ t V$ with a slowly decaying and oscillating potential $V$. We prove that the absolutely continuous spectrum of this operator is essentially suppor...
Singular continuous spectrum of one-dimensional Schrödinger operator with point interactions on a sparse set
Singular continuous spectrum one-dimensional Schrö dinger operator
2010/11/18
We say that a discrete set $X =\{x_n\}_{n\in\dN_0}$ on the half-line $$0=x_0 < x_1 infty$$ is sparse in the case the distances $\Delta x_n = x_{n+1} -x_n$ between neighboring p...
Distillation by repeated measurements: continuous spectrum case
Distillation repeated measurements continuous spectrum case
2010/11/8
Repeated measurements on a part of a bipartite system strongly affect the other part not measured, whose dynamics is regulated by an effective contracted evolution operator. When the spectrum of this ...
Forward-Backward Diffusion With Continuous Spectrum
Forward-Backward Diffusion Continuous Spectrum
2010/2/26
We prove existence and uniqueness of solutions for a class of forward-backward diffusion equations via a representative example, where the second-order part has continuous spectrum, and the initial an...