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Open Quantum Systems Decoherence

Linear nonlocal problem for the abstract time-dependent non-homogeneous Schrödinger equation

arXiv

Authors: Dmytro Sytnyk, Roderick Melnik

Year

2016

Paper ID

43407

Status

Preprint

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~2 min

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Abstract

A nonlocal-in-time problem for the abstract Schrödinger equation is considered. By exploiting the linear nature of nonlocal condition we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem's well-posedness and the existence of its mild, strong solutions. Furthermore, we present new sufficient conditions for the existence of solution which extend the available results to the case when some nonlocal parameters are unbounded. Two examples are provided.

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A nonlocal-in-time problem for the abstract Schrödinger equation is considered.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1609.08670 [2] arXiv https://arxiv.org/abs/1609.08670 [3] Publisher https://arxiv.org/abs/1609.08670

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