On the adiabatic theorem when eigenvalues dive into the continuum

Research output: Working paperResearch

Abstract

For a Wigner-Weisskopf model of an atom consisting of a quantum dot coupled to an energy reservoir described by a three-dimensional Laplacian we study the survival probability of a bound state when the dot energy varies smoothly and adiabatically in time. The initial state corresponds to a discrete eigenvalue which dives into the continuous spectrum and re-emerges from it as the dot energy is varied in time and finally returns to its initial value. Our main result is that for a large class of couplings, the survival probability of this bound state vanishes in the adiabatic limit.
Original languageEnglish
PublisherArXiv
Number of pages21
Publication statusPublished - 8 Dec 2016
SeriesarXiv.org (e-prints)

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eigenvalues
theorems
continuums
continuous spectra
energy
quantum dots
atoms

Cite this

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title = "On the adiabatic theorem when eigenvalues dive into the continuum",
abstract = "For a Wigner-Weisskopf model of an atom consisting of a quantum dot coupled to an energy reservoir described by a three-dimensional Laplacian we study the survival probability of a bound state when the dot energy varies smoothly and adiabatically in time. The initial state corresponds to a discrete eigenvalue which dives into the continuous spectrum and re-emerges from it as the dot energy is varied in time and finally returns to its initial value. Our main result is that for a large class of couplings, the survival probability of this bound state vanishes in the adiabatic limit.",
author = "Cornean, {Decebal Horia} and Arne Jensen and Kn{\"o}rr, {Hans Konrad} and Gheorghe Nenciu",
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AU - Jensen, Arne

AU - Knörr, Hans Konrad

AU - Nenciu, Gheorghe

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N2 - For a Wigner-Weisskopf model of an atom consisting of a quantum dot coupled to an energy reservoir described by a three-dimensional Laplacian we study the survival probability of a bound state when the dot energy varies smoothly and adiabatically in time. The initial state corresponds to a discrete eigenvalue which dives into the continuous spectrum and re-emerges from it as the dot energy is varied in time and finally returns to its initial value. Our main result is that for a large class of couplings, the survival probability of this bound state vanishes in the adiabatic limit.

AB - For a Wigner-Weisskopf model of an atom consisting of a quantum dot coupled to an energy reservoir described by a three-dimensional Laplacian we study the survival probability of a bound state when the dot energy varies smoothly and adiabatically in time. The initial state corresponds to a discrete eigenvalue which dives into the continuous spectrum and re-emerges from it as the dot energy is varied in time and finally returns to its initial value. Our main result is that for a large class of couplings, the survival probability of this bound state vanishes in the adiabatic limit.

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BT - On the adiabatic theorem when eigenvalues dive into the continuum

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