### Abstract

Original language | English |
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Publisher | ArXiv |

Number of pages | 21 |

Publication status | Published - 8 Dec 2016 |

Series | arXiv.org (e-prints) |
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### Cite this

*On the adiabatic theorem when eigenvalues dive into the continuum*. ArXiv. arXiv.org (e-prints)

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**On the adiabatic theorem when eigenvalues dive into the continuum.** / Cornean, Decebal Horia; Jensen, Arne; Knörr, Hans Konrad; Nenciu, Gheorghe.

Research output: Working paper › Research

TY - UNPB

T1 - On the adiabatic theorem when eigenvalues dive into the continuum

AU - Cornean, Decebal Horia

AU - Jensen, Arne

AU - Knörr, Hans Konrad

AU - Nenciu, Gheorghe

PY - 2016/12/8

Y1 - 2016/12/8

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.

M3 - Working paper

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

PB - ArXiv

ER -