On the adiabatic behaviour of a Wigner-Weisskopf atom

Decebal Horia Cornean, Arne Jensen, Hans Konrad Knörr, G. Nenciu

Published Jan 1, 2017• 0 citations

Abstract

In this research announcement we present some recent results of the authors on the adiabatic theorem for a system without a spectral gap [4].

Related papers

On the adiabatic behaviour of a Wigner-Weisskopf atom: Proceedings of the Conference on Spectral and Scattering Theory and Related Topics, 2016

Decebal Horia Cornean, Arne Jensen, Hans Konrad Knörr +1 more

Jan 1, 20170 citations

The Adiabatic Wigner–Weisskopf Model

Alain Joye, Marco Merkli

arXiv:2210.15725Journal of Statistical PhysicsMay 26, 20231 citation

Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap

Joscha Henheik, Stefan Teufel

We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.

arXiv:2012.15238Journal of Mathematical PhysicsJan 1, 20228 citations

Radiative Damping of the Weisskopf-Wigner Atom.

G. Patricio Carrazana

Jan 1, 19770 citations

On the adiabatic theorem in quantum theory

Kurt O. Friedrichs

Jan 1, 19568 citations

Adiabatic theorem in the thermodynamic limit. Part I: Systems with a uniform gap

Joscha Henheik, Stefan Teufel

We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalised super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem holds also for certain perturbations of gapped ground states that close the spectral gap (so it is an adiabatic theorem also for resonances and in this sense `generalised'), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called `super-adiabatic'). In addition to existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations also for infinite systems. While we consider the result and its proof as new and interesting in itself, they also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.

Dec 30, 20202 citations