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Preprints, Working Papers, ... Year : 2021

On quantum dissipative systems: ground states and orbital stability

Thierry Goudon
Léo Vivion
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Abstract

We investigate the existence and stability of ground states for a model coupling the Schrödinger equation to the wave equation in transverse directions. The model is intended to describe complex interactions between quantum particles and their environment. The result can be interpreted as a dissipation statement, induced by the energy exchanges with the environment. The proofs use either concentration-compactness arguments or spectral analysis of the linearized energy. Difficulties arise related to the fact the model does not satisfy scale invariance properties.
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Dates and versions

hal-03115521 , version 1 (19-01-2021)

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  • HAL Id : hal-03115521 , version 1

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Thierry Goudon, Léo Vivion. On quantum dissipative systems: ground states and orbital stability. 2021. ⟨hal-03115521⟩
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