Bistabilities and domain walls in weakly open quantum systems

Weakly pumped systems with approximate conservation laws can be efficiently described by a generalized Gibbs ensemble if the steady state of the system is unique. However, such a description can fail if there are multiple steady state solutions, for example, a bistability. In this case domains an...

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Main Author: Florian Lange, Achim Rosch
Format: Article
Language:English
Published: SciPost 2020-10-01
Series:SciPost Physics
Online Access:https://scipost.org/SciPostPhys.9.4.057
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spelling doaj-de6e08c16b094e56963114be279046f42020-11-25T03:56:36ZengSciPostSciPost Physics2542-46532020-10-019405710.21468/SciPostPhys.9.4.057Bistabilities and domain walls in weakly open quantum systemsFlorian Lange, Achim RoschWeakly pumped systems with approximate conservation laws can be efficiently described by a generalized Gibbs ensemble if the steady state of the system is unique. However, such a description can fail if there are multiple steady state solutions, for example, a bistability. In this case domains and domain walls may form. In one-dimensional (1D) systems any type of noise (thermal or non-thermal) will in general lead to a proliferation of such domains. We study this physics in a 1D spin chain with two approximate conservation laws, energy and the $z$-component of the total magnetization. A bistability in the magnetization is induced by the coupling to suitably chosen Lindblad operators. We analyze the theory for a weak coupling strength $\epsilon$ to the non-equilibrium bath. In this limit, we argue that one can use hydrodynamic approximations which describe the system locally in terms of space- and time-dependent Lagrange parameters. Here noise terms enforce the creation of domains, where the typical width of a domain wall goes as $\sim 1/\sqrt{\epsilon}$ while the density of domain walls is exponentially small in $1/\sqrt{\epsilon}$. This is shown by numerical simulations of a simplified hydrodynamic equation in the presence of noise.https://scipost.org/SciPostPhys.9.4.057
collection DOAJ
language English
format Article
sources DOAJ
author Florian Lange, Achim Rosch
spellingShingle Florian Lange, Achim Rosch
Bistabilities and domain walls in weakly open quantum systems
SciPost Physics
author_facet Florian Lange, Achim Rosch
author_sort Florian Lange, Achim Rosch
title Bistabilities and domain walls in weakly open quantum systems
title_short Bistabilities and domain walls in weakly open quantum systems
title_full Bistabilities and domain walls in weakly open quantum systems
title_fullStr Bistabilities and domain walls in weakly open quantum systems
title_full_unstemmed Bistabilities and domain walls in weakly open quantum systems
title_sort bistabilities and domain walls in weakly open quantum systems
publisher SciPost
series SciPost Physics
issn 2542-4653
publishDate 2020-10-01
description Weakly pumped systems with approximate conservation laws can be efficiently described by a generalized Gibbs ensemble if the steady state of the system is unique. However, such a description can fail if there are multiple steady state solutions, for example, a bistability. In this case domains and domain walls may form. In one-dimensional (1D) systems any type of noise (thermal or non-thermal) will in general lead to a proliferation of such domains. We study this physics in a 1D spin chain with two approximate conservation laws, energy and the $z$-component of the total magnetization. A bistability in the magnetization is induced by the coupling to suitably chosen Lindblad operators. We analyze the theory for a weak coupling strength $\epsilon$ to the non-equilibrium bath. In this limit, we argue that one can use hydrodynamic approximations which describe the system locally in terms of space- and time-dependent Lagrange parameters. Here noise terms enforce the creation of domains, where the typical width of a domain wall goes as $\sim 1/\sqrt{\epsilon}$ while the density of domain walls is exponentially small in $1/\sqrt{\epsilon}$. This is shown by numerical simulations of a simplified hydrodynamic equation in the presence of noise.
url https://scipost.org/SciPostPhys.9.4.057
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