2020/07/31 by Florian Lange, Achim Rosch
Mathematics · Physics and Astronomy · #Algorithm #Computer science #Conservation law #Coupling (piping) #Database #Domain (mathematical analysis) #Materials science #Mathematical analysis #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.21468/scipostphys.9.4.057
published in SciPost Physics 9(4) (SciPost.org) · Improved justification of simplified hydrodynamic model, several other minor modifications
arxiv created 2020/09/12 · arxiv updated 2020/10/21 · openalex publication_date 2020/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Weakly pumped systems with approximate conservation laws can be efficiently described by (generalized) Gibbs ensembles 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>z</mml:mi> </mml:math> -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 ε <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>ϵ</mml:mi> </mml:math> 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 ∼ 1/√(ε) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>1</mml:mn> <mml:mi>/</mml:mi> <mml:msqrt> <mml:mi>ϵ</mml:mi> </mml:msqrt> </mml:mrow> </mml:math> while the density of domain walls is exponentially small in 1/√(ε) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mi>/</mml:mi> <mml:msqrt> <mml:mi>ϵ</mml:mi> </mml:msqrt> </mml:mrow> </mml:math> . This is shown by numerical simulations of a simplified hydrodynamic equation in the presence of noise.