Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1004.4023 · Physical Review A

Casimir effect in the nonequilibrium steady state of a quantum spin chain

Diego Luis González, Zoltàn Ràcz, Frédéric van Wijland

Published May 20, 2010• 4 citations
arXivHTMLPDF

Abstract

We present a fully microscopics-based calculation of the Casimir effect in a nonequilibrium system, namely, an energy-flux-driven quantum $\mathit{XX}$ chain. The force between the walls (transverse-field impurities) is calculated in a nonequilibrium steady state which is prepared by letting the system evolve from an initial state with the two halves of the chain prepared at equilibrium at different temperatures. The steady state emerging in the large-time limit is homogeneous but carries an energy flux. The Casimir force in this nonequilibrium state is calculated analytically in the limit when the transverse fields are small. We find that the the Casimir force range is reduced compared to the equilibrium case, and suggest that the reason for this is the reduction of fluctuations in the flux-carrying steady state.

DOI
10.1103/physreva.81.052512

Related papers

Energy current and Casimir effect with phase transition in the nonequilibrium steady-state of a quantum anisotropic XY spin chain

Georges Collince Fouokeng, F. Kuate Fodouop, Martin Tchoffo +2 more

The dynamics of quantum anisotropic XY spin chain driven out of equilibrium by a transverse magnetic field, that carry an energy current ( J E ) is investigated. Considering the spin exchange and the flow of energy trapped in magnetic field between two defects in the x y -plane separated by a distance d , we derive an analytical expression of the steady state Green's function of the model using the Grassmann algebra in order to determine the Casimir force between two magnetic defects. As soon as done we find that, cooling the system as well as increasing the anisotropic parameter decrease the energy current and accordingly increase the range of the Casimir force. This symmetry is broken with a significant increase of distance between the defects. A critical temperature is then recorded exhibiting a phase transition according to the anisotropic parameter. An interesting feature of this model is that turning the anisotropic parameter as well as the temperature range will better manipulate the energy flux and control the range of the Casimir force.

Journal of Physics Communications•Jan 22, 2019•0 citations

Nonequilibrium thermal transport in the quantum Ising chain

Andrea De Luca, Jacopo Viti, Denis Bernard +1 more

We consider two quantum Ising chains initially prepared at thermal equilibrium but with different temperatures and coupled at a given time through one of their end points. In the long-time limit the system reaches a nonequilibrium steady state. We discuss properties of this nonequilibrium steady state and characterize the convergence to the steady regime. We compute the mean energy flux through the chain and show that the heat transport is ballistic. We derive also the large-deviation function for the quantum and thermal fluctuations of this energy transfer.

arXiv:1305.4984•Physical Review B•Oct 14, 2013•106 citations

Nonequilibrium Steady State in a Quantum System: One-Dimensional Transverse Ising Model with Energy Current

Tibor Antal A, Zoltàn Ràcz, L. Sasvári

We study the nonequilibrium steady states of an Ising chain in a transverse field $h$ by investigating the effect of a field $\ensuremath{\lambda}$, which drives the current of energy. The zero-temperature, $h$- $\ensuremath{\lambda}$ phase diagram is determined exactly, and it is found that the energy current appears continuously above a threshold $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c}(h)$. The long-range magnetic order (present for $h<{h}_{c},\ensuremath{\lambda}<{\ensuremath{\lambda}}_{c}$) is destroyed in the current-carrying state where the correlations are characterized by power-law, oscillatory decay. The mechanism which generates the power-law correlations in the current-carrying state is discussed.

arXiv:cond-mat/9612047•Physical Review Letters•Jan 13, 1997•72 citations

Nonequilibrium phases and phase transitions of the XY model

Tharnier O. Puel, Stefano Chesi, Stefan Kirchner +1 more

We obtain the steady-state phase diagram of a transverse-field XY spin chain coupled at its ends to magnetic reservoirs held at different magnetic potentials. In the long-time limit, the magnetization bias across the system generates a current-carrying nonequilibrium steady state. We characterize the different nonequilibrium phases as functions of the chain's parameters and magnetic potentials, in terms of their correlation functions and entanglement content. The mixed-order transition, previously observed for the case of a transverse-field Ising chain, is established to emerge as a generic feature of a wider class of out-of-equilibrium problems. The critical exponents associated with this universality class are determined analytically. Results are also contrasted with those obtained in the limit of Markovian reservoirs. Our findings should prove helpful in establishing the properties of nonequilibrium phases and phase transitions of extended open quantum systems.

arXiv:2009.06845•Physical review. B./Physical review. B•Jan 7, 2021•9 citations

Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics

Márton Kormos

We investigate the non-equilibrium dynamics of the transverse field quantum Ising chain evolving from an inhomogeneous initial state given by joining two macroscopically different semi-infinite chains. We obtain integral expressions for all two-point correlation functions of the Jordan--Wigner Majorana fermions at any time and for any value of the transverse field. Using this result, we analytically compute the profiles of various physical observables in the space-time scaling limit and show that they can be obtained from a hydrodynamic picture based on ballistically propagating quasiparticles. Going beyond the hydrodynamic limit, we analyze the approach to the non-equilibrium steady state and find that the leading late time corrections display a lattice effect. We also study the fine structure of the propagating fronts which are found to be described by the Airy kernel and its derivatives. Near the front we observe the phenomenon of energy back-flow where the energy locally flows from the colder to the hotter region.

arXiv:1704.03744•SciPost Physics•Sep 8, 2017•91 citations

Exact solution for a diffusive nonequilibrium steady state of an open quantum chain

Marko Žnidarič

We calculate a nonequilibrium steady state of a quantum XX chain in the presence of dephasing and driving due to baths at chain ends. The obtained state is exact in the limit of weak driving while the expressions for one- and two-point correlations are exact for an arbitrary driving strength. In the steady state the magnetization profile and the spin current display diffusive behavior. The spin–spin correlation function, on the other hand, has long-range correlations which, though, decay to zero in either the thermodynamical limit or for equilibrium driving. At zero dephasing a nonequilibrium phase transition occurs from a ballistic transport having short-range correlations to a diffusive transport with long-range correlations.

arXiv:1005.1271•Journal of Statistical Mechanics Theory and Experiment•May 1, 2010•199 citations
We present a fully microscopics-based calculation of the Casimir effect in a nonequilibrium system, namely, an energy-flux-driven quantum XX\mathit{XX}XX chain. The force between the walls (transverse-field impurities) is calculated in a nonequilibrium steady state which is prepared by letting the system evolve from an initial state with the two halves of the chain prepared at equilibrium at different temperatures. The steady state emerging in the large-time limit is homogeneous but carries an energy flux. The Casimir force in this nonequilibrium state is calculated analytically in the limit when the transverse fields are small. We find that the the Casimir force range is reduced compared to the equilibrium case, and suggest that the reason for this is the reduction of fluctuations in the flux-carrying steady state.
The dynamics of quantum anisotropic XY spin chain driven out of equilibrium by a transverse magnetic field, that carry an energy current ( J E ) is investigated. Considering the spin exchange and the flow of energy trapped in magnetic field between two defects in the x y -plane separated by a distance d , we derive an analytical expression of the steady state Green's function of the model using the Grassmann algebra in order to determine the Casimir force between two magnetic defects. As soon as done we find that, cooling the system as well as increasing the anisotropic parameter decrease the energy current and accordingly increase the range of the Casimir force. This symmetry is broken with a significant increase of distance between the defects. A critical temperature is then recorded exhibiting a phase transition according to the anisotropic parameter. An interesting feature of this model is that turning the anisotropic parameter as well as the temperature range will better manipulate the energy flux and control the range of the Casimir force.
We consider two quantum Ising chains initially prepared at thermal equilibrium but with different temperatures and coupled at a given time through one of their end points. In the long-time limit the system reaches a nonequilibrium steady state. We discuss properties of this nonequilibrium steady state and characterize the convergence to the steady regime. We compute the mean energy flux through the chain and show that the heat transport is ballistic. We derive also the large-deviation function for the quantum and thermal fluctuations of this energy transfer.
We study the nonequilibrium steady states of an Ising chain in a transverse field hhh by investigating the effect of a field $\ensuremath{\lambda}$, which drives the current of energy. The zero-temperature, hhh- $\ensuremath{\lambda}$ phase diagram is determined exactly, and it is found that the energy current appears continuously above a threshold $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c}(h)$. The long-range magnetic order (present for $h<{h}_{c},\ensuremath{\lambda}<{\ensuremath{\lambda}}_{c}$) is destroyed in the current-carrying state where the correlations are characterized by power-law, oscillatory decay. The mechanism which generates the power-law correlations in the current-carrying state is discussed.
We obtain the steady-state phase diagram of a transverse-field XY spin chain coupled at its ends to magnetic reservoirs held at different magnetic potentials. In the long-time limit, the magnetization bias across the system generates a current-carrying nonequilibrium steady state. We characterize the different nonequilibrium phases as functions of the chain's parameters and magnetic potentials, in terms of their correlation functions and entanglement content. The mixed-order transition, previously observed for the case of a transverse-field Ising chain, is established to emerge as a generic feature of a wider class of out-of-equilibrium problems. The critical exponents associated with this universality class are determined analytically. Results are also contrasted with those obtained in the limit of Markovian reservoirs. Our findings should prove helpful in establishing the properties of nonequilibrium phases and phase transitions of extended open quantum systems.
We investigate the non-equilibrium dynamics of the transverse field quantum Ising chain evolving from an inhomogeneous initial state given by joining two macroscopically different semi-infinite chains. We obtain integral expressions for all two-point correlation functions of the Jordan--Wigner Majorana fermions at any time and for any value of the transverse field. Using this result, we analytically compute the profiles of various physical observables in the space-time scaling limit and show that they can be obtained from a hydrodynamic picture based on ballistically propagating quasiparticles. Going beyond the hydrodynamic limit, we analyze the approach to the non-equilibrium steady state and find that the leading late time corrections display a lattice effect. We also study the fine structure of the propagating fronts which are found to be described by the Airy kernel and its derivatives. Near the front we observe the phenomenon of energy back-flow where the energy locally flows from the colder to the hotter region.
We calculate a nonequilibrium steady state of a quantum XX chain in the presence of dephasing and driving due to baths at chain ends. The obtained state is exact in the limit of weak driving while the expressions for one- and two-point correlations are exact for an arbitrary driving strength. In the steady state the magnetization profile and the spin current display diffusive behavior. The spin–spin correlation function, on the other hand, has long-range correlations which, though, decay to zero in either the thermodynamical limit or for equilibrium driving. At zero dephasing a nonequilibrium phase transition occurs from a ballistic transport having short-range correlations to a diffusive transport with long-range correlations.