Nonequilibrium discrete nonlinear Schrödinger equation

Iubini, Stefano; Lepri, Stefano; Politi, Antonio

doi:10.1103/physreve.86.011108

Cited by 58 publications

(133 citation statements)

References 34 publications

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“…by the dependence of the transport coefficients Here μ is the chemical potential imposed by the bath and ( ) h t is a complex Gaussian white noise with zero mean and unit variance. In the high-temperature regime transport is normal [18] and fluctuations of conserved fields spread diffusively [42]. However, in the low temperature regime phase slips are rare, with the consequence that phase differences appear as an additional (almost) conserved field, yielding anomalous transport on very long timescales [42].…”

Section: Numerical Simulations Of Coupled Transport In the Xy Chainmentioning

confidence: 99%

“…From the point of view of statistical mechanics, a few works have been so far devoted to coupled transport: they can be grouped in those devoted to interacting particle gases [13][14][15] and to coupled oscillator systems [16][17][18][19][20]. The connection between microscopic interactions and macroscopic thermodynamic properties is still largely unexplored.…”

Section: Introductionmentioning

confidence: 99%

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Coupled transport in rotor models

et al. 2016

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Steady nonequilibrium states are investigated in a one-dimensional setup in the presence of two thermodynamic currents. Two paradigmatic nonlinear oscillators models are investigated: an XY chain and the discrete nonlinear Schrödinger equation. Their distinctive feature is that the relevant variable is an angle in both cases. We point out the importance of clearly distinguishing between energy and heat flux. In fact, even in the presence of a vanishing Seebeck coefficient, a coupling between (angular) momentum and energy arises, mediated by the unavoidable presence of a coherent energy flux. Such a contribution is the result of the 'advection' induced by the position-dependent angular velocity. As a result, in the XY model, the knowledge of the two diagonal elements of the Onsager matrix suffices to reconstruct its transport properties. The analysis of the nonequilibrium steady states finally allows to strengthen the connection between the two models.

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Section: Numerical Simulations Of Coupled Transport In the Xy Chainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Coupled transport in rotor models

et al. 2016

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“…They also show Gaussian cross-correlations, which is possible since density and energy are both even under time reversal. In the previous studies [80] transport coefficients have been measured in the steady state set-up.…”

Section: Other 1d Hamiltonian Systemsmentioning

confidence: 99%

Fluctuating Hydrodynamics Approach to Equilibrium Time Correlations for Anharmonic Chains

Spohn

2016

Thermal Transport in Low Dimensions

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Abstract. Linear fluctuating hydrodynamics is a useful and versatile tool for describing fluids, as well as other systems with conserved fields, on a mesoscopic scale. In one spatial dimension, however, transport is anomalous, which requires to develop a nonlinear extension of fluctuating hydrodynamics. The relevant nonlinearity turns out to be the quadratic part of the Euler currents when expanding relative to a uniform background. We outline the theory and compare with recent molecular dynamics simulations. 1 arXiv:1505.05987v2 [cond-mat.stat-mech]

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“…For instance, this is testified by the discrepancy that still persists, after many years of careful studies, between the most advanced theories of heat conduction and some numerical simulations. The level of difficulty typically increases when one considers coupled transport [5][6][7][8][9][10][11] (i.e. when two or more currents coexist, such as heat and electric ones in thermo-electric effects) or, even worse, far-from-equilibrium.…”

mentioning

confidence: 99%

“…Here below, we show that a similar scenario can be observed for the DNLS equation, iż n = −2|z n | 2 z n − z n+1 − z n−1 , where z n = (p n + iq n )/ √ 2 is a complex variable. The DNLS Hamiltonian has two conserved quantities, the mass/norm a and the energy density h [29,30], so that it is a natural candidate for describing coupled transport [10,31]. We have numerically studied a DNLS chain interacting with two Langevin thermostats at T = 0 and different chemical potentials µ 1 and µ N imposed at the boundaries (see Ref.…”

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confidence: 99%

Boundary-Induced Instabilities in Coupled Oscillators

et al. 2014

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A novel class of nonequilibrium phase-transitions at zero temperature is found in chains of nonlinear oscillators. For two paradigmatic systems, the Hamiltonian XY model and the discrete nonlinear Schrödinger equation, we find that the application of boundary forces induces two synchronized phases, separated by a non-trivial interfacial region where the kinetic temperature is finite. Dynamics in such supercritical state displays anomalous chaotic properties whereby some observables are non-extensive and transport is superdiffusive. At finite temperatures, the transition is smoothed, but the temperature profile is still non-monotonous. The characterization of steady-states is a widely investigated problem within non-equilibrium statistical mechanics [1], since it provides the basis for understanding a large variety of phenomena, including transport processes, pattern formation and the dynamics of living systems. In a nutshell, the simplest setup amounts to determining the currents that emerge as a result of the application of an external force, either across the system, as for electric currents, or at the boundaries, as in heat conduction [2][3][4]. Anyway, it is quite a nontrivial task to be accomplished, even when the departure from equilibrium is minimal and one can rely on the Green-Kubo formalism for establishing a connection between the microscopic and the hydrodynamic descriptions. For instance, this is testified by the discrepancy that still persists, after many years of careful studies, between the most advanced theories of heat conduction and some numerical simulations. The level of difficulty typically increases when one considers coupled transport [5-11] (i.e. when two or more currents coexist, such as heat and electric ones in thermo-electric effects) or, even worse, far-from-equilibrium. This is why most of the theoretical studies concentrate on stochastic models, where fluctuations can be easily controlled, although they lack a truly microscopic justification. This approach proved, nevertheless, very effective, since it has allowed discovering non-equilibrium transitions, such as those exhibited by TASEP-like models, that have been used to describe translation of proteins, or traffic flows [12].In this Letter we describe a novel class of boundaryinduced transitions for two models that are typically used as test beds for a wide range of physical phenomena: the so-called Hamiltonian XY (or rotor) model [13][14][15][16] sub- * Electronic address: stefano.lepri@isc.cnr.it ject to an applied mechanical torque and the Discrete NonLinear Schrödinger (DNLS) equation [17][18][19] under a gradient of the chemical potential. This type of qualitative change of the dynamics results from the joint effect of thermal and mechanical forces. It can be interpreted as a desynchronization phenomenon in a spatially-extended dynamical system, whereby mutual entrainment of oscillators' phases is abruptly destroyed. As a result of such unlocking, a regime characterized by phase-coexistence sets in where, although the chain...

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Nonequilibrium discrete nonlinear Schrödinger equation

Cited by 58 publications

References 34 publications

Coupled transport in rotor models

Coupled transport in rotor models

Fluctuating Hydrodynamics Approach to Equilibrium Time Correlations for Anharmonic Chains

Boundary-Induced Instabilities in Coupled Oscillators

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