The nonequilibrium discrete nonlinear Schroedinger equation
arXiv:1204.2470 · doi:10.1103/PhysRevE.86.011108
Abstract
We study nonequilibrium steady states of the one-dimensional discrete nonlinear Schroedinger equation. This system can be regarded as a minimal model for stationary transport of bosonic particles like photons in layered media or cold atoms in deep optical traps. Due to the presence of two conserved quantities, energy and norm (or number of particles), the model displays coupled transport in the sense of linear irreversible thermodynamics. Monte Carlo thermostats are implemented to impose a given temperature and chemical potential at the chain ends. As a result, we find that the Onsager coefficients are finite in the thermodynamic limit, i.e. transport is normal. Depending on the position in the parameter space, the "Seebeck coefficient" may be either positive or negative. For large differences between the thermostat parameters, density and temperature profiles may display an unusual nonmonotonic shape. This is due to the strong dependence of the Onsager coefficients on the state variables.
Submitted to Phys. Rev. E
References in corpus (14)
- Thermal conduction in classical low-dimensional lattices
- Heat Transport in low-dimensional systems
- Destruction of Anderson localization by a weak nonlinearity
- Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
- Asymmetric Wave Propagation in Nonlinear Systems
- Statistical mechanics of a nonlinear discrete system
- Heat transport in harmonic lattices
- Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
- A simple statistical explanation for the localization of energy in nonlinear lattices with two conserved quantities
- Observation of coupled normal heat and matter transport in a simple model system
- Increasing thermoelectric efficiency towards the Carnot limit
- Discrete Nonlinear Schr{ö}dinger Breathers in a Phonon Bath
- A microscopic mechanism for increasing thermoelectric efficiency
- Microcanonical Entropy and Dynamical Measure of Temperature for Systems with Two First Integrals
Cited by in corpus (41)
- Weakly nonergodic dynamics in the Gross--Pitaevskii lattice
- Statistical Mechanics of Systems with Negative Temperature
- Designing a Spin-Seebeck Diode
- Anomalous heat transport in classical many-body systems: overview and perspectives
- Non-Fourier heat transport in nanosystems
- Dynamical freezing of relaxation to equilibrium
- Off-equilibrium Langevin dynamics of the discrete nonlinear Schroedinger chain
- Low temperature dynamics of the one-dimensional discrete nonlinear Schrödinger equation
- Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
- A Chain, a Bath, a Sink and a Wall
- Inverse Currents in Hamiltonian Coupled Transport
- Transport in perturbed classical integrable systems: the pinned Toda chain
- Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
- Thermoelectric efficiency in momentum-conserving systems
- Statistical mechanics of systems with long-range interactions and negative absolute temperature
- Coupled transport in rotor models
- Chaos and localization in the Discrete Nonlinear Schrödinger Equation
- Thermo-magnonic diode: rectification of energy and magnetization currents
- Boundary-induced instabilities in coupled oscillators
- Modelling Reservoir Computing with the Discrete Nonlinear Schrödinger Equation
- Coherent energy transport in classical nonlinear oscillators: an analogy with the Josephson effect
- Negative temperature states as exact equilibrium solutions of the Wave Kinetic equation for one dimensional lattices
- Entropy production for complex Langevin equations
- Chaotic and quantum dynamics in driven-dissipative bosonic chains
- Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport
- Coupled transport in a linear-stochastic Schrödinger Equation
- Thermalization in the one-dimensional Salerno model lattice
- Condensation induced by coupled transport processes
- Negative-temperature Fourier transport in one-dimensional systems
- Gauge invariance and geometric phase in nonequilibrium thermodynamics
- Intensity pseudo-localized phase in the glassy random laser
- Dynamical regimes of finite temperature discrete nonlinear Schrödinger chain
- Autonomous Circular Heat Engine
- H-theorem at negative temperature: the random exchange model with bounds
- Onsager coefficients in a coupled-transport model displaying a condensation transition
- Nanoscale control of heat and spin conductance in artificial spin chains
- Chaos and quantum regimes in -photon driven, dissipative bosonic chains
- Localization and "classical entanglement'' in the Discrete Non-Linear Schrödinger Equation
- Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization
- Subdiffusive Energy Transport and Antipersistent Correlations Due to the Scattering of Phonons and Discrete Breathers
- Dephasing-assisted macrospin transport