Dynamics and transport in the boundary-driven dissipative Klein-Gordon chain

Abstract

Motivated by experiments on chains of superconducting qubits, we consider the dynamics of a classical Klein-Gordon chain coupled to coherent driving and subject to dissipation solely at its boundaries. As the strength of the boundary driving is increased, this minimal classical model recovers the main features of the "dissipative phase transition" seen experimentally. Between the transmitting and non-transmitting regimes on either side of this transition (which support ballistic and diffusive energy transport respectively), we observe additional dynamical regimes of interest. These include a regime of superdiffusive energy transport at weaker driving strengths, together with a "resonant nonlinear wave" regime at stronger driving strengths, which is characterized by emergent translation symmetry, ballistic energy transport, and coherent oscillations of a nonlinear normal mode. We propose a non-local Lyapunov exponent as an experimentally measurable diagnostic of many-body chaos in this system, and more generally in open systems that are only coupled to an environment at their boundaries.

arXiv comment23 pages, 16 figures; v2: typos fixed and references added; v3: improved ansatz for the resonant nonlinear wave solution, close to published version

References in corpus (53)

• Circuit Quantum Electrodynamics
• Thermal conduction in classical low-dimensional lattices
• Heat Transport in low-dimensional systems
• Spectral signatures of many-body localization with interacting photons
• Finite-temperature transport in one-dimensional quantum lattice models
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• The Fascinating World of Landau-Lifshitz-Gilbert Equation: An Overview
• Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
• Energy transmission in the forbidden bandgap of a nonlinear chain
• Nonequilibrium Green's function method for quantum thermal transport
• Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
• Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model
• Growth and decay of discrete nonlinear Schroedinger breathers interacting with internal modes or standing-wave phonons
• Nonequilibrium density matrix description of steady state quantum transport
• Energy Transport in Weakly Anharmonic Chains
• Light-cone spreading of perturbations and the butterfly effect in a classical spin chain
• Discrete breathers in dissipative lattices
• Non-integrability and the Fourier heat conduction law
• Photon transport in a Bose-Hubbard chain of superconducting artificial atoms
• Temperature dependence of butterfly effect in a classical many-body system
• Photon transport in a dissipative chain of nonlinear cavities
• Fluctuating hydrodynamics for a discrete Gross-Pitaevskii equation: mapping to Kardar-Parisi-Zhang universality class
• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• Nonlinear response and discrete breather excitation in driven micro-mechanical cantilever arrays
• Transmission thresholds in time-periodically driven nonlinear disordered systems
• Normal Heat Conductivity in a strongly pinned chain of anharmonic oscillators
• Dynamical glass in weakly non-integrable Klein-Gordon chains
• Statistical mechanics of an integrable system
• Many-body Chaos in Thermalised Fluids
• Low temperature dynamics of the one-dimensional discrete nonlinear Schrödinger equation
• Superdiffusive transport of energy in one-dimensional metals
• Landauer formula for phonon heat conduction: relation between energy transmittance and transmission coefficient
• Pattern formation and localization in the forced-damped FPU lattice
• Spatio-temporal spread of perturbations in a driven dissipative Duffing chain: an OTOC approach
• Quantum mechanical response to a driven Caldeira-Leggett bath
• Fourier's law based on microscopic dynamics
• Transport properties of the classical Toda chain: effect of a pinning potential
• Boundary-induced instabilities in coupled oscillators
• Diverging fluctuations of the Lyapunov exponents
• Nonequilibrium photonic transport and phase transition in an array of optical cavities
• Multi-resonance of energy transport and absence of heat pump in a force-driven lattice
• Dynamics of Energy Transport in a Toda Ring
• Spontaneous pattern formation in driven nonlinear lattice
• Stability of Nonlinear Normal Modes in the FPU-$\beta$ Chain in the Thermodynamic Limit
• Quantum Brownian Motion: Drude and Ohmic Baths as Continuum Limits of the Rubin Model
• Transport, correlations, and chaos in a classical disordered anharmonic chain
• Spatio-temporal spread of perturbations in power-law models at low temperatures: Exact results for OTOC
• Dynamics of a quantum two-state system in a linearly driven quantum bath
• Surmounting collectively oscillating bottlenecks
• Ballistic transport in integrable quantum chains with degenerate spectra
• Exact Solution for the Heat Conductance in Harmonic Chains
• Decay of Hamiltonian Breathers under Dissipation

Cited by in corpus (5)

• Chaotic and quantum dynamics in driven-dissipative bosonic chains
• Hidden time-reversal in driven XXZ spin chains: exact solutions and new dissipative phase transitions
• Heat flow in a periodically forced, thermostatted chain II
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Chaos and quantum regimes in $n$-photon driven, dissipative bosonic chains