Crossover from ballistic to diffusive thermal transport in quantum Langevin dynamics study of a harmonic chain connected to self-consistent reservoirs

Abstract

Through an exact analysis using quantum Langevin dynamics, we demonstrate the crossover from ballistic to diffusive thermal transport in a harmonic chain with each site connected to Ohmic heat reservoirs. The temperatures of the two heat baths at the boundaries are specified from before whereas the temperatures of the interior heat reservoirs are determined self-consistently by demanding that in the steady state, on average, there is no heat current between any such (self-consistent) reservoir and the harmonic chain. Essence of our study is that the effective mean free path separating the ballistic regime of transport from the diffusive one emerges naturally.

4 pages, 2 figure

References in corpus (11)

• Thermal conduction in classical low-dimensional lattices
• Anomalous heat conduction in one dimensional momentum-conserving systems
• Heat conduction in the disordered harmonic chain revisited
• Heat transport in harmonic lattices
• Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
• Quantum thermal transport from classical molecular dynamics
• Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
• Electron transport in a one dimensional conductor with inelastic scattering by self-consistent reservoirs
• Exactly solvable model of quantum diffusion
• Normal Transport Behavior in Finite One-Dimensional Chaotic Quantum Systems
• Transition from diffusive to ballistic dynamics for a class of finite quantum models

Cited by in corpus (22)

• Heat Transport in low-dimensional systems
• Nonequilibrium Green's function method for quantum thermal transport
• Fourier's Law: insight from a simple derivation
• Quantum heat transfer in harmonic chains with self consistent reservoirs: Exact numerical simulations
• Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths
• Local Temperatures Out of Equilibrium
• Negative differential thermal resistance induced by ballistic transport
• The probe technique far-from-equilibrium: Magnetic field symmetries of nonlinear transport
• Crossover from Fermi-Pasta-Ulam to normal diffusive behaviour in heat conduction through open anharmonic lattices
• Reconstructing Fourier's law from disorder in quantum wires
• Inelastic effects in molecular transport junctions: The probe technique at high bias
• Phononic heat transport in molecular junctions: quantum effects and vibrational mismatch
• Anomalous negative differential thermal resistance in a momentum-conserving lattice
• Effect of quantum resonances on local temperature in nonequilibrium open systems
• Environment dependent vibrational heat transport in molecular Junctions : Rectification, quantum effects, vibrational mismatch
• Quantum stochastic transport along chains
• Thermoelectric phenomena in disordered open quantum systems
• A microscopic model of ballistic-diffusive crossover
• Breakdown of quantum-to-classical correspondence for diffusion in high temperature thermal environment
• Thermal transport in disordered harmonic chains revisited: Formulation of thermal conductivity and local temperatures
• Quantum walk in stochastic environment
• Nonreciprocal electrical transport in linear systems with balanced gain and loss in the bulk