Generalized self-consistent reservoir model for normal and anomalous heat transport in quantum harmonic chains

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Statistical Mechanics

Background:

• Stochastic reservoirs model scattering and dephasing in quantum systems.
• Reservoir-system coupling is often described using nonequilibrium Green's functions or quantum Langevin equations.
• Understanding thermal transport is crucial for nanoscale devices and materials science.

Purpose of the Study:

• Investigate thermal transport in a finite quantum harmonic chain segment.
• Analyze the impact of self-energy and lattice translation invariance on transport properties.
• Elucidate the crossover from ballistic to diffusive transport and its scaling relations.

Main Methods:

• Utilized the self-consistent reservoir approach for a quantum harmonic chain.
• Employed the Landauer-Büttiker equations under a self-consistent adiabatic condition.
• Analyzed systems with equal self-energy at each site, ensuring lattice translation invariance.

Main Results:

• Quantitatively demonstrated a thermally induced crossover from ballistic to diffusive transport.
• Identified a temperature-dependent mean free path governing the transport scaling relation.
• Observed normal transport for linear self-energy and anomalous transport for nonlinear self-energy.

Conclusions:

• The study provides a quantitative understanding of thermal transport crossovers in quantum systems.
• Findings highlight the role of self-energy order in determining transport behavior (normal vs. anomalous).
• Discussed implications related to massless Goldstone modes and linear momentum conservation.