From dissipative dynamics to studies of heat transfer at the nanoscale

TL;DR

This paper compares different theoretical methods to study heat transfer at the nanoscale in a quantum two-bath spin-boson model, highlighting their limitations and the importance of choosing appropriate techniques for accurate results.

Contribution

The study systematically evaluates the applicability and limitations of BR, NIBA, and path integral methods for quantum heat transfer in the spin-boson model.

Findings

BR and NIBA give similar RDM dynamics in certain regimes

Small deviations in RDM can cause large discrepancies in heat transfer predictions

NIBA fails to predict the heat current turnover behavior beyond the non-adiabatic limit

Abstract

We study in a unified manner the dissipative dynamics and the transfer of heat in the two-bath spin-boson model. We use the Bloch-Redfield (BR) formalism, valid in the very weak system-bath coupling limit, the noninteracting-blip approximation (NIBA), applicable in the non-adiabatic limit, and iterative, numerically-exact path integral tools. These methodologies were originally developed for the description of the dissipative dynamics of a quantum system, and here they are applied to explore the problem of quantum energy transport in a non-equilibrium setting. Specifically, we study the weak-to-intermediate system-bath coupling regime at high temperatures $k_BT/\hbar>\epsilon$, with $\epsilon$ as the characteristic frequency of the two-state system. The BR formalism and NIBA can lead to close results for the dynamics of the reduced density matrix (RDM) in a certain range of parameters. However, relatively small deviations in the RDM dynamics propagate into significant qualitative discrepancies in the transport behavior. Similarly, beyond the strict non-adiabatic limit NIBA's prediction for the heat current is qualitatively incorrect: It fails to capture the turnover behavior of the current with tunneling energy and temperature. Thus, techniques that proved meaningful for describing the RDM dynamics, to some extent even beyond their rigorous range of validity, should be used with great caution in heat transfer calculations, since qualitative-serious failures develop once parameters are mildly stretched beyond the techniques' working assumptions.