A Nonequilibrium Variational Polaron Theory to Study Quantum Heat Transport

Abstract

We propose a nonequilibrium variational polaron transformation, based on an ansatz for nonequilibrium steady state (NESS) with an effective temperature, to study quantum heat transport at the nanoscale. By combining the variational polaron transformed master equation with the full counting statistics, we have extended the applicability of the polaron-based framework to study nonequilibrium process beyond the super-Ohmic bath models. Previously, the polaron-based framework for quantum heat transport reduces exactly to the non-interacting blip approximation (NIBA) formalism for Ohmic bath models due to the issue of the infrared divergence associated with the full polaron transformation. The nonequilibrium variational method allows us to appropriately treat the infrared divergence in the low-frequency bath modes and explicitly include cross-bath correlation effects. These improvements provide more accurate calculation of heat current than the NIBA formalism for Ohmic bath models. We illustrate the aforementioned improvements with the nonequilibrium spin-boson model in this work and quantitatively demonstrate the cross-bath correlation, current turnover, and rectification effects in quantum heat transfer.

arXiv comment14 pages, 6 figures, 45 References

References in corpus (20)

• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Phononics: Manipulating heat flow with electronic analogs and beyond
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Quantum heat engines and refrigerators: Continuous devices
• Counting statistics of single-electron transport in a quantum dot
• A spin-boson thermal rectifier
• Heat dissipation in atomic-scale junctions
• A general approach to quantum dynamics using a variational master equation: Application to phonon-damped Rabi rotations in quantum dots
• Vibrational Heat Transport in Molecular Junctions
• Nonequilibrium Energy Transfer at Nanoscale: A Unified Theory from Weak to Strong Coupling
• Efficiency at Maximum Power of Laser Quantum Heat Engine Enhanced by Noise-Induced Coherence
• Nonequilibrium density matrix description of steady state quantum transport
• Electron transfer across a thermal gradient
• Path-integral methodology and simulations of quantum thermal transport: Full counting statistics approach
• Improved Dyson series expansion for steady-state quantum transport beyond the weak coupling limit - divergences and resolution
• Quantum transport in d-dimensional lattices
• Tuning the Aharonov-Bohm effect with dephasing in nonequilibrium transport
• Optimal tunneling enhances quantum photovoltaic effect in double quantum dots
• Nonequilibrium density matrix for simultaneous heat and charge steady-state transport in quantum open systems
• Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics