New analytic solution for the heat flow through a general harmonic network

Abstract

We present a new analytic expression for the heat current through a general harmonic network coupled with Ohmic reservoirs. We use a new method that enables us to express the stationary state of the network in terms of the eigenvectors and eigenvalues of a generalized cubic eigenvalue problem. In this way, we obtain exact formulae for the heat current and the local temperature inside the network. Our method does not rely in the usual assumptions of weak coupling to the environments or on the existence of an infinite cutoff in the environmental spectral densities. We use this method to study non-equilibrium processes without the weak coupling and Markovian approximations. As a first application of our method, we revisit the problem of heat conduction in 2D and 3D crystals with binary mass disorder. We complement previous results showing that for small systems the scaling of the heat current with the system size greatly depends on the strength of the interaction between system and reservoirs. This somewhat counter-intuitive result seems not to have been noticed before.

This paper has been withdrawn by the author due to a crucial error in the derivation of Eqs. (19) and (20). An update with corrected expressions and a detailed derivation will follow soon

References in corpus (4)

• The NumPy array: a structure for efficient numerical computation
• Dissipative preparation of entanglement in optical cavities
• Heat transport in harmonic lattices
• Heat transport in ordered harmonic lattices

Cited by in corpus (13)

• Testing the validity of the local and global GKLS master equations on an exactly solvable model
• Fundamental limits for cooling of linear quantum refrigerators
• Thermal transport in out of equilibrium quantum harmonic chains
• From non-equilibrium Green's functions to quantum master equations for the density matrix and out-of-time-order correlators: steady state and adiabatic dynamics
• A unified diagrammatic approach to quantum transport in few-level junctions for bosonic and fermionic reservoirs: Application to the quantum Rabi model
• Conformal order and Poincar$\acute{\mathrm{e}}$-Klein mapping underlying electrostatics-driven inhomogeneity in tethered membranes
• Stochastic simulation of dissipative quantum oscillators
• Non-equilibrium steady states of long-range coupled harmonic chains
• Heat transport in overdamped quantum systems
• Thermalization of isolated harmonic networks under conservative noise
• Potential renormalisation, Lamb shift and mean-force Gibbs state -- to shift or not to shift?
• Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths
• Bending the rules of low-temperature thermometry with periodic driving