greenWTE: Frequency-domain solver for the phonon Wigner Transport Equation with arbitrary heating using Green's functions
Abstract
Heat transport in solids is usually described in a phenomenological way via Fourier's law. However, at small time and length scales in low thermal conductivity materials, a microscopic description is needed. This is traditionally done by invoking the phonon Boltzmann Transport Equation (BTE), which has been successful in describing transport in high thermal conductivity materials. Recently, a generalization of the BTE, the Wigner Transport Equation, was developed to be able to microscopically describe transport in low thermal conductivity materials by taking into account not only phonon scattering processes but also phonon tunneling processes, so-called coherences. We present a Python package that solves the Wigner Transport Equation (WTE) in spatial and temporal Fourier space for arbitrary source terms, thereby enabling the study of heat transport at small space and time scales. This allows one to compute both static and dynamic thermal conductivities from bulk to nanoscale. Beyond that, it can be used to study the response of phonon systems in materials to arbitrary heat sources.
Related
- Multivariable Painleve'-II equation: connection formulas for arbitrary system size
- Representation of arbitrary rational functions and polynomials by non-Foster resistor-capacitor-inductor networks
- Anisotropic overlap reduction functions for arbitrary equal-arm TDI channels: A fully analytic framework and efficient evaluation
- Stability of Solitons in the Parametrically Driven and Damped Nonlinear Schrödinger Equation in Arbitrary Dimension
- Quantum optomechanics with arbitrary mirror displacement: nonlinear Langevin equation with non-Markovian back-action noises
BibTeX
@misc{kremeyer2026greenwte,
title = {{greenWTE: Frequency-domain solver for the phonon Wigner Transport Equation with arbitrary heating using Green's functions}},
author = {Laurenz Kremeyer and Bradley J. Siwick and Samuel Huberman},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04156},
eprint = {2611.04156},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04156},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - greenWTE: Frequency-domain solver for the phonon Wigner Transport Equation with arbitrary heating using Green's functions
AU - Laurenz Kremeyer
AU - Bradley J. Siwick
AU - Samuel Huberman
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04156
UR - https://arxiv.org/abs/2611.04156
AB - Heat transport in solids is usually described in a phenomenological way via Fourier's law. However, at small time and length scales in low thermal conductivity materials, a microscopic description is needed. This is traditionally done by invoking the phonon Boltzmann Transport Equation (BTE), which has been successful in describing transport in high thermal conductivity materials. Recently, a generalization of the BTE, the Wigner Transport Equation, was developed to be able to microscopically describe transport in low thermal conductivity materials by taking into account not only phonon scattering processes but also phonon tunneling processes, so-called coherences. We present a Python package that solves the Wigner Transport Equation (WTE) in spatial and temporal Fourier space for arbitrary source terms, thereby enabling the study of heat transport at small space and time scales. This allows one to compute both static and dynamic thermal conductivities from bulk to nanoscale. Beyond that, it can be used to study the response of phonon systems in materials to arbitrary heat sources.
ER -