Quantum kinetic equation and thermal conductivity tensor for bosons
arXiv:2402.17329 · doi:10.1103/PhysRevB.109.235137
Abstract
We systematically derive the quantum kinetic equation in full phase space for any quadratic hamiltonian of bosonic fields, including in the absence of translational invariance. This enables the treatment of boundaries, inhomogeneous systems and states with non-trivial textures, such as skyrmions in the context of magnetic bosons. We relate the evolution of the distribution of bosons in phase space to single-electron, band-diagonal, physical quantities such as Berry curvature and energy magnetization, by providing a procedure to "diagonalize" the Hamiltonian in phase space, using the formalism of the Moyal product. We obtain exact equations, which can be expanded order by order, for example in the "smallness" of the spatial gradients, providing a "semiclassical" approximation. In turn, at first order, we recover the usual full Boltzmann equation and give a self-contained and exact derivation of the intrinsic thermal Hall effect of bosons. The formulation clarifies the contribution from "energy magnetization" in natural manner, and does not require the inclusion of Luttinger's pseudo-gravitational field to obtain thermal transport quantities.
arXiv comment10 + 9 pages (main text + appendices), 1 figure, 1 table
References in corpus (18)
- Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
- Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
- Berry phase correction to electron density of states in solids
- Phase space representation of quantum dynamics
- Theory of Thermal Hall Effect in Quantum Magnets
- Semiclassical theories of the anomalous Hall effect
- Thermoelectric Response of an Interacting Two-Dimensional Electron Gas in Quantizing Magnetic Field
- Energy Magnetization and Thermal Hall Effect
- Berry Curvature and Phonon Hall Effect
- Berry phase of phonons and thermal Hall effect in nonmagnetic insulators
- Dissipationless Phonon Hall Viscosity
- Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections
- Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems
- Phonon Thermal Hall Conductivity from Scattering with Collective Fluctuations
- Thermal Conductivity and Theory of Inelastic Scattering of Phonons by Collective Fluctuations
- Equilibrium currents in chiral systems with non-zero Chern number
- Effective Quantum Theories for Transport in Inhomogeneous Systems with Non-trivial Band Structure
- Degeneracy-projected polarization formulas for Hall-type conductivities