Boltzmann equation solver adapted to emergent chemical non-equilibrium

Non-Markovian Boltzmann equation

A quantum kinetic equation for strongly interacting particles (generalized binary collision approximation, ladder or T-matrix approximation) is derived in the framework of the density operator technique. In contrast to conventional kinetic theory, which is valid on time scales large as compared to the collision (correlation) time only, our approach retains the full time dependencies, especially...

Approach to equilibrium for the phonon Boltzmann equation

We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the initial condition is a small perturbation of an equilibrium state, and vanishes at infinity, the dynamics tends diffusively to equilibrium. The solution is the sum of a local equilibrium state, associated to conserved qu...

Investigation of a Discrete Velocity Monte Carlo Boltzmann Equation Solver

Discontinuous Galerkin Solver for the Semiconductor Boltzmann Equation

We present preliminary results of a discontinuous Galerkin scheme applied to deterministic computations of the transients for the Boltzmann-Poisson system describing electron transport in semiconductor devices. The collisional term models optical-phonon interactions which become dominant under strong energetic conditions corresponding to nanoscale active regions under applied bias. The proposed...

From Lattice Boltzmann Method to Lattice Boltzmann Flux Solver

Based on the lattice Boltzmann method (LBM), the lattice Boltzmann flux solver (LBFS), which combines the advantages of conventional Navier–Stokes solvers and lattice Boltzmann solvers, was proposed recently. Specifically, LBFS applies the finite volume method to solve the macroscopic governing equations which provide solutions for macroscopic flow variables at cell centers. In the meantime, nu...