Approach to Equilibrium for the Phonon Boltzmann Equation
نویسندگان
چکیده
منابع مشابه
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...
متن کاملTowards a Microscopic Derivation of the Phonon Boltzmann Equation
The thermal conductivity of insulating (dielectric) crystals is computed almost exclusively on the basis of the phonon Boltzmann equation. We refer to [1] for a discussion more complete than possible in this contribution. On the microscopic level the starting point is the Born-Oppenheimer approximation (see [2] for a modern version), which provides an effective Hamiltonian for the slow motion o...
متن کاملQuasi-equilibrium closure hierarchies for the Boltzmann equation
ester, UK. In this paper, explicit method of constructing approximations (the triangle entropy is developed for nonequilibrium problems. This method enables one to treat any com nonlinear functionals that fit best the physics of a problem (such as, for example processes) as new independent variables. The work of the method is demonstrated on the Boltzmann’s-type kinet macroscopic variables are ...
متن کاملSolution of the Phonon Boltzmann Transport Equation Employing Rigorous Implementation of Phonon Conservation Rules
A finite volume scheme is developed to solve the phonon Boltzmann transport equation in an energy form accounting for phonon dispersion and polarization. The physical space and the first Brillouin zone are discretized into finite volumes and the phonon BTE is integrated over them. Second-order accurate differencing schemes are used for the discretization. The scattering term employs a rigorous ...
متن کاملBoltzmann Solver for Phonon Transport
Boltzmann Transport Equation is solved numerically to model phonon transport in a subcontinuum domain in order to study heat transfer in thin film semiconductors. The phonon distribution function is modified to get an Energy equation from the Boltzmann Transport Equation. Gray form of the Energy equation is solved in the Relaxation time approximation to get the Phonon Energy Density distributio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2008
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-008-0480-y