ABSTRACT
This chapter discusses numerical generation of random variates relevant for Phonon Monte Carlo (PMC), assuming that the uniformly distributed variates on the interval are accessible. It also discusses the relative merits of different approaches – direct inversion versus the rejection technique – from both theoretical and practical standpoints, which are sometimes at odds. The chapter shows that several specific examples of nonuniform distributions relevant for phonon transport. It identifies common themes in phonon generation and scattering that are useful for reusing code in a simulation. The chapter reviews the two main methods for generating random variates and the PMC method. It provides several applications: generating the attributes for phonons in equilibrium with full and isotropic dispersions, randomizing outgoing momentum upon diffuse boundary scattering, implementing contacts, and conserving energy in the simulations. PMC is a versatile stochastic technique for solving the Boltzmann equation for phonons in structures that can have real-space roughness and experimentally relevant sizes.
