incorporate hundreds of millions of semiconductor devices (transistors, diodes, optical devices, etc.). To predict the performance of the VLSI circuits, the current-voltage (I-V) characteristics of the semiconductor device are required. Semiconductor device simulation codes provide a way of predicting I-V curves as device parameters are varied, without having to fabricate the device first. (The...

describes the evolution of a density of particles in a medium in which the particles don’t interact among themselves. The motion of each particle is described by a jump process: The speed of a particle is constant (equal to one), and also the direction is constant in exponentially distributed time intervals. At the end of such an interval, the direction jumps according to a law that corresponds...

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start from the standard Boltzmann equation, averaging over frequencies leads to appearance of fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of the fractional mater...

The lattice Boltzmann equation was introduced about 20 years ago as a new paradigm for computational fluid dynamics. In this paper, we revisit the main formulation of the lattice Boltzmann collision integral (matrix model) and introduce a new two-parametric family of collision operators, which permits us to combine enhanced stability and accuracy of matrix models with the outstanding simplicity...

Semiclassical Boltzmann transport has been the principal theory in the field of modeling and simulation of semiconductor technology since its early development. To date, most commer‐ cial device simulations including the full-band Monte Carlo (FBMC) method are based on the solution of the Boltzmann transport equation (BTE) and its simplified derivatives such as the hydrodynamic (HD) equations a...

In this paper, by introducing a different distribution function and starting from the Boltzmann equation as well as the Maxwell-Boltzmann distribution, we obtain a Boltzmann Bhatnagar-Gross-Krook (BGK) equation for thermal flows with viscous heat dissipation in the incompressible limit. The continuous thermal BGK model is then discretized over both time and phase space to form a lattice BGK mod...

In this paper we present a new one-particle Monte Carlo iteration scheme to self-consistently take into account generation-recombination processes as well as quantum corrections. The basic idea is to couple the Boltzmann transport equation (or the Boltzmann-Wigner equation) not only with the Poisson equation, but also with the continuity equation by using exact transport coefficients from the M...

Equilibrium stellar-dynamical systems are described by the time-independent Collisionless Boltzmann Equation (CBE). Two methods of building equilibrium stellar-dynamical systems are described. One begins by defining integrals of motion I1, I2, . . .; Jeans theorem implies that any function F = F(I1, I2, ...), is a solution of the time-independent CBE. Another begins by defining the mass distrib...

For low density gases the validity of the Boltzmann transport equation is well established. The central object is the one-particle distribution function, f , which in the Boltzmann-Grad limit satisfies the Boltzmann equation. Grad and, much refined, Cercignani argue for the existence of this limit on the basis of the BBGKY hierarchy for hard spheres. At least for a short kinetic time span, the ...