## Journals

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### Open Access Journals

KRM

The paper is concerned with the construction of a
stochastic model for the spatially discretized
time-dependent Schrödinger equation.
The model is based on a particle system with
a Markov jump evolution.
The particles are characterized by a sign (plus or minus),
a position (discrete grid) and a type (real or imaginary).
The jumps are determined by the creation of offspring.
The main result is the construction of a family of complex-valued random
variables such that their expected
values coincide with the solution of the
Schrödinger equation.

KRM

A probabilistic model for the Wigner equation is studied.
The model is based on a particle system with
the time evolution of a piecewise deterministic
Markov process.
Each particle is characterized by a
real-valued weight, a position and a wave-vector.
The particle position changes continuously, according to the
velocity determined by the wave-vector.
New particles are created randomly and added to the system.
The main result is that
appropriate functionals of the process
satisfy a weak form of the Wigner equation.

KRM

The paper studies the kinetic equation for
electron transport in semiconductors.
New formulas for the heat generation rate are derived
by analyzing the basic scattering mechanisms.
In addition, properties of the
steady state distribution are discussed and possible
extensions of the deviational particle Monte Carlo method
to the area of electron transport are proposed.

KRM

This paper studies a Boltzmann transport equation with several
electron-phonon scattering mechanisms, which describes the charge
transport in semiconductors.
The electric field is coupled to the electron distribution function via
Poisson's equation.
Both the parabolic and the quasi-parabolic band approximations are considered.
The steady state behaviour
of the electron distribution function is investigated by
a Monte Carlo algorithm.
More precisely, several nonlinear functionals of the solution are calculated
that quantify the deviation of the steady state from a
Maxwellian distribution with respect to the wave-vector.
On the one hand, the numerical
results illustrate known theoretical statements about the steady state
and indicate directions for further studies.
On the other hand, the nonlinear functionals
provide tools that can be used in the framework of
Monte Carlo algorithms for detecting regions in which the steady state
distribution has a relatively simple structure, thus providing a basis
for domain decomposition methods.

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