15,565 research outputs found
Generalized Pearson distributions for charged particles interacting with an electric and/or a magnetic field
The linear Boltzmann equation for elastic and/or inelastic scattering is
applied to derive the distribution function of a spatially homogeneous system
of charged particles spreading in a host medium of two-level atoms and
subjected to external electric and/or magnetic fields. We construct a
Fokker-Planck approximation to the kinetic equations and derive the most
general class of distributions for the given problem by discussing in detail
some physically meaningful cases. The equivalence with the transport theory of
electrons in a phonon background is also discussed.Comment: 24 pages, version accepted on Physica
Inelastic quantum transport in superlattices: success and failure of the Boltzmann equation
Electrical transport in semiconductor superlattices is studied within a fully
self-consistent quantum transport model based on nonequilibrium Green
functions, including phonon and impurity scattering. We compute both the drift
velocity-field relation and the momentum distribution function covering the
whole field range from linear response to negative differential conductivity.
The quantum results are compared with the respective results obtained from a
Monte Carlo solution of the Boltzmann equation. Our analysis thus sets the
limits of validity for the semiclassical theory in a nonlinear transport
situation in the presence of inelastic scattering.Comment: final version with minor changes, to appear in Physical Review
Letters, sceduled tentatively for July, 26 (1999
Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models
We consider the linear dissipative Boltzmann equation describing inelastic
interactions of particles with a fixed background. For the simplified model of
Maxwell molecules first, we give a complete spectral analysis, and deduce from
it the optimal rate of exponential convergence to equilibrium. Moreover we show
the convergence to the heat equation in the diffusive limit and compute
explicitely the diffusivity. Then for the physical model of hard spheres we use
a suitable entropy functional for which we prove explicit inequality between
the relative entropy and the production of entropy to get exponential
convergence to equilibrium with explicit rate. The proof is based on
inequalities between the entropy production functional for hard spheres and
Maxwell molecules. Mathematical proof of the convergence to some heat equation
in the diffusive limit is also given. From the last two points we deduce the
first explicit estimates on the diffusive coefficient in the Fick's law for
(inelastic hard-spheres) dissipative gases.Comment: 25 page
Kinetic Solvers with Adaptive Mesh in Phase Space
An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for
solving multi-dimensional kinetic equations by the discrete velocity method. A
Cartesian mesh for both configuration (r) and velocity (v) spaces is produced
using a tree of trees data structure. The mesh in r-space is automatically
generated around embedded boundaries and dynamically adapted to local solution
properties. The mesh in v-space is created on-the-fly for each cell in r-space.
Mappings between neighboring v-space trees implemented for the advection
operator in configuration space. We have developed new algorithms for solving
the full Boltzmann and linear Boltzmann equations with AMPS. Several recent
innovations were used to calculate the discrete Boltzmann collision integral
with dynamically adaptive mesh in velocity space: importance sampling,
multi-point projection method, and the variance reduction method. We have
developed an efficient algorithm for calculating the linear Boltzmann collision
integral for elastic and inelastic collisions in a Lorentz gas. New AMPS
technique has been demonstrated for simulations of hypersonic rarefied gas
flows, ion and electron kinetics in weakly ionized plasma, radiation and light
particle transport through thin films, and electron streaming in
semiconductors. We have shown that AMPS allows minimizing the number of cells
in phase space to reduce computational cost and memory usage for solving
challenging kinetic problems
Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials
We develop a diagrammatic scattering theory for interacting bosons in a
three-dimensional, weakly disordered potential. We show how collisional energy
transfer between the bosons induces the thermalization of the inelastic
single-particle current which, after only few collision events, dominates over
the elastic contribution described by the Gross-Pitaevskii ansatz.Comment: 5 pages, 3 figures, very close to published versio
Comparison of inelastic and quasi-elastic scattering effects on nonlinear electron transport in quantum wires
When impurity and phonon scattering coexist, the Boltzmann equation has been
solved accurately for nonlinear electron transport in a quantum wire. Based on
the calculated non-equilibrium distribution of electrons in momentum space, the
scattering effects on both the non-differential (for a fixed dc field) and
differential (for a fixed temperature) mobilities of electrons as functions of
temperature and dc field were demonstrated. The non-differential mobility of
electrons is switched from a linearly increasing function of temperature to a
parabolic-like temperature dependence as the quantum wire is tuned from an
impurity-dominated system to a phonon-dominated one [see T. Fang, {\em et al.},
\prb {\bf 78}, 205403 (2008)]. In addition, a maximum has been obtained in the
dc-field dependence of the differential mobility of electrons. The low-field
differential mobility is dominated by the impurity scattering, whereas the
high-field differential mobility is limited by the phonon scattering [see M.
Hauser, {\em et al.}, Semicond. Sci. Technol. {\bf 9}, 951 (1994)]. Once a
quantum wire is dominated by quasi-elastic scattering, the peak of the
momentum-space distribution function becomes sharpened and both tails of the
equilibrium electron distribution centered at the Fermi edges are raised by the
dc field after a redistribution of the electrons is fulfilled in a symmetric
way in the low-field regime. If a quantum wire is dominated by inelastic
scattering, on the other hand, the peak of the momentum-space distribution
function is unchanged while both shoulders centered at the Fermi edges shift
leftward correspondingly with increasing dc field through an asymmetric
redistribution of the electrons even in low-field regime [see C. Wirner, {\em
et al.}, \prl {\bf 70}, 2609 (1993)]
Nonequilibrium mesoscopic transport: a genealogy
Models of nonequilibrium quantum transport underpin all modern electronic
devices, from the largest scales to the smallest. Past simplifications such as
coarse graining and bulk self-averaging served well to understand electronic
materials. Such particular notions become inapplicable at mesoscopic
dimensions, edging towards the truly quantum regime. Nevertheless a unifying
thread continues to run through transport physics, animating the design of
small-scale electronic technology: microscopic conservation and nonequilibrium
dissipation. These fundamentals are inherent in quantum transport and gain even
greater and more explicit experimental meaning in the passage to atomic-sized
devices. We review their genesis, their theoretical context, and their
governing role in the electronic response of meso- and nanoscopic systems.Comment: 21p
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