200 research outputs found

### Low Momentum Classical Mechanics with Effective Quantum Potentials

A recently introduced effective quantum potential theory is studied in a low
momentum region of phase space. This low momentum approximation is used to show
that the new effective quantum potential induces a space-dependent mass and a
smoothed potential both of them constructed from the classical potential. The
exact solution of the approximated theory in one spatial dimension is found.
The concept of effective transmission and reflection coefficients for effective
quantum potentials is proposed and discussed in comparison with an analogous
quantum statistical mixture problem. The results are applied to the case of a
square barrier.Comment: 4 figure

### A nonlinear equation for ionic diffusion in a strong binary electrolyte

The problem of the one dimensional electro-diffusion of ions in a strong
binary electrolyte is considered. In such a system the solute dissociates
completely into two species of ions with unlike charges. The mathematical
description consists of a diffusion equation for each species augmented by
transport due to a self consistent electrostatic field determined by the
Poisson equation. This mathematical framework also describes other important
problems in physics such as electron and hole diffusion across semi-conductor
junctions and the diffusion of ions in plasmas. If concentrations do not vary
appreciably over distances of the order of the Debye length, the Poisson
equation can be replaced by the condition of local charge neutrality first
introduced by Planck. It can then be shown that both species diffuse at the
same rate with a common diffusivity that is intermediate between that of the
slow and fast species (ambipolar diffusion). Here we derive a more general
theory by exploiting the ratio of Debye length to a characteristic length scale
as a small asymptotic parameter. It is shown that the concentration of either
species may be described by a nonlinear integro-differential equation which
replaces the classical linear equation for ambipolar diffusion but reduces to
it in the appropriate limit. Through numerical integration of the full set of
equations it is shown that this nonlinear equation provides a better
approximation to the exact solution than the linear equation it replaces.Comment: 4 pages, 1 figur

### On the Long Time Behavior of the Quantum Fokker-Planck equation

We analyze the long time behavior of transport equations for a class of
dissipative quantum systems with Fokker-planck type scattering operator,
subject to confining potentials of harmonic oscillator type. We establish the
conditions under which there exists a thermal equilibrium state and prove
exponential decay towards it, using (classical) entropy-methods. Additionally,
we give precise dispersion estimates in the cases were no equilibrium state
exists

### Heavy-Fermion Instability in Double-Degenerate Plasmas

In this work we study the propagations of normal frequency modes for quantum
hydrodynamic (QHD) waves in the linear limit and introduce a new kind of
instability in a double-degenerate plasma. Three different regimes, namely,
low, intermediate and high magnetic field strengths are considered which span
the applicability of the work to a wide variety of environments. Distinct
behavior is observed for different regimes, for instance, in the
laboratory-scale field regime no frequency-mode instability occurs unlike those
of intermediate and high magnetic-field strength regimes. It is also found that
the instability of this kind is due to the heavy-fermions which appear below a
critical effective-mass parameter ($\mu_{cr}=\sqrt{3}$) and that the responses
of the two (lower and upper frequency) modes to fractional effective-mass
change in different effective-mass parameter ranges (below and above the
critical value) are quite opposite to each other. It is shown that, the
heavy-fermion instability due to extremely high magnetic field such as that
encountered for a neutron-star crust can lead to confinement of stable
propagations in both lower and upper frequency modes to the magnetic poles.
Current study can have important implications for linear wave dynamics in both
laboratory and astrophysical environments possessing high magnetic fields

### Dynamics of spin 1/2 quantum plasmas

The fully nonlinear governing equations for spin 1/2 quantum plasmas are
presented. Starting from the Pauli equation, the relevant plasma equations are
derived, and it is shown that nontrivial quantum spin couplings arise, enabling
studies of the combined collective and spin dynamics. The linear response of
the quantum plasma in an electron--ion system is obtained and analyzed.
Applications of the theory to solid state and astrophysical systems as well as
dusty plasmas are pointed out.Comment: 4 pages, 2 figures, to appear in Physical Review Letter

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