66 research outputs found
Evolution of a model quantum system under time periodic forcing: conditions for complete ionization
We analyze the time evolution of a one-dimensional quantum system with an
attractive delta function potential whose strength is subjected to a time
periodic (zero mean) parametric variation . We show that for generic
, which includes the sum of any finite number of harmonics, the
system, started in a bound state will get fully ionized as . This
is irrespective of the magnitude or frequency (resonant or not) of .
There are however exceptional, very non-generic , that do not lead to
full ionization, which include rather simple explicit periodic functions. For
these the system evolves to a nontrivial localized stationary state
which is related to eigenfunctions of the Floquet operator
Kinetics of a Model Weakly Ionized Plasma in the Presence of Multiple Equilibria
We study, globaly in time, the velocity distribution of a spatially
homogeneous system that models a system of electrons in a weakly ionized
plasma, subjected to a constant external electric field . The density
satisfies a Boltzmann type kinetic equation containing a full nonlinear
electron-electron collision term as well as linear terms representing
collisions with reservoir particles having a specified Maxwellian distribution.
We show that when the constant in front of the nonlinear collision kernel,
thought of as a scaling parameter, is sufficiently strong, then the
distance between and a certain time dependent Maxwellian stays small
uniformly in . Moreover, the mean and variance of this time dependent
Maxwellian satisfy a coupled set of nonlinear ODE's that constitute the
``hydrodynamical'' equations for this kinetic system. This remain true even
when these ODE's have non-unique equilibria, thus proving the existence of
multiple stabe stationary solutions for the full kinetic model. Our approach
relies on scale independent estimates for the kinetic equation, and entropy
production estimates. The novel aspects of this approach may be useful in other
problems concerning the relation between the kinetic and hydrodynamic scales
globably in time.Comment: 30 pages, in TeX, to appear in Archive for Rational Mechanics and
Analysis: author's email addresses: [email protected],
[email protected], [email protected],
[email protected], [email protected]
Space Charge Limited 2-d Electron Flow between Two Flat Electrodes in a Strong Magnetic Field
An approximate analytic solution is constructed for the 2-d space charge
limited emission by a cathode surrounded by non emitting conducting ledges of
width Lambda. An essentially exact solution (via conformal mapping) of the
electrostatic problem in vacuum is matched to the solution of a linearized
problem in the space charge region whose boundaries are sharp due to the
presence of a strong magnetic field. The current density growth in a narrow
interval near the edges of the cathode depends strongly on Lambda. We obtain an
empirical formula for the total current as a function of Lambda which extends
to more general cathode geometries.Comment: 4 pages, LaTex, e-mail addresses: [email protected],
[email protected]
Transport across nanogaps using semiclassically consistent boundary conditions
Charge particle transport across nanogaps is studied theoretically within the
Schrodinger-Poisson mean field framework and the existence of limiting current
investigated. It is shown that the choice of a first order WKB wavefunction as
the transmitted wave leads to self consistent boundary conditions and gives
results that are significantly different in the non-classical regime from those
obtained using a plane transmitted wave. At zero injection energies, the
quantum limiting current density, J_c, is found to obey the local scaling law
J_c ~ (V_g)^alpha/(D)^{5-2alpha} with the gap separation D and voltage V_g. The
exponent alpha > 1.1 with alpha --> 3/2 in the classical regime of small de
Broglie wavelengths. These results are consistent with recent experiments using
nanogaps most of which are found to be in a parameter regime where classical
space charge limited scaling holds away from the emission dominated regime.Comment: 4 pages, 4 ps figure
Decay of a Bound State under a Time-Periodic Perturbation: a Toy Case
We study the time evolution of a three dimensional quantum particle,
initially in a bound state, under the action of a time-periodic zero range
interaction with ``strength'' (\alpha(t)). Under very weak generic conditions
on the Fourier coefficients of (\alpha(t)), we prove complete ionization as (t
\to \infty). We prove also that, under the same conditions, all the states of
the system are scattering states.Comment: LaTeX2e, 15 page
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