14 research outputs found
A dressing of zero-range potentials and electron-molecule scattering problem at Ramsauer-Townsend minimum
A dressing technique is used to improve zero range potential (ZRP) model. We
consider a Darboux transformation starting with a ZRP, the result of the
"dressing" gives a potential with non-zero range that depends on a seed
solution parameters. Concepts of the partial waves and partial phases for
non-spherical potential are used in order to perform Darboux transformation.
The problem of scattering on the regular X and YX
structures is studied. The results of the low-energy electron-molecule
scattering on the dressed ZRPs are illustrated by model calculation for the
configuration and parameters of the silane () molecule.
\center{Key words: low-energy scattering, multiple scattering,
Ramsauer-Townsend minimum, silane, zero range potential.Comment: 13 pages, 1 figur
Piecewise continuous partition function method in the theory of wave perturbations of inhomogeneous gas
The problem of wave disturbance propagation in rarefied gas in gravity field
is explored. The system of hydrodynamic-type equations for a stratified gas in
gravity field is derived from BGK equation by method of piecewise continuous
partition function. The obtained system of the equations generalizes the
Navier-Stokes at arbitrary density (Knudsen numbers). The verification of the
model is made for a limiting case of a homogeneous medium. Results are in the
good agreement with experiment and former theories at arbitrary Knudsen
numbers.Comment: 12 pages, 5 figure
Piecewise continuous distribution function method: Fluid equations and wave disturbances at stratified gas
Wave disturbances of a stratified gas are studied. The description is built
on a basis of the Bhatnagar -- Gross -- Krook (BGK) kinetic equation which is
reduced down the level of fluid mechanics. The double momenta set is introduced
inside a scheme of iterations of the equations operators, dividing the velocity
space along and opposite gravity field direction. At both half-spaces the local
equilibrium is supposed. As the result, the momenta system is derived. It
reproduce Navier-Stokes and Barnett equations at the first and second order in
high collision frequencies. The homogeneous background limit gives the known
results obtained by direct kinetics applications by Loyalka and Cheng as the
recent higher momentum fluid mechanics results of Chen, Rao and Spiegel. The
ground state declines from exponential at the Knudsen regime. The WKB solutions
for ultrasound in exponentially stratified medium are constructed in explicit
form, evaluated and plotted.Comment: 20 pages, 7 figures, 14 ISNA conference, 199
General estimate of the first eigenvalue on manifolds
Ten sharp lower estimates of the first non-trivial eigenvalue of Laplacian on
compact Riemannian manifolds are reviewed and compared. An improved variational
formula, a general common estimate, and a new sharp one are added. The best
lower estimates are now updated. The new estimates provide a global picture of
what one can expect by our approach.Comment: 19 page
Von Neumann equations with time-dependent Hamiltonians and supersymmetric quantum mechanics
Starting with a time-independent Hamiltonian and an appropriately chosen
solution of the von Neumann equation we construct
its binary-Darboux partner and an exact scattering solution of
where is time-dependent and not
isospectral to . The method is analogous to supersymmetric quantum mechanics
but is based on a different version of a Darboux transformation. We illustrate
the technique by the example where corresponds to a 1-D harmonic
oscillator. The resulting represents a scattering of a soliton-like
pulse on a three-level system.Comment: revtex, 3 eps file
Generalized Zero Range Potentials and Multi-Channel Electron-Molecule Scattering
A multi-channel scattering problem is studied from a point of view of
integral equations system. The system appears while natural one-particle wave
function equation of the electron under action of a potential with
non-intersecting ranges is considered.
Spherical functions basis expansion of the potentials introduces partial
amplitudes and corresponding radial functions. The approach is generalized to
multi-channel case by a matrix formulation in which a state vector component is
associated with a scattering channel.
The zero-range potentials naturally enter the scheme when the class of
operators of multiplication is widen to distributions. %Analog of multipolar
expansion is treated. Spin variables, o Oscillations and rotations are
incorporated into the scheme.Comment: 11 pages, 1 figure, CEPAS2 con
Darboux Transformations for a Lax Integrable System in -Dimensions
A -dimensional Lax integrable system is proposed by a set of specific
spectral problems. It contains Takasaki equations, the self-dual Yang-Mills
equations and its integrable hierarchy as examples. An explicit formulation of
Darboux transformations is established for this Lax integrable system. The
Vandermonde and generalized Cauchy determinant formulas lead to a description
for deriving explicit solutions and thus some rational and analytic solutions
are obtained.Comment: Latex, 14 pages, to be published in Lett. Math. Phy
Quantum feedback with weak measurements
The problem of feedback control of quantum systems by means of weak
measurements is investigated in detail. When weak measurements are made on a
set of identical quantum systems, the single-system density matrix can be
determined to a high degree of accuracy while affecting each system only
slightly. If this information is fed back into the systems by coherent
operations, the single-system density matrix can be made to undergo an
arbitrary nonlinear dynamics, including for example a dynamics governed by a
nonlinear Schr\"odinger equation. We investigate the implications of such
nonlinear quantum dynamics for various problems in quantum control and quantum
information theory, including quantum computation. The nonlinear dynamics
induced by weak quantum feedback could be used to create a novel form of
quantum chaos in which the time evolution of the single-system wave function
depends sensitively on initial conditions.Comment: 11 pages, TeX, replaced to incorporate suggestions of Asher Pere