74 research outputs found
Action scales for quantum decoherence and their relation to structures in phase space
A characteristic action is defined whose magnitude determines some
properties of the expectation value of a general quantum displacement operator.
These properties are related to the capability of a given environmental
`monitoring' system to induce decoherence in quantum systems coupled to it. We
show that the scale for effective decoherence is given by . We relate this characteristic action with a complementary
quantity, , and analyse their connection with the main features of
the pattern of structures developed by the environmental state in different
phase space representations. The relevance of the -action scale is
illustrated using both a model quantum system solved numerically and a set of
model quantum systems for which analytical expressions for the time-averaged
expectation value of the displacement operator are obtained explicitly.Comment: 12 pages, 3 figure
Electron impact double ionization of helium from classical trajectory calculations
With a recently proposed quasiclassical ansatz [Geyer and Rost, J. Phys. B 35
(2002) 1479] it is possible to perform classical trajectory ionization
calculations on many electron targets. The autoionization of the target is
prevented by a M\o{}ller type backward--forward propagation scheme and allows
to consider all interactions between all particles without additional
stabilization. The application of the quasiclassical ansatz for helium targets
is explained and total and partially differential cross sections for electron
impact double ionization are calculated. In the high energy regime the
classical description fails to describe the dominant TS1 process, which leads
to big deviations, whereas for low energies the total cross section is
reproduced well. Differential cross sections calculated at 250 eV await their
experimental confirmation.Comment: LaTeX, 22 pages, 10 figures, submitted to J. Phys.
Husimi Transform of an Operator Product
It is shown that the series derived by Mizrahi, giving the Husimi transform
(or covariant symbol) of an operator product, is absolutely convergent for a
large class of operators. In particular, the generalized Liouville equation,
describing the time evolution of the Husimi function, is absolutely convergent
for a large class of Hamiltonians. By contrast, the series derived by
Groenewold, giving the Weyl transform of an operator product, is often only
asymptotic, or even undefined. The result is used to derive an alternative way
of expressing expectation values in terms of the Husimi function. The advantage
of this formula is that it applies in many of the cases where the anti-Husimi
transform (or contravariant symbol) is so highly singular that it fails to
exist as a tempered distribution.Comment: AMS-Latex, 13 page
A quasi classical approach to electron impact ionization
A quasi classical approximation to quantum mechanical scattering in the
Moeller formalism is developed. While keeping the numerical advantage of a
standard Classical--Trajectory--Monte--Carlo calculation, our approach is no
longer restricted to use stationary initial distributions. This allows one to
improve the results by using better suited initial phase space distributions
than the microcanonical one and to gain insight into the collision mechanism by
studying the influence of different initial distributions on the cross section.
A comprehensive account of results for single, double and triple differential
cross sections for atomic hydrogen will be given, in comparison with experiment
and other theories.Comment: 21 pages, 10 figures, submitted to J Phys
Features of Time-independent Wigner Functions
The Wigner phase-space distribution function provides the basis for Moyal's
deformation quantization alternative to the more conventional Hilbert space and
path integral quantizations. General features of time-independent Wigner
functions are explored here, including the functional ("star") eigenvalue
equations they satisfy; their projective orthogonality spectral properties;
their Darboux ("supersymmetric") isospectral potential recursions; and their
canonical transformations. These features are illustrated explicitly through
simple solvable potentials: the harmonic oscillator, the linear potential, the
Poeschl-Teller potential, and the Liouville potential.Comment: 18 pages, plain LaTex, References supplemente
Product rule for gauge invariant Weyl symbols and its application to the semiclassical description of guiding center motion
We derive a product rule for gauge invariant Weyl symbols which provides a
generalization of the well-known Moyal formula to the case of non-vanishing
electromagnetic fields. Applying our result to the guiding center problem we
expand the guiding center Hamiltonian into an asymptotic power series with
respect to both Planck's constant and an adiabaticity parameter already
present in the classical theory. This expansion is used to determine the
influence of quantum mechanical effects on guiding center motion.Comment: 24 pages, RevTeX, no figures; shortened version will be published in
J.Phys.
The Pauli Equation for Probability Distributions
The "marginal" distributions for measurable coordinate and spin projection is
introduced. Then, the analog of the Pauli equation for spin-1/2 particle is
obtained for such probability distributions instead of the usual wave
functions. That allows a classical-like approach to quantum mechanics. Some
illuminating examples are presented.Comment: 14 pages, ReVTe
Magnetic fields in noncommutative quantum mechanics
We discuss various descriptions of a quantum particle on noncommutative space
in a (possibly non-constant) magnetic field. We have tried to present the basic
facts in a unified and synthetic manner, and to clarify the relationship
between various approaches and results that are scattered in the literature.Comment: Dedicated to the memory of Julius Wess. Work presented by F. Gieres
at the conference `Non-commutative Geometry and Physics' (Orsay, April 2007
A finite model of two-dimensional ideal hydrodynamics
A finite-dimensional su() Lie algebra equation is discussed that in the
infinite limit (giving the area preserving diffeomorphism group) tends to
the two-dimensional, inviscid vorticity equation on the torus. The equation is
numerically integrated, for various values of , and the time evolution of an
(interpolated) stream function is compared with that obtained from a simple
mode truncation of the continuum equation. The time averaged vorticity moments
and correlation functions are compared with canonical ensemble averages.Comment: (25 p., 7 figures, not included. MUTP/92/1
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