82 research outputs found
Caldirola-Kanai Oscillator in Classical Formulation of Quantum Mechanics
The quadrature distribution for the quantum damped oscillator is introduced
in the framework of the formulation of quantum mechanics based on the
tomography scheme. The probability distribution for the coherent and Fock
states of the damped oscillator is expressed explicitly in terms of Gaussian
and Hermite polynomials, correspondingly.Comment: LaTeX, 5 pages, 1 Postscript figure, Contribution to the VIII
International Conference on Symmetry Methods in Physics, Dubna 1997, to be
published in the Proceedings of the Conferenc
Scaling Separability Criterion: Application To Gaussian States
We introduce examples of three- and four-mode entangled Gaussian mixed states
that are not detected by the scaling and Peres-Horodecki separability criteria.
The presented modification of the scaling criterion resolves this problem. Also
it is shown that the new criterion reproduces the main features of the scaling
pictures for different cases of entangled states, while the previous versions
lead to completely different outcomes. This property of the presented scheme is
evidence of its higher generality.Comment: 7 pages, 4 figure
Time-Dependent Invariants and Green's Functions in the Probability Representation of Quantum Mechanics
In the probability representation of quantum mechanics, quantum states are
represented by a classical probability distribution, the marginal distribution
function (MDF), whose time dependence is governed by a classical evolution
equation. We find and explicitly solve, for a wide class of Hamiltonians, new
equations for the Green's function of such an equation, the so-called classical
propagator. We elucidate the connection of the classical propagator to the
quantum propagator for the density matrix and to the Green's function of the
Schr\"odinger equation. Within the new description of quantum mechanics we give
a definition of coherence solely in terms of properties of the MDF and we test
the new definition recovering well known results. As an application, the forced
parametric oscillator is considered . Its classical and quantum propagator are
found, together with the MDF for coherent and Fock states.Comment: 29 pages, RevTex, 6 eps-figures, to appear on Phys. Rev.
On calculating the mean values of quantum observables in the optical tomography representation
Given a density operator the optical tomography map defines a
one-parameter set of probability distributions on the real line allowing to reconstruct . We
introduce a dual map from the special class of quantum observables
to a special class of generalized functions such that the
mean value is given by the formula
. The class
includes all the symmetrized polynomials of canonical variables
and .Comment: 8 page
Dynamics of entropy and nonclassical properties of the state of a -type three-level atom interacting with a single-mode cavity field with intensity-dependent coupling in a Kerr medium
In this paper, we study the interaction between a three-level atom and a
quantized single-mode field with intensity-dependent coupling in a Kerr medium.
The three-level atom is considered to be in a -type configuration.
Under particular initial conditions, which may be prepared for the atom and
the field, the dynamical state vector of the entire system will be explicitly
obtained, for arbitrary nonlinearity function associated to any physical
system.
Then, after evaluating the variation of the field entropy against time, we
will investigate the quantum statistics as well as some of the nonclassical
properties of the introduced state. During our calculations we investigate the
effects of intensity-dependent coupling, Kerr medium and detuning parameters on
the depth and domain of the nonclassicality features of the atom-field state
vector. Finally, we compare our obtained results with those of -type
three-level atoms.Comment: 18 pages, 7 Figure
Energy-Sensitive and "Classical-like" Distances Between Quantum States
We introduce the concept of the ``polarized'' distance, which distinguishes
the orthogonal states with different energies. We also give new inequalities
for the known Hilbert-Schmidt distance between neighbouring states and express
this distance in terms of the quasiprobability distributions and the normally
ordered moments. Besides, we discuss the distance problem in the framework of
the recently proposed ``classical-like'' formulation of quantum mechanics,
based on the symplectic tomography scheme. The examples of the Fock, coherent,
``Schroedinger cats,'' squeezed, phase, and thermal states are considered.Comment: 23 pages, LaTex, 2 eps figures, to appear in Physica Script
Tomographic Probability Representation for States of Charge moving in Varying Field
The coherent and Fock states of a charge moving in varying homogeneous
magnetic field are studied in the tomographic probability representation of
quantum mechanics. The states are expressed in terms of quantum tomograms. The
coherent states tomograms are shown to be described by normal distributions
with varying dispersions and means. The Fock state tomograms are given in the
form of probability distributions described by multivariable Hermite
polynomials with time-dependent arguments.Comment: 12 pages, submitted to "Optics and Spectroscopy
Cosmological waveguides for gravitational waves
We study the linearized equations describing the propagation of gravitational
waves through dust. In the leading order of the WKB approximation, dust behaves
as a non-dispersive, non-dissipative medium. Taking advantage of these
features, we explore the possibility that a gravitational wave from a distant
source gets trapped by the gravitational field of a long filament of galaxies
of the kind seen in the large scale structure of the Universe. Such a
waveguiding effect may lead to a huge magnification of the radiation from
distant sources, thus lowering the sensitivity required for a successful
detection of gravitational waves by detectors like VIRGO, LIGO and LISA.Comment: 19 pages, compressed Latex fil
Quantum Characterization of a Werner-like Mixture
We introduce a Werner-like mixture [R. F. Werner, Phys. Rev. A {\bf 40}, 4277
(1989)] by considering two correlated but different degrees of freedom, one
with discrete variables and the other with continuous variables. We evaluate
the mixedness of this state, and its degree of entanglement establishing its
usefulness for quantum information processing like quantum teleportation. Then,
we provide its tomographic characterization. Finally, we show how such a
mixture can be generated and measured in a trapped system like one electron in
a Penning trap.Comment: 8 pages ReVTeX, 8 eps figure
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