69 research outputs found
Phase space localization of antisymmetric functions
Upper and lower bounds are written down for the minimum information entropy
in phase space of an antisymmetric wave function in any number of dimensions.
Similar bounds are given when the wave function is restricted to belong to any
of the proper subspaces of the Fourier transform operator.Comment: 5 pages, REVTEX, no figure
Structure of nonlinear gauge transformations
Nonlinear Doebner-Goldin [Phys. Rev. A 54, 3764 (1996)] gauge transformations
(NGT) defined in terms of a wave function do not form a group. To get
a group property one has to consider transformations that act differently on
different branches of the complex argument function and the knowledge of the
value of is not sufficient for a well defined NGT. NGT that are well
defined in terms of form a semigroup parametrized by a real number
and a nonzero which is either an integer or . An extension of NGT to projectors and general density matrices
leads to NGT with complex . Both linearity of evolution and Hermiticity
of density matrices are gauge dependent properties.Comment: Final version, to be published in Phys.Rev.A (Rapid Communication),
April 199
Regularization as quantization in reducible representations of CCR
A covariant quantization scheme employing reducible representations of
canonical commutation relations with positive-definite metric and Hermitian
four-potentials is tested on the example of quantum electrodynamic fields
produced by a classical current. The scheme implies a modified but very
physically looking Hamiltonian. We solve Heisenberg equations of motion and
compute photon statistics. Poisson statistics naturally occurs and no infrared
divergence is found even for pointlike sources. Classical fields produced by
classical sources can be obtained if one computes coherent-state averages of
Heisenberg-picture operators. It is shown that the new form of representation
automatically smears out pointlike currents. We discuss in detail Poincar\'e
covariance of the theory and the role of Bogoliubov transformations for the
issue of gauge invariance. The representation we employ is parametrized by a
number that is related to R\'enyi's . It is shown that the ``Shannon
limit" plays here a role of correspondence principle with the
standard regularized formalism.Comment: minor extensions, version submitted for publicatio
Conservation laws and symmetry transformations of the electromagnetic field with sources
Quantum Matter and Optic
Entropic trade-off relations for quantum operations
Spectral properties of an arbitrary matrix can be characterized by the
entropy of its rescaled singular values. Any quantum operation can be described
by the associated dynamical matrix or by the corresponding superoperator. The
entropy of the dynamical matrix describes the degree of decoherence introduced
by the map, while the entropy of the superoperator characterizes the a priori
knowledge of the receiver of the outcome of a quantum channel Phi. We prove
that for any map acting on a N--dimensional quantum system the sum of both
entropies is not smaller than ln N. For any bistochastic map this lower bound
reads 2 ln N. We investigate also the corresponding R\'enyi entropies,
providing an upper bound for their sum and analyze entanglement of the
bi-partite quantum state associated with the channel.Comment: 10 pages, 4 figure
Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles
The EPRB experiment with massive partcles can be formulated if one defines
spin in a relativistic way. Two versions are discussed: The one using the spin
operator defined via the relativistic center-of-mass operator, and the one
using the Pauli-Lubanski vector. Both are shown to lead to the SAME prediction
for the EPRB experiment: The degree of violation of the Bell inequality
DECREASES with growing velocity of the EPR pair of spin-1/2 particles. The
phenomenon can be physically understood as a combined effect of the Lorentz
contraction and the Moller shift of the relativistic center of mass. The effect
is therefore stronger than standard relativistic phenomena such as the Lorentz
contraction or time dilatation. The fact that the Bell inequality is in general
less violated than in the nonrelativistic case will have to be taken into
account in tests for eavesdropping if massive particles will be used for a key
transfer.Comment: Figures added as appeared in PRA, two typos corrected (one important
in the formula for eigenvector in Sec. IV); link to the unpublished 1984
paper containing the results (without typos!) of Sec. IV is adde
Nonperturbative calculation of Born-Infeld effects on the Schroedinger spectrum of the hydrogen atom
We present the first nonperturbative numerical calculations of the
nonrelativistic hydrogen spectrum as predicted by first-quantized
electrodynamics with nonlinear Maxwell-Born-Infeld field equations. We also
show rigorous upper and lower bounds on the ground state.
When judged against empirical data our results significantly restrict the
range of viable values of the new electromagnetic constant which is introduced
by the Born-Infeld theory.
We assess Born's own proposal for the value of his constant.Comment: 4p., 2 figs, 1 table; submitted for publicatio
Information dynamics: Temporal behavior of uncertainty measures
We carry out a systematic study of uncertainty measures that are generic to
dynamical processes of varied origins, provided they induce suitable continuous
probability distributions. The major technical tool are the information theory
methods and inequalities satisfied by Fisher and Shannon information measures.
We focus on a compatibility of these inequalities with the prescribed
(deterministic, random or quantum) temporal behavior of pertinent probability
densities.Comment: Incorporates cond-mat/0604538, title, abstract changed, text
modified, to appear in Cent. Eur. J. Phy
Complete positivity of nonlinear evolution: A case study
Simple Hartree-type equations lead to dynamics of a subsystem that is not
completely positive in the sense accepted in mathematical literature. In the
linear case this would imply that negative probabilities have to appear for
some system that contains the subsystem in question. In the nonlinear case this
does not happen because the mathematical definition is physically unfitting as
shown on a concrete example.Comment: extended version, 3 appendices added (on mixed states, projection
postulate, nonlocality), to be published in Phys. Rev.
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