450 research outputs found
Misleading signposts along the de Broglie-Bohm road to quantum mechanics
Eighty years after de Broglie's, and a little more than half a century after
Bohm's seminal papers, the de Broglie--Bohm theory (a.k.a. Bohmian mechanics),
which is presumably the simplest theory which explains the orthodox quantum
mechanics formalism, has reached an exemplary state of conceptual clarity and
mathematical integrity. No other theory of quantum mechanics comes even close.
Yet anyone curious enough to walk this road to quantum mechanics is soon being
confused by many misleading signposts that have been put up, and not just by
its detractors, but unfortunately enough also by some of its proponents.
This paper outlines a road map to help navigate ones way.Comment: Dedicated to Jeffrey Bub on occasion of his 65th birthday. Accepted
for publication in Foundations of Physics. A "slip of pen" in the
bibliography has been corrected -- thanks go to Oliver Passon for catching
it
Quantum Mechanical Properties of Bessel Beams
Bessel beams are studied within the general framework of quantum optics. The
two modes of the electromagnetic field are quantized and the basic dynamical
operators are identified. The algebra of these operators is analyzed in detail;
it is shown that the operators that are usually associated to linear momentum,
orbital angular momentum and spin do not satisfy the algebra of the translation
and rotation group. In particular, what seems to be the spin is more similar to
the helicity. Some physical consequences of these results are examined.Comment: 17 pages, no figures. New versio
Resonance NLS Solitons as Black Holes in Madelung Fluid
A new resonance version of NLS equation is found and embedded to the
reaction-diffusion system, equivalent to the anti-de Sitter valued Heisenberg
model, realizing a particular gauge fixing condition of the Jackiw-Teitelboim
gravity. The space-time points where dispersion change the sign correspond to
the event horizon, and the soliton solutions to the AdS black holes. The
soliton with velocity bounded above describes evolution on the hyperboloid with
nontrivial winding number and create under collisions the resonance states with
a specific life time.Comment: Plain Tex, 12 pages, 6 figure
Rotational Effects of Twisted Light on Atoms Beyond the Paraxial Approximation
The transition probability for the emission of a Bessel photon by an atomic
system is calculated within first order perturbation theory. We derive a closed
expression for the electromagnetic potentials beyond the paraxial approximation
that permits a systematic multipole approximation . The matrix elements between
center of mass and internal states are evaluated for some specially relevant
cases. This permits to clarify the feasibility of observing the rotational
effects of twisted light on atoms predicted by the calculations. It is shown
that the probability that the internal state of an atom acquires orbital
angular momentum from light is, in general, maximum for an atom located at the
axis of a Bessel mode. For a Gaussian packet, the relevant parameter is the
ratio of the spread of the atomic center of mass wave packet to the transversal
wavelength of the photon.Comment: 10 pages, no 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.
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
The wave nature of biomolecules and fluorofullerenes
We demonstrate quantum interference for tetraphenylporphyrin, the first
biomolecule exhibiting wave nature, and for the fluorofullerene C60F48 using a
near-field Talbot-Lau interferometer. For the porphyrins, which are
distinguished by their low symmetry and their abundant occurence in organic
systems, we find the theoretically expected maximal interference contrast and
its expected dependence on the de Broglie wavelength. For C60F48 the observed
fringe visibility is below the expected value, but the high contrast still
provides good evidence for the quantum character of the observed fringe
pattern. The fluorofullerenes therefore set the new mark in complexity and mass
(1632 amu) for de Broglie wave experiments, exceeding the previous mass record
by a factor of two.Comment: 5 pages, 4 figure
Solitons of the Resonant Nonlinear Schrodinger Equation with Nontrivial Boundary Conditions and Hirota Bilinear Method
Physically relevant soliton solutions of the resonant nonlinear Schrodinger
(RNLS) equation with nontrivial boundary conditions, recently proposed for
description of uniaxial waves in a cold collisionless plasma, are considered in
the Hirota bilinear approach. By the Madelung representation, the model is
transformed to the reaction-diffusion analog of the NLS equation for which the
bilinear representation, soliton solutions and their mutual interactions are
studied.Comment: 15 pages, 1 figure, talk presented in Workshop `Nonlinear Physics IV:
Theory and Experiment`, 22-30 June 2006, Gallipoli, Ital
Dirac equation from the Hamiltonian and the case with a gravitational field
Starting from an interpretation of the classical-quantum correspondence, we
derive the Dirac equation by factorizing the algebraic relation satisfied by
the classical Hamiltonian, before applying the correspondence. This derivation
applies in the same form to a free particle, to one in an electromagnetic
field, and to one subjected to geodesic motion in a static metric, and leads to
the same, usual form of the Dirac equation--in special coordinates. To use the
equation in the static-gravitational case, we need to rewrite it in more
general coordinates. This can be done only if the usual, spinor transformation
of the wave function is replaced by the 4-vector transformation. We show that
the latter also makes the flat-space-time Dirac equation Lorentz-covariant,
although the Dirac matrices are not invariant. Because the equation itself is
left unchanged in the flat case, the 4-vector transformation does not alter the
main physical consequences of that equation in that case. However, the equation
derived in the static-gravitational case is not equivalent to the standard
(Fock-Weyl) gravitational extension of the Dirac equation.Comment: 27 pages, standard LaTeX. v2: minor style changes, accepted for
publication in Found. Phys. Letter
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