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

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

Action at a distance as a full-value solution of Maxwell equations: basis and application of separated potential's method

The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe the whole electromagnetic phenomena and the incompleteness of a set of solutions of Maxwell equations are discussed and mathematically proved. Reasons of the introduction of the so-called ``electrodynamics dualism concept" (simultaneous coexistence of instantaneous Newton long-range and Faraday-Maxwell short-range interactions) have been displayed. It is strictly shown that the new concept presents itself as the direct consequence of the complete set of Maxwell equations and makes it possible to consider classical electrodynamics as a self-consistent and complete theory, devoid of inward contradictions. In the framework of the new approach, all main concepts of classical electrodynamics are reconsidered. In particular, a limited class of motion is revealed when accelerated charges do not radiate electromagnetic field.Comment: ReVTeX file, 24pp. Small corrections which do not have influence results of the paper. Journal reference is adde

From Einstein's Theorem to Bell's Theorem: A History of Quantum Nonlocality

In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to popular opinion, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality-locality-completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality-locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full nonlocality of the quantum world for the first time.Comment: 18 pages. To be published in Contemporary Physics. (Minor changes; references and author info added

Corpuscular model of two-beam interference and double-slit experiments with single photons

We introduce an event-based corpuscular simulation model that reproduces the wave mechanical results of single-photon double slit and two-beam interference experiments and (of a one-to-one copy of an experimental realization) of a single-photon interference experiment with a Fresnel biprism. The simulation comprises models that capture the essential features of the apparatuses used in the experiment, including the single-photon detectors recording individual detector clicks. We demonstrate that incorporating in the detector model, simple and minimalistic processes mimicking the memory and threshold behavior of single-photon detectors is sufficient to produce multipath interference patterns. These multipath interference patterns are built up by individual particles taking one single path to the detector where they arrive one-by-one. The particles in our model are not corpuscular in the standard, classical physics sense in that they are information carriers that exchange information with the apparatuses of the experimental set-up. The interference pattern is the final, collective outcome of the information exchanges of many particles with these apparatuses. The interference patterns are produced without making reference to the solution of a wave equation and without introducing signalling or non-local interactions between the particles or between different detection points on the detector screen.Comment: Accepted for publication in J. Phys. Soc. Jpn