Madelung Fluid Model for The Most Likely Wave Function of a Single Free Particle in Two Dimensional Space with a Given Average Energy

We consider spatially two dimensional Madelung fluid whose irrotational motion reduces into the Schr\"odinger equation for a single free particle. In this respect, we regard the former as a direct generalization of the latter, allowing a rotational quantum flow. We then ask for the most likely wave function possessing a given average energy by maximizing the Shannon information entropy over the quantum probability density. We show that there exists a class of solutions in which the wave function is self-trapped, rotationally symmetric, spatially localized with finite support, and spinning around its center, yet stationary. The stationarity comes from the balance between the attractive quantum force field of a trapping quantum potential generated by quantum probability density and the repulsive centrifugal force of a rotating velocity vector field. We further show that there is a limiting case where the wave function is non-spinning and yet still stationary. This special state turns out to be the lowest stationary state of the ordinary Schr\"odinger equation for a particle in a cylindrical tube classical potential.Comment: 19 page

A dynamical time operator in Dirac's relativistic quantum mechanics

A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in interference in time, in Zitterbewegung like effects in spintronics, grapheme and superconducting systems and in cosmology is noted

Might EPR particles communicate through a wormhole?

We consider the two-particle wave function of an Einstein-Podolsky-Rosen system, given by a two dimensional relativistic scalar field model. The Bohm-de Broglie interpretation is applied and the quantum potential is viewed as modifying the Minkowski geometry. In this way an effective metric, which is analogous to a black hole metric in some limited region, is obtained in one case and a particular metric with singularities appears in the other case, opening the possibility, following Holland, of interpreting the EPR correlations as being originated by an effective wormhole geometry, through which the physical signals can propagate.Comment: Corrected version, to appears in EP

On the influence of resonance photon scattering on atom interference

Here, the influence of resonance photon-atom scattering on the atom interference pattern at the exit of a three-grating Mach-Zehnder interferometer is studied. It is assumed that the scattering process does not destroy the atomic wave function describing the state of the atom before the scattering process takes place, but only induces a certain shift and change of its phase. We find that the visibility of the interference strongly depends on the statistical distribution of transferred momenta to the atom during the photon-atom scattering event. This also explains the experimentally observed (Chapman et al 1995 Phys. Rev. Lett. 75 2783) dependence of the visibility on the ratio d_p/\lambda_i = y'_{12} (2\pi/kd\lambda_i), where y'_{12} is distance between the place where the scattering event occurs and the first grating, k is the wave number of the atomic center-of-mass motion, $d$ is the grating constant and \lambda_i is the photon wavelength. Furthermore, it is remarkable that photon-atom scattering events happen experimentally within the Fresnel region, i.e. the near field region, associated with the first grating, which should be taken into account when drawing conclusions about the relevance of "which-way" information for the interference visibility.Comment: 9 pages, 1 figur

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

Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation

The Klein-Gordon equation is interpreted in the de Broglie-Bohm manner as a single-particle relativistic quantum mechanical equation that defines unique time-like particle trajectories. The particle trajectories are determined by the conserved flow of the intrinsic energy density which can be derived from the specification of the Klein-Gordon energy-momentum tensor in an Einstein-Riemann space. The approach is illustrated by application to the simple single-particle phenomena associated with square potentials.Comment: 14 pages, 11 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

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

Quantum vortices and trajectories in particle diffraction

We investigate the phenomenon of the diffraction of charged particles by thin material targets using the method of the de Broglie-Bohm quantum trajectories. The particle wave function can be modeled as a sum of two terms $\psi=\psi_{ingoing}+\psi_{outgoing}$. A thin separator exists between the domains of prevalence of the ingoing and outgoing wavefunction terms. The structure of the quantum-mechanical currents in the neighborhood of the separator implies the formation of an array of \emph{quantum vortices}. The flow structure around each vortex displays a characteristic pattern called `nodal point - X point complex'. The X point gives rise to stable and unstable manifolds. We find the scaling laws characterizing a nodal point-X point complex by a local perturbation theory around the nodal point. We then analyze the dynamical role of vortices in the emergence of the diffraction pattern. In particular, we demonstrate the abrupt deflections, along the direction of the unstable manifold, of the quantum trajectories approaching an X-point along its stable manifold. Theoretical results are compared to numerical simulations of quantum trajectories. We finally calculate the {\it times of flight} of particles following quantum trajectories from the source to detectors placed at various scattering angles $\theta$, and thereby propose an experimental test of the de Broglie - Bohm formalism.Comment: 17 pages, 7 figures, accepted by IJB

Coherence loss and revivals in atomic interferometry: A quantum-recoil analysis

The coherence effects induced by external photons coupled to matter waves inside a Mach-Zehnder three-grating interferometer are analyzed. Alternatively to atom-photon entanglement scenarios, the model considered here only relies on the atomic wave function and the momentum shift induced in it by the photon scattering events. A functional dependence is thus found between the observables, namely the fringe visibility and the phase shift, and the transversal momentum transfer distribution. A good quantitative agreement is found when comparing the results obtained from our model with the experimental data.Comment: 18 pages, 4 figure