The time-reversal test for stochastic quantum dynamics

The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultra-cold atomic Bose-Einstein condensates (BEC) to condensed matter, biology, and even astrophysics. Here we demonstrate a conceptually simple method of determining the regime of validity of stochastic simulations of unitary quantum dynamics by employing a time-reversal test. We apply this test to a simulation of the evolution of a quantum anharmonic oscillator with up to $6.022\times10^{23}$ (Avogadro's number) of particles. This system is realisable as a Bose-Einstein condensate in an optical lattice, for which the time-reversal procedure could be implemented experimentally.Comment: revtex4, two figures, four page

Phenomenology of Noncommutative Field Theories

Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and suggest a possible means of evading them: noncommutativity may be restricted to extra, compactified spatial dimensions. Such theories have a number of interesting features, including Abelian gauge fields whose Kaluza-Klein excitations have self couplings. We consider six-dimensional QED in a noncommutative bulk, and discuss the collider signatures of the model.Comment: 7 pages RevTeX, 4 eps figures, Invited plenary talk, IX Mexican Workshop on Particles and Fields, November 17-22, 2003, Universidad de Colima, Mexic

Quantum deformation of the Dirac bracket

The quantum deformation of the Poisson bracket is the Moyal bracket. We construct quantum deformation of the Dirac bracket for systems which admit global symplectic basis for constraint functions. Equivalently, it can be considered as an extension of the Moyal bracket to second-class constraints systems and to gauge-invariant systems which become second class when gauge-fixing conditions are imposed.Comment: 18 pages, REVTe

Action scales for quantum decoherence and their relation to structures in phase space

A characteristic action $\Delta S$ is defined whose magnitude determines some properties of the expectation value of a general quantum displacement operator. These properties are related to the capability of a given environmental `monitoring' system to induce decoherence in quantum systems coupled to it. We show that the scale for effective decoherence is given by $\Delta S\approx\hbar$. We relate this characteristic action with a complementary quantity, $\Delta Z$, and analyse their connection with the main features of the pattern of structures developed by the environmental state in different phase space representations. The relevance of the $\Delta S$-action scale is illustrated using both a model quantum system solved numerically and a set of model quantum systems for which analytical expressions for the time-averaged expectation value of the displacement operator are obtained explicitly.Comment: 12 pages, 3 figure

Wigner Trajectory Characteristics in Phase Space and Field Theory

Exact characteristic trajectories are specified for the time-propagating Wigner phase-space distribution function. They are especially simple---indeed, classical---for the quantized simple harmonic oscillator, which serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase space. Applications to duality transformations in field theory are discussed.Comment: 9 pages, LaTex2

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

Landau damping of partially incoherent Langmuir waves

It is shown that partial incoherence, in the form of stochastic phase noise, of a Langmuir wave in an unmagnetized plasma gives rise to a Landau-type damping. Starting from the Zakharov equations, which describe the nonlinear interaction between Langmuir and ion-acoustic waves, a kinetic equation is derived for the plasmons by introducing the Wigner-Moyal transform of the complex Langmuir wave field. This equation is then used to analyze the stability properties of small perturbations on a stationary solution consisting of a constant amplitude wave with stochastic phase noise. The concomitant dispersion relation exhibits the phenomenon of Landau-like damping. However, this damping differs from the classical Landau damping in which a Langmuir wave, interacting with the plasma electrons, loses energy. In the present process, the damping is non-dissipative and is caused by the resonant interaction between an instantaneously-produced disturbance, due to the parametric interactions, and a partially incoherent Langmuir wave, which can be considered as a quasi-particle composed of an ensemble of partially incoherent plasmons.Comment: 12 page

Remarks on the Formulation of Quantum Mechanics on Noncommutative Phase Spaces

We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry.Comment: 25 pages, JHEP3 style; minor changes; Published in JHE

Relational time in generally covariant quantum systems: four models

We analize the relational quantum evolution of generally covariant systems in terms of Rovelli's evolving constants of motion and the generalized Heisenberg picture. In order to have a well defined evolution, and a consistent quantum theory, evolving constants must be self-adjoint operators. We show that this condition imposes strong restrictions to the choices of the clock variables. We analize four cases. The first one is non- relativistic quantum mechanics in parametrized form. We show that, for the free particle case, the standard choice of time is the only one leading to self-adjoint evolving constants. Secondly, we study the relativistic case. We show that the resulting quantum theory is the free particle representation of the Klein Gordon equation in which the position is a perfectly well defined quantum observable. The admissible choices of clock variables are the ones leading to space-like simultaneity surfaces. In order to mimic the structure of General Relativity we study the SL(2R) model with two Hamiltonian constraints. The evolving constants depend in this case on three independent variables. We show that it is possible to find clock variables and inner products leading to a consistent quantum theory. Finally, we discuss the quantization of a constrained model having a compact constraint surface. All the models considered may be consistently quantized, although some of them do not admit any time choice such that the equal time surfaces are transversal to the orbits.Comment: 18 pages, revtex fil