Ballistic transport: A view from the quantum theory of motion

Ballistic transport of electrons through a quantum wire with a constriction is studied in terms of Bohm's interpretation of quantum mechanics, in which the concept of a particle orbit is permitted. The classical bouncing ball trajectories, which justify the name ``ballistic transport'', are established in the large wave number limit. The formation and the vital role of quantum vortices is investigated.Comment: 14 pages, revtex, 4 postscript figure

Solutions of Quantum Gravity Coupled to the Scalar Field

We consider the Wheeler-De Witt equation for canonical quantum gravity coupled to massless scalar field. After regularizing and renormalizing this equation, we find a one-parameter class of its solutions.Comment: 8 pages, LaTe

Topological Aspects of the Non-adiabatic Berry Phase

The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a critical frequency. The first Chern number that classifies these bundles is proportional to angular momentum. The non-adiabatic principal bundle over the parameter space is not well-defined at the critical frequency.Comment: 14 pages, Dep. of Physics, Uni. of Texas at Austin, Austin, Texas 78712, to appear in J. Physics

Black Hole Solution of Quantum Gravity

We present a spherically symmetric and static exact solution of Quantum Einstein Equations. This solution is asymptotically (for large $r$) identical with the black hole solution on the anti--De Sitter background and, for some range of values of the mass possesses two horizons. We investigate thermodynamical properties of this solution.Comment: Plain Latex, 10 page

Quantal Time Asymmetry: Mathematical Foundation And Physical Interpretation

Time in standard quantum mechanics extends from -infinity -infinity since according to causality, a quantum state phi(+) must be prepared first at a particular time t = t(0), before the probability vertical bar(psi(-)(t),phi+(t(0))vertical bar(2) for an observable psi(-) can be measured in it at t > t(0) (Feynman (1948)). In experiments on single Ba(+) ions, Dehmelt and others observed this finite preparation time as the ensemble of onset-times t(0)(1),t(0)(2), ..., t(0)(n) of dark periods. How the semigroup time evolution, t(0) equivalent to 0 < t < infinity with a beginning of time t(0), can suggest the parametrization of the resonance pole position of the Z-boson at S= s(R) as s(R) = (M(R) - i Gamma(R)/2)(2) in terms of a mass M(R) and a width Gamma(R) given by a lifetime tau = (h) over bar/Gamma(R), is the subject of this contribution dedicated to Augusto Garcia.Physic

Topological Black Holes in Quantum Gravity

We derive the black hole solutions with horizons of non-trivial topology and investigate their properties in the framework of an approach to quantum gravity being an extension of Bohm's formulation of quantum mechanics. The solutions we found tend asymptotically (for large $r$) to topological black holes. We also analyze the thermodynamics of these space-times.Comment: 4pages, no figures, plain LaTe

Relativistic Partial Wave Analysis Using the Velocity Basis of the Poincare Group

The velocity basis of the Poincare group is used in the direct product space of two irreducible unitary representations of the Poincare group. The velocity basis with total angular momentum j will be used for the definition of relativistic Gamow vectors.Comment: 14 pages; revte

Fast growing instabilities for non-parallel flows

Unstable modes growing when two plasma shells cross over a background plasma at arbitrary angle $\theta$, are investigated using a non-relativistic three cold fluids model. Parallel flows with $\theta=0$ are slightly more unstable than anti-parallel ones with $\theta=\pi$. The case $\theta=\pi/2$ is as unstable as the $\theta=0$ one, but the fastest growing modes are oblique. While the most unstable wave vector varies with orientation, its growth rate slightly evolves and there is no such thing as a stable configuration. A number of exact results can be derived, especially for the $\theta=\pi/2$ case.Comment: 4 pages, 3 figures, to appear in Phys. Lett.

Quantum Adiabatic Approximation, Quantum Action, and Berry's Phase

An alternative interpretation of the quantum adiabatic approximation is presented. This interpretation is based on the ideas originally advocated by David Bohm in his quest for establishing a hidden variable alternative to quantum mechanics. It indicates that the validity of the quantum adiabatic approximation is a sufficient condition for the separability of the quantum action function in the time variable. The implications of this interpretation for Berry's adiabatic phase and its semi-classical limit are also discussed.Comment: uuencoded LaTeX file, 5 page

Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics

We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of Hilbert spaces. We also construct a couple of examples illustrative of the key features of group representations in rigged Hilbert spaces. Finally, we establish a simple criterion for the integrability of an operator Lie algebra in a rigged Hilbert space