Anomalous particle-number fluctuations in a three-dimensional interacting Bose-Einstein condensate

The particle-number fluctuations originated from collective excitations are investigated for a three-dimensional, repulsively interacting Bose-Einstein condensate (BEC) confined in a harmonic trap. The contribution due to the quantum depletion of the condensate is calculated and the explicit expression of the coefficient in the formulas denoting the particle-number fluctuations is given. The results show that the particle-number fluctuations of the condensate follow the law $\sim N^{22/15}$ and the fluctuations vanish when temperature approaches to the BEC critical temperature.Comment: RevTex, 4 page

Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal Spacetimes

Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike surfaces, as in the case of spacetimes with closed timelike curves, a more general formulation of quantum mechanics is required. In such generalizations the transition matrix between alternatives in regions of spacetime where states {\it can} be defined may be non-unitary. This paper describes a generalized quantum mechanics whose probabilities consistently obey the rules of probability theory even in the presence of such non-unitarity. The usual notion of state on a spacelike surface is lost in this generalization and familiar notions of causality are modified. There is no signaling outside the light cone, no non-conservation of energy, no ``Everett phones'', and probabilities of present events do not depend on particular alternatives of the future. However, the generalization is acausal in the sense that the existence of non-chronal regions of spacetime in the future can affect the probabilities of alternatives today. The detectability of non-unitary evolution and violations of causality in measurement situations are briefly considered. The evolution of information in non-chronal spacetimes is described.Comment: 40pages, UCSBTH92-0

On the Behavior of the Effective QCD Coupling alpha_tau(s) at Low Scales

The hadronic decays of the tau lepton can be used to determine the effective charge alpha_tau(m^2_tau') for a hypothetical tau-lepton with mass in the range 0 < m_tau' < m_tau. This definition provides a fundamental definition of the QCD coupling at low mass scales. We study the behavior of alpha_tau at low mass scales directly from first principles and without any renormalization-scheme dependence by looking at the experimental data from the OPAL Collaboration. The results are consistent with the freezing of the physical coupling at mass scales s = m^2_tau' of order 1 GeV^2 with a magnitude alpha_tau ~ 0.9 +/- 0.1.Comment: 15 pages, 4 figures, submitted to Physical Review D, added references, some text added, no results nor figures change

Number Fluctuation and the Fundamental Theorem of Arithmetic

We consider N bosons occupying a discrete set of single-particle quantum states in an isolated trap. Usually, for a given excitation energy, there are many combinations of exciting different number of particles from the ground state, resulting in a fluctuation of the ground state population. As a counter example, we take the quantum spectrum to be logarithms of the prime number sequence, and using the fundamental theorem of arithmetic, find that the ground state fluctuation vanishes exactly for all excitations. The use of the standard canonical or grand canonical ensembles, on the other hand, gives substantial number fluctuation for the ground state. This difference between the microcanonical and canonical results cannot be accounted for within the framework of equilibrium statistical mechanics.Comment: 4 pages, 4 figures. To be submitted to Phys. Rev. Let

Spiral Multi-component Structure in Pade - Approximant QCD

We present a graphical method of analyzing the infra-red fixed point structure of Pade approximant QCD. The analysis shows a spiral multi-component couplant structure as well as an infra-red attractor behavior of PQCD couplant for all flavors $0 \le N_{f} \le 16$.Comment: 78 pages, 4 tables, 44 graph

Leptonic and Semileptonic Decays of Charm and Bottom Hadrons

We review the experimental measurements and theoretical descriptions of leptonic and semileptonic decays of particles containing a single heavy quark, either charm or bottom. Measurements of bottom semileptonic decays are used to determine the magnitudes of two fundamental parameters of the standard model, the Cabibbo-Kobayashi-Maskawa matrix elements $V_{cb}$ and $V_{ub}$. These parameters are connected with the physics of quark flavor and mass, and they have important implications for the breakdown of CP symmetry. To extract precise values of $|V_{cb}|$ and $|V_{ub}|$ from measurements, however, requires a good understanding of the decay dynamics. Measurements of both charm and bottom decay distributions provide information on the interactions governing these processes. The underlying weak transition in each case is relatively simple, but the strong interactions that bind the quarks into hadrons introduce complications. We also discuss new theoretical approaches, especially heavy-quark effective theory and lattice QCD, which are providing insights and predictions now being tested by experiment. An international effort at many laboratories will rapidly advance knowledge of this physics during the next decade.Comment: This review article will be published in Reviews of Modern Physics in the fall, 1995. This file contains only the abstract and the table of contents. The full 168-page document including 47 figures is available at http://charm.physics.ucsb.edu/papers/slrevtex.p