Valence Quark Spin Distribution Functions

The hyperfine interactions of the constituent quark model provide a natural explanation for many nucleon properties, including the Delta-N splitting, the charge radius of the neutron, and the observation that the proton's quark distribution function ratio d(x)/u(x)->0 as x->1. The hyperfine-perturbed quark model also makes predictions for the nucleon spin-dependent distribution functions. Precision measurements of the resulting asymmetries A_1^p(x) and A_1^n(x) in the valence region can test this model and thereby the hypothesis that the valence quark spin distributions are "normal".Comment: 16 pages, 2 Postscript figure

Topological Expansion and Exponential Asymptotics in 1D Quantum Mechanics

Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed for the corresponding Borel functions. Its main property is to order the singularity structure of the Borel plane in a hierarchical way by an increasing complexity of this structure starting from the analytic one. This allows us to study the Borel plane singularity structure in a systematic way. Examples of such structures are considered for linear, harmonic and anharmonic potentials. Together with the best approximation provided by the semiclassical series the exponentially small contribution completing the approximation are considered. A natural method of constructing such an exponential asymptotics relied on the Borel plane singularity structures provided by the topological expansion is developed. The method is used to form the semiclassical series including exponential contributions for the energy levels of the anharmonic oscillator.Comment: 46 pages, 22 EPS figure

Uniformly Accelerated Mirrors. Part 1: Mean Fluxes

The Davies-Fulling model describes the scattering of a massless field by a moving mirror in 1+1 dimensions. When the mirror travels under uniform acceleration, one encounters severe problems which are due to the infinite blue shift effects associated with the horizons. On one hand, the Bogoliubov coefficients are ill-defined and the total energy emitted diverges. On the other hand, the instantaneous mean flux vanishes. To obtained well-defined expressions we introduce an alternative model based on an action principle. The usefulness of this model is to allow to switch on and off the interaction at asymptotically large times. By an appropriate choice of the switching function, we obtain analytical expressions for the scattering amplitudes and the fluxes emitted by the mirror. When the coupling is constant, we recover the vanishing flux. However it is now followed by transients which inevitably become singular when the switching off is performed at late time. Our analysis reveals that the scattering amplitudes (and the Bogoliubov coefficients) should be seen as distributions and not as mere functions. Moreover, our regularized amplitudes can be put in a one to one correspondence with the transition amplitudes of an accelerated detector, thereby unifying the physics of uniformly accelerated systems. In a forthcoming article, we shall use our scattering amplitudes to analyze the quantum correlations amongst emitted particles which are also ill-defined in the Davies-Fulling model in the presence of horizons.Comment: 23 pages, 7 postscript figure

Black Hole Emission in String Theory and the String Phase of Black Holes

String theory properly describes black-hole evaporation. The quantum string emission by Black Holes is computed. The black-hole temperature is the Hawking temperature in the semiclassical quantum field theory (QFT) regime and becomes the intrinsic string temperature, T_s, in the quantum (last stage) string regime. The QFT-Hawking temperature T_H is upper bounded by the string temperature T_S. The black hole emission spectrum is an incomplete gamma function of (T_H - T_S). For T_H << T_S, it yields the QFT-Hawking emission. For T_H \to T_S, it shows highly massive string states dominate the emission and undergo a typical string phase transition to a microscopic `minimal' black hole of mass M_{\min} or radius r_{\min} (inversely proportional to T_S) and string temperature T_S. The string back reaction effect (selfconsistent black hole solution of the semiclassical Einstein equations) is computed. Both, the QFT and string black hole regimes are well defined and bounded.The string `minimal' black hole has a life time tau_{min} simeq (k_B c)/(G hbar [T_S]^3). The semiclassical QFT black hole (of mass M and temperature T_H) and the string black hole (of mass M_{min} and temperature T_S) are mapped one into another by a `Dual' transform which links classical/QFT and quantum string regimes.Comment: LaTex, 22 pages, Lectures delivered at the Chalonge School, Nato ASI: Phase Transitions in the Early Universe: Theory and Observations. To appear in the Proceedings, Editors H. J. de Vega, I. Khalatnikov, N. Sanchez. (Kluwer Pub

The Wigner function associated to the Rogers-Szego polynomials

We show here that besides the well known Hermite polynomials, the q-deformed harmonic oscillator algebra admits another function space associated to a particular family of q-polynomials, namely the Rogers-Szego polynomials. Their main properties are presented, the associated Wigner function is calculated and its properties are discussed. It is shown that the angle probability density obtained from the Wigner function is a well-behaved function defined in the interval [-Pi,Pi), while the action probability only assumes integer values greater or equal than zero. It is emphasized the fact that the width of the angle probability density is governed by the free parameter q characterizing the polynomial.Comment: 12 pages, 2 (mathemathica) figure

Hot String Soup

Above the Hagedorn energy density closed fundamental strings form a long string phase. The dynamics of weakly interacting long strings is described by a simple Boltzmann equation which can be solved explicitly for equilibrium distributions. The average total number of long strings grows logarithmically with total energy in the microcanonical ensemble. This is consistent with calculations of the free single string density of states provided the thermodynamic limit is carefully defined. If the theory contains open strings the long string phase is suppressed.Comment: 13 pages, no figures, uses LaTex, some errors in equations have been corrected, NSF-ITP-94-83, UCSBTH-94-3

A New Class of Non-Linear Stability Preserving Operators

We extend Br\"and\'en's recent proof of a conjecture of Stanley and describe a new class of non-linear operators that preserve weak Hurwitz stability and the Laguerre-P\'olya class.Comment: Fixed typos, spelling, and updated links in reference

On the Anomalous Discrete Symmetry

We examine an interesting scenario to solve the domain wall problem recently suggested by Preskill, Trivedi, Wilczek and Wise. The effective potential is calculated in the presence of the QCD axial anomaly. It is shown that some discrete symmetries such as CP and Z_2 can be anomalous due to a so-called $K$-term induced by instantons. We point out that Z_2 domain-wall problem in the two-doublet standard model can be resolved by two types of solutions: the CP-conserving one and the CP-breaking one. In the first case, there exist two Z_2-related local minima whose energy splitting is provided by the instanton effect. In the second case, there is only one unique vacuum so that the domain walls do not form at all. The consequences of this new source of CP violation are discussed and shown to be well within the experimental limits in weak interactions.Comment: 10 papges in LaTeX, SFU-Preprint-92-

Uniformly Accelerated Mirrors. Part 2: Quantum Correlations

We study the correlations between the particles emitted by a moving mirror. To this end, we first analyze $$, the two-point function of the stress tensor of the radiation field. In this we generalize the work undertaken by Carlitz and Willey. To further analyze how the vacuum correlations on $I^-$ are scattered by the mirror and redistributed among the produced pairs of particles, we use a more powerful approach based on the value of $T_{\mu\nu}$ which is conditional to the detection of a given particle on $I^+$. We apply both methods to the fluxes emitted by a uniformly accelerated mirror. This case is particularly interesting because of its strong interferences which lead to a vanishing flux, and because of its divergences which are due to the infinite blue shift effects associated with the horizons. Using the conditional value of $T_{\mu\nu}$, we reveal the existence of correlations between created particles and their partners in a domain where the mean fluxes and the two-point function vanish. This demonstrates that the scattering by an accelerated mirror leads to a steady conversion of vacuum fluctuations into pairs of quanta. Finally, we study the scattering by two uniformly accelerated mirrors which follow symmetrical trajectories (i.e. which possess the same horizons). When using the Davies-Fulling model, the Bogoliubov coefficients encoding pair creation vanish because of perfectly destructive interferences. When using regularized amplitudes, these interferences are inevitably lost thereby giving rise to pair creation.Comment: 30 pages, 9 postscript figure