Statistical mechanics of Kerr-Newman dilaton black holes and the bootstrap condition

The Bekenstein-Hawking ``entropy'' of a Kerr-Newman dilaton black hole is computed in a perturbative expansion in the charge-to-mass ratio. The most probable configuration for a gas of such black holes is analyzed in the microcanonical formalism and it is argued that it does not satisfy the equipartition principle but a bootstrap condition. It is also suggested that the present results are further support for an interpretation of black holes as excitations of extended objects.Comment: RevTeX, 5 pages, 2 PS figures included (requires epsf), submitted to Phys. Rev. Let

Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields

We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible ones (irreducible but reducible over an extension field). One approach employs generating functions, another one uses a combinatorial method. They yield exact formulas and approximations with relative errors that essentially decrease exponentially in the input size.Comment: to appear in SIAM Journal on Discrete Mathematic

Why is the B -> eta' X decay width so large ?

New mechanism for the observed inclusive B -> \eta'X decay is suggested. We argue that the dominant contribution to this amplitude is due to the Cabbibo favored b -> \bar{c}cs process followed by the transition \bar{c}c -> \eta'. A large magnitude of the "intrinsic charm" component of \eta' is of critical importance in our approach. Our results are consistent with an unexpectedly large Br(B -> \eta'+X) \sim 10^{-3} recently announced by CLEO. We stress the uniqueness of this channel for 0^{-+} gluonia search.Comment: Comments on a mixing model for intrinsic charm and pre-asymptotic effects and some references are added. Latex, 9 page

How Fast Does Information Leak out from a Black Hole?

Hawking's radiance, even as computed without account of backreaction, departs from blackbody form due to the mode dependence of the barrier penetration factor. Thus the radiation is not the maximal entropy radiation for given energy. By comparing estimates of the actual entropy emission rate with the maximal entropy rate for the given power, and using standard ideas from communication theory, we set an upper bound on the permitted information outflow rate. This is several times the rates of black hole entropy decrease or radiation entropy production. Thus, if subtle quantum effects not heretofore accounted for code information in the radiance, the information that was thought to be irreparably lost down the black hole may gradually leak back out from the black hole environs over the full duration of the hole's evaporation.Comment: 8 pages, plain TeX, UCSBTH-93-0

An Alternative Method to Obtain the Quark Polarization of the Nucleon

An alternate method is described to extract the quark contribution to the spin of the nucleon directly from the first moment of the deuteron structure function, $g^d_1$. It is obtained without recourse to the use of input on the nucleon wave function from hyperon decays involving the flavor symmetry parameters, F and D. The result for the quark polarization of the nucleon, $\Delta\Sigma_ N,$ is in good agreement with the values of the singlet axial current matrix element, $a_0$, obtained from recent next-to-leading order analyses of current proton, neutron and deuteron data.Comment: 7 pages, 1 figur

On the Deconfinement Phase Transition in the Resonance Gas

We obtain the constraints on the ruling parameters of the dense hadronic gas model at the critical temperature and propose the quasiuniversal ratios of the thermodynamic quantities. The possible appearence of thermodynamical instability in such a model is discussed.Comment: 7 pages, plain LaTeX, BI-TP 94/4

Nucleon QCD sum rules in nuclear matter including four-quark condensates

We calculate the nucleon parameters in nuclear matter using the QCD sum rules approach in Fermi gas approximation. Terms up to 1/q^2 in the operator product expansion (OPE) are taken into account. The higher moments of the nucleon structure functions are included. The complete set of the nucleon expectation values of the four-quark operators is employed. Earlier the lack of information on these values has been the main obstacle for the further development of the approach. We show that the four-quark condensates provide the corrections of the order 20% to the results obtained in the leading orders of the OPE. This is consistent with the assumption about the convergence of the OPE. The nucleon vector self-energy \Sigma_v and the nucleon effective mass m^* are expressed in terms of the in-medium values of QCD condensates. The numerical results for these parameters at the saturation value of the density agree with those obtained by the methods of nuclear physics.Comment: 38 pages, 5 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

Random walk generated by random permutations of {1,2,3, ..., n+1}

We study properties of a non-Markovian random walk $X^{(n)}_l$, $l =0,1,2, >...,n$, evolving in discrete time $l$ on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the \text{rise-and-descent} sequences characterizing random permutations $\pi$ of $[n+1] = \{1,2,3, ...,n+1\}$. We determine exactly the probability of finding the end-point $X_n = X^{(n)}_n$ of the trajectory of such a permutation-generated random walk (PGRW) at site $X$, and show that in the limit $n \to \infty$ it converges to a normal distribution with a smaller, compared to the conventional P\'olya random walk, diffusion coefficient. We formulate, as well, an auxiliary stochastic process whose distribution is identic to the distribution of the intermediate points $X^{(n)}_l$, $l < n$, which enables us to obtain the probability measure of different excursions and to define the asymptotic distribution of the number of "turns" of the PGRW trajectories.Comment: text shortened, new results added, appearing in J. Phys.

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