New Types of Thermodynamics from (1+1)(1+1)-Dimensional Black Holes

For normal thermodynamic systems superadditivity $\S$, homogeneity \H and concavity \C of the entropy hold, whereas for $(3+1)$-dimensional black holes the latter two properties are violated. We show that $(1+1)$-dimensional black holes exhibit qualitatively new types of thermodynamic behaviour, discussed here for the first time, in which \C always holds, \H is always violated and $\S$ may or may not be violated, depending of the magnitude of the black hole mass. Hence it is now seen that neither superadditivity nor concavity encapsulate the meaning of the second law in all situations.Comment: WATPHYS-TH93/05, Latex, 10 pgs. 1 figure (available on request), to appear in Class. Quant. Gra

Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems

We consider the statistical mechanics of a general relativistic one-dimensional self-gravitating system. The system consists of $N$-particles coupled to lineal gravity and can be considered as a model of $N$ relativistically interacting sheets of uniform mass. The partition function and one-particle distitrubion functions are computed to leading order in $1/c$ where $c$ is the speed of light; as $c\to\infty$ results for the non-relativistic one-dimensional self-gravitating system are recovered. We find that relativistic effects generally cause both position and momentum distribution functions to become more sharply peaked, and that the temperature of a relativistic gas is smaller than its non-relativistic counterpart at the same fixed energy. We consider the large-N limit of our results and compare this to the non-relativistic case.Comment: latex, 60 pages, 22 figure

N-body Gravity and the Schroedinger Equation

We consider the problem of the motion of $N$ bodies in a self-gravitating system in two spacetime dimensions. We point out that this system can be mapped onto the quantum-mechanical problem of an N-body generalization of the problem of the H$_{2}^{+}$ molecular ion in one dimension. The canonical gravitational N-body formalism can be extended to include electromagnetic charges. We derive a general algorithm for solving this problem, and show how it reduces to known results for the 2-body and 3-body systems.Comment: 15 pages, Latex, references added, typos corrected, final version that appears in CQ

Quasiclassical Equations of Motion for Nonlinear Brownian Systems

Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional formalism of quantum mechanics, using a path-integral description. This is done explicitly for the case of a system interacting with a ``bath'' of harmonic oscillators whose individual motions are neglected. The results are compared to the equations derived from the purely classical theory. The case of linear interactions is treated exactly, and nonlinear interactions are compared using classical and quantum perturbation theory.Comment: 24 pages, CALT-68-1848 (RevTeX 2.0 macros

Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History

Decoherent histories quantum theory is reformulated with the assumption that there is one "real" fine-grained history, specified in a preferred complete set of sum-over-histories variables. This real history is described by embedding it in an ensemble of comparable imagined fine-grained histories, not unlike the familiar ensemble of statistical mechanics. These histories are assigned extended probabilities, which can sometimes be negative or greater than one. As we will show, this construction implies that the real history is not completely accessible to experimental or other observational discovery. However, sufficiently and appropriately coarse-grained sets of alternative histories have standard probabilities providing information about the real fine-grained history that can be compared with observation. We recover the probabilities of decoherent histories quantum mechanics for sets of histories that are recorded and therefore decohere. Quantum mechanics can be viewed as a classical stochastic theory of histories with extended probabilities and a well-defined notion of reality common to all decoherent sets of alternative coarse-grained histories.Comment: 11 pages, one figure, expanded discussion and acknowledgment

Reactor antineutrino spectra and their application to antineutrino-induced reactions. II

The antineutrino and electron spectra associated with various nuclear fuels are calculated. While there are substantial differences between the spectra of different uranium and plutonium isotopes, the dependence on the energy and flux of the fission-inducing neutrons is very weak. The resulting spectra can be used for the calculation of the antineutrino and electron spectra of an arbitrary nuclear reactor at various stages of its refueling cycle. The sources of uncertainties in the spectrum are identified and analyzed in detail. The exposure time dependence of the spectrum is also discussed. The averaged cross sections of the inverse neutron β decay, weak charged and neutral-current-induced deuteron disintegration, and the antineutrino-electron scattering are then evaluated using the resulting ν̅_e spectra. [RADIOACTIVITY, FISSION 235U, 238U, (^239)Pu, (^240)Pu, (^241)Pu, antineutrino and electron spectra calculated. σ for ν̅ induced reactions analyzed.

Fermion Mass Hierarchy in Lifshitz Type Gauge Theory

We study the origin of fermion mass hierarchy and flavor mixing in a Lifshitz type extension of the standard model including an extra scalar field. We show that the hierarchical structure can originate from renormalizable interactions. In contrast to the Froggatt-Nielsen mechanism, the higher the dimension of associated operators, the heavier the fermion masses. Tiny masses for left-handed neutrinos are obtained without introducing right-handed neutrinos.Comment: 13 pages; clarifications of some point

Two-dimensional gravitation and Sine-Gordon-Solitons

Some aspects of two-dimensional gravity coupled to matter fields, especially to the Sine-Gordon-model are examined. General properties and boundary conditions of possible soliton-solutions are considered. Analytic soliton-solutions are discovered and the structure of the induced space-time geometry is discussed. These solutions have interesting features and may serve as a starting point for further investigations.Comment: 23 pages, latex, references added, to appear in Phys.Rev.

Symmetry Breaking Using Value Precedence

We present a comprehensive study of the use of value precedence constraints to break value symmetry. We first give a simple encoding of value precedence into ternary constraints that is both efficient and effective at breaking symmetry. We then extend value precedence to deal with a number of generalizations like wreath value and partial interchangeability. We also show that value precedence is closely related to lexicographical ordering. Finally, we consider the interaction between value precedence and symmetry breaking constraints for variable symmetries.Comment: 17th European Conference on Artificial Intelligenc