The Poisson Bracket for Poisson Forms in Multisymplectic Field Theory

We present a general definition of the Poisson bracket between differential forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories and, more generally, on exact multisymplectic manifolds. It is well defined for a certain class of differential forms that we propose to call Poisson forms and turns the space of Poisson forms into a Lie superalgebra.Comment: 40 pages LaTe

Remarks on the Configuration Space Approach to Spin-Statistics

The angular momentum operators for a system of two spin-zero indistinguishable particles are constructed, using Isham's Canonical Group Quantization method. This mathematically rigorous method provides a hint at the correct definition of (total) angular momentum operators, for arbitrary spin, in a system of indistinguishable particles. The connection with other configuration space approaches to spin-statistics is discussed, as well as the relevance of the obtained results in view of a possible alternative proof of the spin-statistics theorem.Comment: 18 page

Electrically tunable GHz oscillations in doped GaAs-AlAs superlattices

Tunable oscillatory modes of electric-field domains in doped semiconductor superlattices are reported. The experimental investigations demonstrate the realization of tunable, GHz frequencies in GaAs-AlAs superlattices covering the temperature region from 5 to 300 K. The orgin of the tunable oscillatory modes is determined using an analytical and a numerical modeling of the dynamics of domain formation. Three different oscillatory modes are found. Their presence depends on the actual shape of the drift velocity curve, the doping density, the boundary condition, and the length of the superlattice. For most bias regions, the self-sustained oscillations are due to the formation, motion, and recycling of the domain boundary inside the superlattice. For some biases, the strengths of the low and high field domain change periodically in time with the domain boundary being pinned within a few quantum wells. The dependency of the frequency on the coupling leads to the prediction of a new type of tunable GHz oscillator based on semiconductor superlattices.Comment: Tex file (20 pages) and 16 postscript figure

Gauge Theory of the String Geodesic Field

A relativistic string is usually represented by the Nambu-Goto action in terms of the extremal area of a 2-dimensional timelike submanifold of Minkowski space. Alternatively, a family of classical solutions of the string equation of motion can be globally described in terms of the associated geodesic field. In this paper we propose a new gauge theory for the geodesic field of closed and open strings. Our approach solves the technical and conceptual problems affecting previous attempts to describe strings in terms of local field variables. The connection between the geodesic field, the string current and the Kalb-Ramond gauge potential is discussed and clarified. A non-abelian generalization and the generally covariant form of the model are also discussed.Comment: 38 pages, PHYZZX, UTS-DFT-92-2

Semiclassical Black Hole States and Entropy

We discuss semiclassical states in quantum gravity corresponding to Schwarzschild as well as Reissner Nordstr\"om black holes. We show that reduced quantisation of these models is equivalent to Wheeler-DeWitt quantisation with a particular factor ordering. We then demonstrate how the entropy of black holes can be consistently calculated from these states. While this leads to the Bekenstein-Hawking entropy in the Schwarzschild and non-extreme Reissner-Nordstr\"om cases, the entropy for the extreme Reissner-Nordstr\"om case turns out to be zero.Comment: Revtex, 15 pages, some clarifying comments and additional references included, to appear in Phys. Rev.

Building blocks of a black hole

What is the nature of the energy spectrum of a black hole ? The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As stressed long ago by by Mukhanov, such eigenvalues must be exponentially degenerate with respect to the area quantum number if one is to understand black hole entropy as reflecting degeneracy of the observable states. Here we construct the black hole states by means of a pair of "creation operators" subject to a particular simple algebra, a slight generalization of that for the harmonic oscillator. We then prove rigorously that the n-th area eigenvalue is exactly 2 raised to the n-fold degenerate. Thus black hole entropy qua logarithm of the number of states for fixed horizon area comes out proportional to that area.Comment: PhysRevTeX, 14 page

Current-voltage characteristic and stability in resonant-tunneling n-doped semiconductor superlattices

We review the occurrence of electric-field domains in doped superlattices within a discrete drift model. A complete analysis of the construction and stability of stationary field profiles having two domains is carried out. As a consequence, we can provide a simple analytical estimation for the doping density above which stable stable domains occur. This bound may be useful for the design of superlattices exhibiting self-sustained current oscillations. Furthermore we explain why stable domains occur in superlattices in contrast to the usual Gunn diode.Comment: Tex file and 3 postscript figure

Quantum Black Holes from Quantum Collapse

The Schwarzschild black hole can be viewed as the special case of the marginally bound Lema\^\i tre-Tolman-Bondi models of dust collapse which corresponds to a constant mass function. We have presented a midi-superspace quantization of this model for an arbitrary mass-function in a separate publication. In this communication we show that our solution leads both to Bekenstein's area spectrum for black holes as well as to the black hole entropy, which, in this context, is naturally interpreted as the loss of information of the original matter distribution within the collapsing dust cloud.Comment: LaTeX file, 6 pages, 1 figure, Paper re-written into sections, some references added, some elaborations, conclusions unchanged, to appear in Physical Review

Nonlinear resonant tunneling in systems coupled to quantum reservoirs

An adiabatic approximation in terms of instantaneous resonances is developed to study the steady-state and time-dependent transport of interacting electrons in biased resonant tunneling heterostructures. The resulting model consists of quantum reservoirs coupled to regions where the system is described by nonlinear ordinary differential equations and has a general conceptual interest.Comment: 4 pages, 3 postscript figure

Temperature dependence of current self-oscillations and electric field domains in sequential tunneling doped superlattices

We examine how the current--voltage characteristics of a doped weakly coupled superlattice depends on temperature. The drift velocity of a discrete drift model of sequential tunneling in a doped GaAs/AlAs superlattice is calculated as a function of temperature. Numerical simulations and theoretical arguments show that increasing temperature favors the appearance of current self-oscillations at the expense of static electric field domain formation. Our findings agree with available experimental evidence.Comment: 7 pages, 5 figure