2,207 research outputs found
Constraints on Area Variables in Regge Calculus
We describe a general method of obtaining the constraints between area
variables in one approach to area Regge calculus, and illustrate it with a
simple example. The simplicial complex is the simplest tessellation of the
4-sphere. The number of independent constraints on the variations of the
triangle areas is shown to equal the difference between the numbers of
triangles and edges, and a general method of choosing independent constraints
is described. The constraints chosen by using our method are shown to imply the
Regge equations of motion in our example.Comment: Typographical errors correcte
N-qubit states as points on the Bloch sphere
We show how the Majorana representation can be used to express the pure
states of an N-qubit system as points on the Bloch sphere. We compare this
geometrical representation of N-qubit states with an alternative one, proposed
recently by the present authors.Comment: 9 pages, 2 figures, contribution to CEWQO 2009 proceedings. v2: Minor
changes, published versio
Spacetime Foam Model of the Schwarzschild Horizon
We consider a spacetime foam model of the Schwarzschild horizon, where the
horizon consists of Planck size black holes. According to our model the entropy
of the Schwarzschild black hole is proportional to the area of its event
horizon. It is possible to express geometrical arguments to the effect that the
constant of proportionality is, in natural units, equal to one quarter.Comment: 16 pages, 2 figures, improved and extended version with some
significant changes. Accepted for publication in Phys.Rev.
Regional similarities in the distributions of well yield from crystalline rocks in Fennoscandia
Well yields from Precambrian and Palaeozoic bedrock in Norway, Sweden and Finland exhibit very
similar and approximately log-normal distributions: all three data sets exhibit a median yield of
600–700 L hr-1, despite the differences in climate and lithology. This similarity is tentatively reflected
on a larger geographical scale by a meta-analysis of the international data sets on crystalline rock aquifers from other recently glaciated areas (i.e., without a thick regolith of weathered rock). An heuristic treatment of the Fennoscandian data sets suggests that this median yield is consistent with the following bulk properties of shallow (to c. 70–80 m depth) crystalline bedrock: transmissivity of
0.56 ± 0.30 m2 d-1 (6.4 ± 3.4 x 10-6 m2 s-1) and hydraulic conductivity of around 1.1 (± 0.6) x 10-7 m s-1
Microscopic Black Hole Pairs in Highly-Excited States
We consider the quantum mechanics of a system consisting of two identical,
Planck-size Schwarzschild black holes revolving around their common center of
mass. We find that even in a very highly-excited state such a system has very
sharp, discrete energy eigenstates, and the system performs very rapid
transitions from a one stationary state to another. For instance, when the
system is in the 100th excited state, the life times of the energy eigenstates
are of the order of s, and the energies of gravitons released in
transitions between nearby states are of the order of eV.Comment: 22 pages, 3 figures, uses RevTe
Quantum-mechanical model of the Kerr-Newman black hole
We consider a Hamiltonian quantum theory of stationary spacetimes containing
a Kerr-Newman black hole. The physical phase space of such spacetimes is just
six-dimensional, and it is spanned by the mass , the electric charge and
angular momentum of the hole, together with the corresponding canonical
momenta. In this six-dimensional phase space we perform a canonical
transformation such that the resulting configuration variables describe the
dynamical properties of Kerr-Newman black holes in a natural manner. The
classical Hamiltonian written in terms of these variables and their conjugate
momenta is replaced by the corresponding self-adjoint Hamiltonian operator and
an eigenvalue equation for the Arnowitt-Deser-Misner (ADM) mass of the hole,
from the point of view of a distant observer at rest, is obtained. In a certain
very restricted sense, this eigenvalue equation may be viewed as a sort of
"Schr\"odinger equation of black holes". Our "Schr\"odinger equation" implies
that the ADM mass, electric charge and angular momentum spectra of black holes
are discrete, and the mass spectrum is bounded from below. Moreover, the
spectrum of the quantity , where is the angular momentum per
unit mass of the hole, is strictly positive when an appropriate self-adjoint
extension is chosen. The WKB analysis yields the result that the large
eigenvalues of , and are of the form , where is an
integer. It turns out that this result is closely related to Bekenstein's
proposal on the discrete horizon area spectrum of black holes.Comment: 30 pages, 3 figures, RevTe
Explicit expressions for the topological defects of spinor Bose-Einstein condensates
In this paper we first derive a general method which enables one to create
expressions for vortices and monopoles. By using this method we construct
several order-parameters describing the vortices and monopoles of Bose-Einstein
condensates with hyperfine spin F=1 and F=2. We concentrate on defects which
are topologically stable in the absence of an external magnetic field. In
particular we show that in a ferromagnetic condensate there can be a vortex
which does not produce any superfluid flow. We also point out that the
order-parameter space of the cyclic phase of F=2 condensate consists of two
disconnected sets. Finally we examine the effect of an external magnetic field
on the vortices of a ferromagnetic F=1 condensate and discuss the experimental
preparation of a vortex in this system.Comment: 17 pages, partly rewritten to improve clarity, conclusions unchange
Gravitation and thermodynamics: The einstein equation of state revisited
We perform an analysis where Einstein\u27s field equation is derived by means of very simple thermodynamical arguments. Our derivation is based on a consideration of the properties of a very small, spacelike two-plane in a uniformly accelerating motion. © 2009 World Scientific Publishing Company
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