4,849 research outputs found
Renormalization and Essential Singularity
In usual dimensional counting, momentum has dimension one. But a function
f(x), when differentiated n times, does not always behave like one with its
power smaller by n. This inevitable uncertainty may be essential in general
theory of renormalization, including quantum gravity. As an example, we
classify possible singularities of a potential for the Schr\"{o}dinger
equation, assuming that the potential V has at least one class eigen
function. The result crucially depends on the analytic property of the eigen
function near its 0 point.Comment: 12 pages, no figures, PTPTeX with amsfonts. 2 pages added for detail
Mathematics of random growing interfaces
We establish a thermodynamic limit and Gaussian fluctuations for the height
and surface width of the random interface formed by the deposition of particles
on surfaces. The results hold for the standard ballistic deposition model as
well as the surface relaxation model in the off-lattice setting. The results
are proved with the aid of general limit theorems for stabilizing functionals
of marked Poisson point processes.Comment: 12 page
Modelling of Phase Separation in Alloys with Coherent Elastic Misfit
Elastic interactions arising from a difference of lattice spacing between two
coherent phases can have a strong influence on the phase separation
(coarsening) of alloys. If the elastic moduli are different in the two phases,
the elastic interactions may accelerate, slow down or even stop the phase
separation process. If the material is elastically anisotropic, the
precipitates can be shaped like plates or needles instead of spheres and can
form regular precipitate superlattices. Tensions or compressions applied
externally to the specimen may have a strong effect on the shapes and
arrangement of the precipitates. In this paper, we review the main theoretical
approaches that have been used to model these effects and we relate them to
experimental observations. The theoretical approaches considered are (i)
`macroscopic' models treating the two phases as elastic media separated by a
sharp interface (ii) `mesoscopic' models in which the concentration varies
continuously across the interface (iii) `microscopic' models which use the
positions of individual atoms.Comment: 106 pages, in Latex, figures available upon request, e-mail
addresses: [email protected], [email protected],
[email protected], submitted to the Journal of Statistical Physic
Towards Quantum Superpositions of a Mirror: an Exact Open Systems Analysis
We analyze the recently proposed mirror superposition experiment of Marshall,
Simon, Penrose, and Bouwmeester, assuming that the mirror's dynamics contains a
non-unitary term of the Lindblad type proportional to -[q,[q,\rho]], with q the
position operator for the center of mass of the mirror, and \rho the
statistical operator. We derive an exact formula for the fringe visibility for
this system. We discuss the consequences of our result for tests of
environmental decoherence and of collapse models. In particular, we find that
with the conventional parameters for the CSL model of state vector collapse,
maintenance of coherence is expected to within an accuracy of at least 1 part
in 10^{8}. Increasing the apparatus coupling to environmental decoherence may
lead to observable modifications of the fringe visibility, with time dependence
given by our exact result.Comment: 4 pages, RevTeX. Substantial changes mad
Off-Diagonal Long-Range Order: Meissner Effect and Flux Quantization
There has been a proof by Sewell that the hypothesis of off-diagonal
long-range order in the reduced density matrix implies the Meissner
effect. We present in this note an elementary and straightforward proof that
not only the Meissner effect but also the property of magnetic flux
quantization follows from the hypothesis. It is explicitly shown that the two
phenomena are closely related, and phase coherence is the origin for both.Comment: 11 pages, Latex fil
Twistors, special relativity, conformal symmetry and minimal coupling - a review
An approach to special relativistic dynamics using the language of spinors
and twistors is presented. Exploiting the natural conformally invariant
symplectic structure of the twistor space, a model is constructed which
describes a relativistic massive, spinning and charged particle, minimally
coupled to an external electro-magnetic field. On the two-twistor phase space
the relativistic Hamiltonian dynamics is generated by a Poincare scalar
function obtained from the classical limit (appropriately defined by us) of the
second order, to an external electro-magnetic field minimally coupled, Dirac
operator. In the so defined relativistic classical limit there are no Grassman
variables. Besides, the arising equation that describes dynamics of the
relativistic spin differs significantly from the so called Thomas Bergman
Michel Telegdi equation.Comment: 39 pages, no figures, few erronous statements (not affecting anything
else in the papper) on page 23 delete
Non-Abelian Tensor Multiplet Equations from Twistor Space
We establish a Penrose-Ward transform yielding a bijection between
holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual
tensor fields on six-dimensional flat space-time. Extending the twistor space
to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0)
supersymmetric non-Abelian constraint equations containing the tensor
multiplet. We also demonstrate how this construction leads to constraint
equations for non-Abelian supersymmetric self-dual strings.Comment: v3: 23 pages, revised version published in Commun. Math. Phy
Degeneracy measures for the algebraic classification of numerical spacetimes
We study the issue of algebraic classification of the Weyl curvature tensor,
with a particular focus on numerical relativity simulations. The spacetimes of
interest in this context, binary black hole mergers, and the ringdowns that
follow them, present subtleties in that they are generically, strictly
speaking, Type I, but in many regions approximately, in some sense, Type D. To
provide meaning to any claims of "approximate" Petrov class, one must define a
measure of degeneracy on the space of null rays at a point. We will investigate
such a measure, used recently to argue that certain binary black hole merger
simulations ring down to the Kerr geometry, after hanging up for some time in
Petrov Type II. In particular, we argue that this hangup in Petrov Type II is
an artefact of the particular measure being used, and that a geometrically
better-motivated measure shows a black hole merger produced by our group
settling directly to Petrov Type D.Comment: 14 pages, 7 figures. Version 2 adds two references
The frictional Schr\"odinger-Newton equation in models of wave function collapse
Replacing the Newtonian coupling G by -iG, the Schrodinger-Newton equation
becomes ``frictional''. Instead of the reversible Schrodinger-Newton equation,
we advocate its frictional version to generate the set of pointer states for
macroscopic quantum bodies.Comment: 6pp LaTeX for J.Phys.Conf.Ser.+2 figs. Talk given at the Int.
Workshop DICE2006 "Quantum Mechanics between Decoherence and Determinism: new
aspects from particle physics to cosmology" Piombino, Sept 11-15, 200
Spin-Raising Operators and Spin-3/2 Potentials in Quantum Cosmology
Local boundary conditions involving field strengths and the normal to the
boundary, originally studied in anti-de Sitter space-time, have been recently
considered in one-loop quantum cosmology. This paper derives the conditions
under which spin-raising operators preserve these local boundary conditions on
a 3-sphere for fields of spin 0,1/2,1,3/2 and 2. Moreover, the two-component
spinor analysis of the four potentials of the totally symmetric and independent
field strengths for spin 3/2 is applied to the case of a 3-sphere boundary. It
is shown that such boundary conditions can only be imposed in a flat Euclidean
background, for which the gauge freedom in the choice of the potentials
remains.Comment: 13 pages, plain-tex, recently appearing in Classical and Quantum
Gravity, volume 11, April 1994, pages 897-903. Apologies for the delay in
circulating the file, due to technical problems now fixe
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