12,719 research outputs found
Localization of Eigenfunctions in the Stadium Billiard
We present a systematic survey of scarring and symmetry effects in the
stadium billiard. The localization of individual eigenfunctions in Husimi phase
space is studied first, and it is demonstrated that on average there is more
localization than can be accounted for on the basis of random-matrix theory,
even after removal of bouncing-ball states and visible scars. A major point of
the paper is that symmetry considerations, including parity and time-reversal
symmetries, enter to influence the total amount of localization. The properties
of the local density of states spectrum are also investigated, as a function of
phase space location. Aside from the bouncing-ball region of phase space,
excess localization of the spectrum is found on short periodic orbits and along
certain symmetry-related lines; the origin of all these sources of localization
is discussed quantitatively and comparison is made with analytical predictions.
Scarring is observed to be present in all the energy ranges considered. In
light of these results the excess localization in individual eigenstates is
interpreted as being primarily due to symmetry effects; another source of
excess localization, scarring by multiple unstable periodic orbits, is smaller
by a factor of .Comment: 31 pages, including 10 figure
Conceptual Unification of Gravity and Quanta
We present a model unifying general relativity and quantum mechanics. The
model is based on the (noncommutative) algebra \mbox{{\cal A}} on the groupoid
\Gamma = E \times G where E is the total space of the frame bundle over
spacetime, and G the Lorentz group. The differential geometry, based on
derivations of \mbox{{\cal A}}, is constructed. The eigenvalue equation for the
Einstein operator plays the role of the generalized Einstein's equation. The
algebra \mbox{{\cal A}}, when suitably represented in a bundle of Hilbert
spaces, is a von Neumann algebra \mathcal{M} of random operators representing
the quantum sector of the model. The Tomita-Takesaki theorem allows us to
define the dynamics of random operators which depends on the state \phi . The
same state defines the noncommutative probability measure (in the sense of
Voiculescu's free probability theory). Moreover, the state \phi satisfies the
Kubo-Martin-Schwinger (KMS) condition, and can be interpreted as describing a
generalized equilibrium state. By suitably averaging elements of the algebra
\mbox{{\cal A}}, one recovers the standard geometry of spacetime. We show that
any act of measurement, performed at a given spacetime point, makes the model
to collapse to the standard quantum mechanics (on the group G). As an example
we compute the noncommutative version of the closed Friedman world model.
Generalized eigenvalues of the Einstein operator produce the correct components
of the energy-momentum tensor. Dynamics of random operators does not ``feel''
singularities.Comment: 28 LaTex pages. Substantially enlarged version. Improved definition
of generalized Einstein's field equation
Controllable quantum scars in semiconductor quantum dots
Quantum scars are enhancements of quantum probability density along classical
periodic orbits. We study the recently discovered phenomenon of strong,
perturbation-induced quantum scarring in the two-dimensional harmonic
oscillator exposed to a homogeneous magnetic field. We demonstrate that both
the geometry and the orientation of the scars are fully controllable with a
magnetic field and a focused perturbative potential, respectively. These
properties may open a path into an experimental scheme to manipulate electric
currents in nanostructures fabricated in a two-dimensional electron gas.Comment: 5 pages, 4 figure
Black brane entropy and hydrodynamics: the boost-invariant case
The framework of slowly evolving horizons is generalized to the case of black
branes in asymptotically anti-de Sitter spaces in arbitrary dimensions. The
results are used to analyze the behavior of both event and apparent horizons in
the gravity dual to boost-invariant flow. These considerations are motivated by
the fact that at second order in the gradient expansion the hydrodynamic
entropy current in the dual Yang-Mills theory appears to contain an ambiguity.
This ambiguity, in the case of boost-invariant flow, is linked with a similar
freedom on the gravity side. This leads to a phenomenological definition of the
entropy of black branes. Some insights on fluid/gravity duality and the
definition of entropy in a time-dependent setting are elucidated.Comment: RevTeX, 42 pages, 4 figure
An interacting quark-diquark model of baryons
A simple quark-diquark model of baryons with direct and exchange interactions
is constructed. Spectrum and form factors are calculated and compared with
experimental data. Advantages and disadvantages of the model are discussed.Comment: 13 pages, 3 eps-figures, accepted by Phys.Rev. C Rapid Communication
The use of multispectral sensing techniques to detect ponderosa pine trees under stress from insect or pathogenic organisms
Application of multispectral sensors to detect insect and disease infestation of ponderosa pine tree
Relaxation and Localization in Interacting Quantum Maps
We quantise and study several versions of finite multibaker maps. Classically
these are exactly solvable K-systems with known exponential decay to global
equilibrium. This is an attempt to construct simple models of relaxation in
quantum systems. The effect of symmetries and localization on quantum transport
is discussed.Comment: 32 pages. LaTex file. 9 figures, not included. For figures send mail
to first author at '[email protected]
Clebsch-Gordan Construction of Lattice Interpolating Fields for Excited Baryons
Large sets of baryon interpolating field operators are developed for use in
lattice QCD studies of baryons with zero momentum. Operators are classified
according to the double-valued irreducible representations of the octahedral
group. At first, three-quark smeared, local operators are constructed for each
isospin and strangeness and they are classified according to their symmetry
with respect to exchange of Dirac indices. Nonlocal baryon operators are
formulated in a second step as direct products of the spinor structures of
smeared, local operators together with gauge-covariant lattice displacements of
one or more of the smeared quark fields. Linear combinations of direct products
of spinorial and spatial irreducible representations are then formed with
appropriate Clebsch-Gordan coefficients of the octahedral group. The
construction attempts to maintain maximal overlap with the continuum SU(2)
group in order to provide a physically interpretable basis. Nonlocal operators
provide direct couplings to states that have nonzero orbital angular momentum.Comment: This manuscript provides an anlytical construction of operators and
is related to hep-lat/0506029, which provides a computational construction.
This e-print version contains a full set of Clebsch-Gordan coefficients for
the octahedral grou
Husimi Maps in Lattices
We build upon previous work that used coherent states as a measurement of the
local phase space and extended the flux operator by adapting the Husimi
projection to produce a vector field called the Husimi map. In this article, we
extend its definition from continuous systems to lattices. This requires making
several adjustments to incorporate effects such as group velocity and multiple
bands. Several phenomena which uniquely occur in lattice systems, like
group-velocity warping and internal Bragg diffraction, are explained and
demonstrated using Husimi maps. We also show that scattering points between
bands and valleys can be identified in the divergence of the Husimi map
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