18,888 research outputs found
Quantum Flux and Reverse Engineering of Quantum Wavefunctions
An interpretation of the probability flux is given, based on a derivation of
its eigenstates and relating them to coherent state projections on a quantum
wavefunction. An extended definition of the flux operator is obtained using
coherent states. We present a "processed Husimi" representation, which makes
decisions using many Husimi projections at each location. The processed Husimi
representation reverse engineers or deconstructs the wavefunction, yielding the
underlying classical ray structure. Our approach makes possible interpreting
the dynamics of systems where the probability flux is uniformly zero or
strongly misleading. The new technique is demonstrated by the calculation of
particle flow maps of the classical dynamics underlying a quantum wavefunction.Comment: Accepted to EP
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
Framework for non-perturbative analysis of a Z(3)-symmetric effective theory of finite temperature QCD
We study a three dimensional Z(3)-symmetric effective theory of high
temperature QCD. The exact lattice-continuum relations, needed in order to
perform lattice simulations with physical parameters, are computed to order
O(a^0) in lattice perturbation theory. Lattice simulations are performed to
determine the phase structure of a subset of the parameter space.Comment: 28 pages, 11 figures; v3: references rearranged, typos corrected,
figs changed, published versio
Anatomy of Malicious Singularities
As well known, the b-boundaries of the closed Friedman world model and of
Schwarzschild solution consist of a single point. We study this phenomenon in a
broader context of differential and structured spaces. We show that it is an
equivalence relation , defined on the Cauchy completed total space
of the frame bundle over a given space-time, that is responsible for
this pathology. A singularity is called malicious if the equivalence class
related to the singularity remains in close contact with all other
equivalence classes, i.e., if for every . We
formulate conditions for which such a situation occurs. The differential
structure of any space-time with malicious singularities consists only of
constant functions which means that, from the topological point of view,
everything collapses to a single point. It was noncommutative geometry that was
especially devised to deal with such situations. A noncommutative algebra on
, which turns out to be a von Neumann algebra of random operators,
allows us to study probabilistic properties (in a generalized sense) of
malicious singularities. Our main result is that, in the noncommutative regime,
even the strongest singularities are probabilistically irrelevant.Comment: 16 pages in LaTe
Scarring by homoclinic and heteroclinic orbits
In addition to the well known scarring effect of periodic orbits, we show
here that homoclinic and heteroclinic orbits, which are cornerstones in the
theory of classical chaos, also scar eigenfunctions of classically chaotic
systems when associated closed circuits in phase space are properly quantized,
thus introducing strong quantum correlations. The corresponding quantization
rules are also established. This opens the door for developing computationally
tractable methods to calculate eigenstates of chaotic systems.Comment: 5 pages, 4 figure
Single spin asymmetries in inclusive hadron production from SIDIS to hadronic collisions: universality and phenomenology
In a perturbative QCD approach, with inclusion of spin and transverse
momentum effects, experimental data on azimuthal asymmetries observed in
polarized semi-inclusive deeply inelastic scattering and e+ e- annihilations
can be used to determine the Sivers, transversity and Collins soft functions.
By using these functions, within the same scheme, we predict p(transv.
polarized) p -> h + X single spin asymmetries in remarkable agreement with RHIC
experimental data.Comment: 5 pages, 6 ps figure
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