473 research outputs found
Noncommutative differential calculus for Moyal subalgebras
We build a differential calculus for subalgebras of the Moyal algebra on R^4
starting from a redundant differential calculus on the Moyal algebra, which is
suitable for reduction. In some cases we find a frame of 1-forms which allows
to realize the complex of forms as a tensor product of the noncommutative
subalgebras with the external algebra Lambda^*.Comment: 13 pages, no figures. One reference added, minor correction
The time-reversal test for stochastic quantum dynamics
The calculation of quantum dynamics is currently a central issue in
theoretical physics, with diverse applications ranging from ultra-cold atomic
Bose-Einstein condensates (BEC) to condensed matter, biology, and even
astrophysics. Here we demonstrate a conceptually simple method of determining
the regime of validity of stochastic simulations of unitary quantum dynamics by
employing a time-reversal test. We apply this test to a simulation of the
evolution of a quantum anharmonic oscillator with up to
(Avogadro's number) of particles. This system is realisable as a Bose-Einstein
condensate in an optical lattice, for which the time-reversal procedure could
be implemented experimentally.Comment: revtex4, two figures, four page
Newton's law in an effective non commutative space-time
The Newtonian Potential is computed exactly in a theory that is fundamentally
Non Commutative in the space-time coordinates. When the dispersion for the
distribution of the source is minimal (i.e. it is equal to the non commutative
parameter ), the behavior for large and small distances is analyzed.Comment: 5 page
Physical Wigner functions
In spite of their potential usefulness, the characterizations of Wigner
functions for Bose and Fermi statistics given by O'Connell and Wigner himself
almost thirty years ago has drawn little attention. With an eye towards
applications in quantum chemistry, we revisit and reformulate them in a more
convenient way.Comment: Latex, 10 page
Star product formula of theta functions
As a noncommutative generalization of the addition formula of theta
functions, we construct a class of theta functions which are closed with
respect to the Moyal star product of a fixed noncommutative parameter. These
theta functions can be regarded as bases of the space of holomorphic
homomorphisms between holomorphic line bundles over noncommutative complex
tori.Comment: 12 page
Filamentational Instability of Partially Coherent Femtosecond Optical Pulses in Air
The filamentational instability of spatially broadband femtosecond optical
pulses in air is investigated by means of a kinetic wave equation for spatially
incoherent photons. An explicit expression for the spatial amplification rate
is derived and analyzed. It is found that the spatial spectral broadening of
the pulse can lead to stabilization of the filamentation instability. Thus,
optical smoothing techniques could optimize current applications of ultra-short
laser pulses, such as atmospheric remote sensing.Comment: 8 pages, 2 figures, to appear in Optics Letter
Differential calculus and gauge transformations on a deformed space
Deformed gauge transformations on deformed coordinate spaces are considered
for any Lie algebra. The representation theory of this gauge group forces us to
work in a deformed Lie algebra as well. This deformation rests on a twisted
Hopf algebra, thus we can represent a twisted Hopf algebra on deformed spaces.
That leads to the construction of Lagrangian invariant under a twisted Lie
algebra.Comment: 14 pages, to appear in General Relativity and Gravitation Journal,
Obregon's Festschrift 2006, V2: misprints correcte
SL(2,R) model with two Hamiltonian constraints
We describe a simple dynamical model characterized by the presence of two
noncommuting Hamiltonian constraints. This feature mimics the constraint
structure of general relativity, where there is one Hamiltonian constraint
associated with each space point. We solve the classical and quantum dynamics
of the model, which turns out to be governed by an SL(2,R) gauge symmetry,
local in time. In classical theory, we solve the equations of motion, find a
SO(2,2) algebra of Dirac observables, find the gauge transformations for the
Lagrangian and canonical variables and for the Lagrange multipliers. In quantum
theory, we find the physical states, the quantum observables, and the physical
inner product, which is determined by the reality conditions. In addition, we
construct the classical and quantum evolving constants of the system. The model
illustrates how to describe physical gauge-invariant relative evolution when
coordinate time evolution is a gauge.Comment: 9 pages, 1 figure, revised version, to appear in Phys. Rev.
On the concepts of radial and angular kinetic energies
We consider a general central-field system in D dimensions and show that the
division of the kinetic energy into radial and angular parts proceeds
differently in the wavefunction picture and the Weyl-Wigner phase-space
picture. Thus, the radial and angular kinetic energies are different quantities
in the two pictures, containing different physical information, but the
relation between them is well defined. We discuss this relation and illustrate
its nature by examples referring to a free particle and to a ground-state
hydrogen atom.Comment: 10 pages, 2 figures, accepted by Phys. Rev.
Feynman Path Integral on the Noncommutative Plane
We formulate Feynman path integral on a non commutative plane using coherent
states. The propagator for a free particle exhibits UV cut-off induced by the
parameter of non commutativity.Comment: 7pages, latex 2e, no figures. Accepted for publication on J.Phys.
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