473 research outputs found
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
Phenomenology of Noncommutative Field Theories
Experimental limits on the violation of four-dimensional Lorentz invariance
imply that noncommutativity among ordinary spacetime dimensions must be small.
In this talk, I review the most stringent bounds on noncommutative field
theories and suggest a possible means of evading them: noncommutativity may be
restricted to extra, compactified spatial dimensions. Such theories have a
number of interesting features, including Abelian gauge fields whose
Kaluza-Klein excitations have self couplings. We consider six-dimensional QED
in a noncommutative bulk, and discuss the collider signatures of the model.Comment: 7 pages RevTeX, 4 eps figures, Invited plenary talk, IX Mexican
Workshop on Particles and Fields, November 17-22, 2003, Universidad de
Colima, Mexic
Noncommutative Field Theory from twisted Fock space
We construct a quantum field theory in noncommutative spacetime by twisting
the algebra of quantum operators (especially, creation and annihilation
operators) of the corresponding quantum field theory in commutative spacetime.
The twisted Fock space and S-matrix consistent with this algebra have been
constructed. The resultant S-matrix is consistent with that of Filk\cite{Filk}.
We find from this formulation that the spin-statistics relation is not violated
in the canonical noncommutative field theories.Comment: 13 pages, 1 figure, minor changes, add reference
A New Quantization Map
In this paper we find a simple rule to reproduce the algebra of quantum
observables using only the commutators and operators which appear in the
Koopman-von Neumann (KvN) formulation of classical mechanics. The usual Hilbert
space of quantum mechanics becomes embedded in the KvN Hilbert space: in
particular it turns out to be the subspace on which the quantum positions Q and
momenta P act irreducibly.Comment: 12 pages, 1 figure, Late
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.
Action scales for quantum decoherence and their relation to structures in phase space
A characteristic action is defined whose magnitude determines some
properties of the expectation value of a general quantum displacement operator.
These properties are related to the capability of a given environmental
`monitoring' system to induce decoherence in quantum systems coupled to it. We
show that the scale for effective decoherence is given by . We relate this characteristic action with a complementary
quantity, , and analyse their connection with the main features of
the pattern of structures developed by the environmental state in different
phase space representations. The relevance of the -action scale is
illustrated using both a model quantum system solved numerically and a set of
model quantum systems for which analytical expressions for the time-averaged
expectation value of the displacement operator are obtained explicitly.Comment: 12 pages, 3 figure
Quantum deformation of the Dirac bracket
The quantum deformation of the Poisson bracket is the Moyal bracket. We
construct quantum deformation of the Dirac bracket for systems which admit
global symplectic basis for constraint functions. Equivalently, it can be
considered as an extension of the Moyal bracket to second-class constraints
systems and to gauge-invariant systems which become second class when
gauge-fixing conditions are imposed.Comment: 18 pages, REVTe
Wigner Trajectory Characteristics in Phase Space and Field Theory
Exact characteristic trajectories are specified for the time-propagating
Wigner phase-space distribution function. They are especially simple---indeed,
classical---for the quantized simple harmonic oscillator, which serves as the
underpinning of the field theoretic Wigner functional formulation introduced.
Scalar field theory is thus reformulated in terms of distributions in field
phase space. Applications to duality transformations in field theory are
discussed.Comment: 9 pages, LaTex2
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