619 research outputs found
Wave Packets in Discrete Quantum Phase Space
The properties of quantum mechanics with a discrete phase space are studied.
The minimum uncertainty states are found, and these states become the Gaussian
wave packets in the continuum limit. With a suitably chosen Hamiltonian that
gives free particle motion in the continuum limit, it is found that full or
approximate periodic time evolution can result. This represents an example of
revivals of wave packets that in the continuum limit is the familiar free
particle motion on a line. Finally we examine the uncertainty principle for
discrete phase space and obtain the correction terms to the continuum case.Comment: 19 pages, 6 figure
Kostant partition functions for affine Kac-Moody algebras
Employing the method of generating functions in conjunction with various number-thoretic identities, we obtain recursion relations for the Kostant partition functions for the affine Kac-Moody algebras The partition functions for the higher rank algebras are expressed in terms of SUˆ(2)
partition functions. We derive certain number-theoretic identities using the equivalence of our result with
the expressions derived by Kac and Peterson
Finite-Dimensional Calculus
We discuss topics related to finite-dimensional calculus in the context of
finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is
called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of
orthofermions. It is shown how to use a matrix approach to implement analytic
representations of the Heisenberg-Weyl algebra in univariate and multivariate
settings. We provide examples for the univariate case. Krawtchouk polynomials
are presented in detail, including a review of Krawtchouk polynomials that
illustrates some curious properties of the Heisenberg-Weyl algebra, as well as
presenting an approach to computing Krawtchouk expansions. From a mathematical
perspective, we are providing indications as to how to implement in finite
terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional
references include
Quantum information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit
We show that for any Hilbert-space dimension, the optimal universal quantum
cloner can be constructed from essentially the same quantum circuit, i.e., we
find a universal design for universal cloners. In the case of infinite
dimensions (which includes continuous variable quantum systems) the universal
cloner reduces to an essentially classical device. More generally, we construct
a universal quantum circuit for distributing qudits in any dimension which acts
covariantly under generalized displacements and momentum kicks. The behavior of
this covariant distributor is controlled by its initial state. We show that
suitable choices for this initial state yield both universal cloners and
optimized cloners for limited alphabets of states whose states are related by
generalized phase-space displacements.Comment: 10 revtex pages, no figure
Origin of unitary symmetry and charge conservation in strong interactions
We discuss the relation of the existence of multiplets of (strongly) interacting particles and the possible unitary symmetry of their interactions. We present here a dynamical principle which concerns the one-particle propagators (two-point functions) but yielding the existence of a (unitary) symmetry group for their trilinear interactions. We derive, as a by-product, electric charge (and hypercharge) conservation in the interaction of these particles
Statistics of Atmospheric Correlations
For a large class of quantum systems the statistical properties of their
spectrum show remarkable agreement with random matrix predictions. Recent
advances show that the scope of random matrix theory is much wider. In this
work, we show that the random matrix approach can be beneficially applied to a
completely different classical domain, namely, to the empirical correlation
matrices obtained from the analysis of the basic atmospheric parameters that
characterise the state of atmosphere. We show that the spectrum of atmospheric
correlation matrices satisfy the random matrix prescription. In particular, the
eigenmodes of the atmospheric empirical correlation matrices that have physical
significance are marked by deviations from the eigenvector distribution.Comment: 8 pages, 9 figs, revtex; To appear in Phys. Rev.
Entangling power of quantized chaotic systems
We study the quantum entanglement caused by unitary operators that have
classical limits that can range from the near integrable to the completely
chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is
studied through the von Neumann entropy of the reduced density matrices. We
demonstrate that classical chaos can lead to substantially enhanced
entanglement. Conversely, entanglement provides a novel and useful
characterization of quantum states in higher dimensional chaotic or complex
systems. Information about eigenfunction localization is stored in a graded
manner in the Schmidt vectors, and the principal Schmidt vectors can be scarred
by the projections of classical periodic orbits onto subspaces. The eigenvalues
of the reduced density matrices are sensitive to the degree of wavefunction
localization, and are roughly exponentially arranged. We also point out the
analogy with decoherence, as reduced density matrices corresponding to
subsystems of fully chaotic systems are diagonally dominant.Comment: 21 pages including 9 figs. (revtex
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