1,250 research outputs found
Some basic properties of infinite dimensional Hamiltonian systems
We consider some fundamental properties of infinite dimensional Hamiltonian systems,
both linear and nonlinear. For exemple, in the case of linear systems, we prove a symplectic
version of the teorem of M. Stone. In the general case we establish conservation of energy
and the moment function for system with symmetry. (The moment function was introduced
by B. Kostant and J .M. Souriau). For infinite dimensional systems these conservation
laws are more delicate than those for finite dimensional systems because we are dealing with
partial as opposed to ordinary differential equations
Quantum Canonical Transformations revisited
A preferred form for the path integral discretization is suggested that
allows the implementation of canonical transformations in quantum theory.Comment: 8 pages, LaTe
On the Groenewold-Van Hove problem for R^{2n}
We discuss the Groenewold-Van Hove problem for R^{2n}, and completely solve
it when n = 1. We rigorously show that there exists an obstruction to
quantizing the Poisson algebra of polynomials on R^{2n}, thereby filling a gap
in Groenewold's original proof without introducing extra hypotheses. Moreover,
when n = 1 we determine the largest Lie subalgebras of polynomials which can be
unambiguously quantized, and explicitly construct all their possible
quantizations.Comment: 15 pages, Latex. Error in the proof of Prop. 3 corrected; minor
rewritin
Recent revisions to corporate profits: what we know and when we knew it
Initial estimates in the National Income and Product Accounts significantly overstated U.S. corporate profits for the 1998-2000 period. Subsequent revisions reveal that the profitability of the nation's corporate sector in the late 1990s was substantially weaker than "real-time" data indicated. An unexpected surge in employee stock options exercised-and perhaps, in some sectors, firms' inflated statements of profit-may help explain the large downward revisions.Corporate profits ; Stock options ; Statistics ; Economic indicators
The Effect of Retinoids on the Regenerating Axolotl Spinal Cord
In order to further elucidate the mechanics of the retinoid pathway on Urodele spinal cord regeneration, we employed Antibody/Horseradish Peroxidase Staining of both intact and regenerating Axolotl spinal cord tissues obtained from adult and juvenile animals to determine expression of two retinoid pathway components: Cellular Retinoic Acid Binding Protein II (CRABP II) and Cellular Retinol Binding Protein I (CRBP I). Current results demonstrate that CRABP II is heavily expressed in the arachnoid mater meningeal layer; CRPB I, however, is expressed in the following locations: the pia mater meningeal layer, the nuclei and cytoplasm of gray matter neuroblasts, as well as processes derived from neuroblasts and ependyma. Moreover, the morphogenic nature of the retinoids may possess a significant role in the regeneration-permissive interaction of the meninges and ependyma of the Axolotl spinal cord
Sufficient conditions for the anti-Zeno effect
The ideal anti-Zeno effect means that a perpetual observation leads to an
immediate disappearance of the unstable system. We present a straightforward
way to derive sufficient conditions under which such a situation occurs
expressed in terms of the decaying states and spectral properties of the
Hamiltonian. They show, in particular, that the gap between Zeno and anti-Zeno
effects is in fact very narrow.Comment: LatEx2e, 9 pages; a revised text, to appear in J. Phys. A: Math. Ge
Dynamics and Lax-Phillips scattering for generalized Lamb models
This paper treats the dynamics and scattering of a model of coupled
oscillating systems, a finite dimensional one and a wave field on the half
line. The coupling is realized producing the family of selfadjoint extensions
of the suitably restricted self-adjoint operator describing the uncoupled
dynamics. The spectral theory of the family is studied and the associated
quadratic forms constructed. The dynamics turns out to be Hamiltonian and the
Hamiltonian is described, including the case in which the finite dimensional
systems comprises nonlinear oscillators; in this case the dynamics is shown to
exist as well. In the linear case the system is equivalent, on a dense
subspace, to a wave equation on the half line with higher order boundary
conditions, described by a differential polynomial explicitely
related to the model parameters. In terms of such structure the Lax-Phillips
scattering of the system is studied. In particular we determine the incoming
and outgoing translation representations, the scattering operator, which turns
out to be unitarily equivalent to the multiplication operator given by the
rational function , and the Lax-Phillips semigroup,
which describes the evolution of the states which are neither incoming in the
past nor outgoing in the future
Geometrical Description of Quantum Mechanics - Transformations and Dynamics
In this paper we review a proposed geometrical formulation of quantum
mechanics. We argue that this geometrization makes available mathematical
methods from classical mechanics to the quantum frame work. We apply this
formulation to the study of separability and entanglement for states of
composite quantum systems.Comment: 22 pages, to be published in Physica Script
Equivalence of Local and Separable Realizations of the Discontinuity-Inducing Contact Interaction and Its Perturbative Renormalizability
We prove that the separable and local approximations of the
discontinuity-inducing zero-range interaction in one-dimensional quantum
mechanics are equivalent. We further show that the interaction allows the
perturbative treatment through the coupling renormalization.
Keywords: one-dimensional system, generalized contact interaction,
renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.MdComment: ReVTeX 7pgs, doubl column, no figure, See also the website
http://www.mech.kochi-tech.ac.jp/cheon
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