1,397 research outputs found
Quantization Of Cyclotron Motion and Quantum Hall Effect
We present a two dimensional model of IQHE in accord with the cyclotron
motion. The quantum equation of the QHE curve and a new definition of filling
factor are also given.Comment: 13 Pages, Latex, 1 figure, to appear in Europhys. Lett. September
199
Effective Equations of Motion for Quantum Systems
In many situations, one can approximate the behavior of a quantum system,
i.e. a wave function subject to a partial differential equation, by effective
classical equations which are ordinary differential equations. A general method
and geometrical picture is developed and shown to agree with effective action
results, commonly derived through path integration, for perturbations around a
harmonic oscillator ground state. The same methods are used to describe
dynamical coherent states, which in turn provide means to compute quantum
corrections to the symplectic structure of an effective system.Comment: 31 pages; v2: a new example, new reference
Synchronizing nitrogen application with uptake using urease and nitrification inhibitors to maximize nitrogen use in forage seed stands in northeastern Saskatchewan
Non-Peer Reviewe
Noncentral extensions as anomalies in classical dynamical systems
A two cocycle is associated to any action of a Lie group on a symplectic
manifold. This allows to enlarge the concept of anomaly in classical dynamical
systems considered by F. Toppan [in J. Nonlinear Math. Phys. 8, no.3 (2001)
518-533] so as to encompass some extensions of Lie algebras related to
noncanonical actions.Comment: arxiv version is already officia
The existence of time
Of those gauge theories of gravity known to be equivalent to general
relativity, only the biconformal gauging introduces new structures - the
quotient of the conformal group of any pseudo-Euclidean space by its Weyl
subgroup always has natural symplectic and metric structures. Using this metric
and symplectic form, we show that there exist canonically conjugate,
orthogonal, metric submanifolds if and only if the original gauged space is
Euclidean or signature 0. In the Euclidean cases, the resultant configuration
space must be Lorentzian. Therefore, in this context, time may be viewed as a
derived property of general relativity.Comment: 21 pages (Reduced to clarify and focus on central argument; some
calculations condensed; typos corrected
Abelian BF theory and Turaev-Viro invariant
The U(1) BF Quantum Field Theory is revisited in the light of
Deligne-Beilinson Cohomology. We show how the U(1) Chern-Simons partition
function is related to the BF one and how the latter on its turn coincides with
an abelian Turaev-Viro invariant. Significant differences compared to the
non-abelian case are highlighted.Comment: 47 pages and 6 figure
Geometrical aspects of integrable systems
We review some basic theorems on integrability of Hamiltonian systems, namely
the Liouville-Arnold theorem on complete integrability, the Nekhoroshev theorem
on partial integrability and the Mishchenko-Fomenko theorem on noncommutative
integrability, and for each of them we give a version suitable for the
noncompact case. We give a possible global version of the previous local
results, under certain topological hypotheses on the base space. It turns out
that locally affine structures arise naturally in this setting.Comment: It will appear on International Journal of Geometric Methods in
Modern Physics vol.5 n.3 (May 2008) issu
Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty
We analyze the quantum dynamics of the non-relativistic two-dimensional
isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken
as toy model to analyze some of the various quantum theories that can be built
from the application of Dirac's quantization rule to the various symplectic
structures recently reported for this classical system. It is pointed out that
that these quantum theories are inequivalent in the sense that the mean values
for the operators (observables) associated with the same physical classical
observable do not agree with each other. The inequivalence does not arise from
ambiguities in the ordering of operators but from the fact of having several
symplectic structures defined with respect to the same set of coordinates. It
is also shown that the uncertainty relations between the fundamental
observables depend on the particular quantum theory chosen. It is important to
emphasize that these (somehow paradoxical) results emerge from the combination
of two paradigms: Dirac's quantization rule and the usual Copenhagen
interpretation of quantum mechanics.Comment: 8 pages, LaTex file, no figures. Accepted for publication in Phys.
Rev.
Effects of off great-circle propagation on the phase of long-period surface waves
Surface wave phase corrections for departures from great-circle propagation are computed using two-point ray-tracing through the aspherical earth model M84C of Woodhouse & Dziewonski (1984). For Rayleigh and Love waves with periods in the range 100–250 s, we determine whether these corrections provide significant variance reductions in source determinations compared with corrections calculated assuming great-circle propagation through the heterogeneous structure. For most source-receiver geometries, the off great-circle travel-time effects are small (< 10 s) for second and third orbits (e.g. R2 and R3), and their application in source determinations does not significantly reduce the data variance. This suggests that for the loworder heterogeneous models currently available the geometrical optics approximation is valid for long-period low orbit surface waves. Off great-circle phase anomalies increase quasi-linearly with increasing orbit number, indicating that the geometrical optics approximation degrades for higher orbits, which emphasizes the importance of developing higher order approximations for free-oscillation studies.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73147/1/j.1365-246X.1987.tb05217.x.pd
A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry
We introduce an antisymplectic Dirac operator and antisymplectic gamma
matrices. We explore similarities between, on one hand, the
Schroedinger-Lichnerowicz formula for spinor bundles in Riemannian spin
geometry, which contains a zeroth-order term proportional to the Levi-Civita
scalar curvature, and, on the other hand, the nilpotent, Grassmann-odd,
second-order \Delta operator in antisymplectic geometry, which in general has a
zeroth-order term proportional to the odd scalar curvature of an arbitrary
antisymplectic and torsionfree connection that is compatible with the measure
density. Finally, we discuss the close relationship with the two-loop scalar
curvature term in the quantum Hamiltonian for a particle in a curved Riemannian
space.Comment: 55 pages, LaTeX. v2: Subsection 3.10 expanded. v3: Reference added.
v4: Published versio
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