3,662 research outputs found
Quantum integrability of quadratic Killing tensors
Quantum integrability of classical integrable systems given by quadratic
Killing tensors on curved configuration spaces is investigated. It is proven
that, using a "minimal" quantization scheme, quantum integrability is insured
for a large class of classic examples.Comment: LaTeX 2e, no figure, 35 p., references added, minor modifications. To
appear in the J. Math. Phy
Corrections to: \'Constrained normalization of Hamiltonian systems and perturbed Keplerian motion\'
Consider a Hamiltonian system (H, 2n ,). LetM be a symplectic submanifold of (2n ,). The system (H, 2n ,) constrained toM is (HM, M, M). In this paper we give an algorithm which normalizes the system on 2n in such a way that restricted toM we have normalized the constrained system. This procedure is then applied to perturbed Kepler systems such as the lunar problem and the main problem of artificial satellite theory. Wir betrachten ein Hamiltonisches System (H, 2n ,). SeiMein symplectisches Submanifold von (2n ,). Das System (H, 2n ,), aufM beschränkt, ist (HM,M,M). In der vorliegenden Arbeit wird ein Algorithmus vorgeschlagen, der dieses System so auf 2n normalisiert, daß das aufM beschränkte System auch normalisiert ist. Dieser Algorithmus wird dann auf gestörte Keplersysteme, wie z. B. das Hill-sche Mondproblem und das Hauptproblem der Theorie der künstlichen Satelliten, angewendet
Evolution of spectral properties along the O(6)-U(5) transition in the interacting boson model. II. Classical trajectories
This article continues our previous study of level dynamics in the
[O(6)-U(5)]O(5) transition of the interacting boson model
[nucl-th/0504016] using the semiclassical theory of spectral fluctuations. We
find classical monodromy, related to a singular bundle of orbits with infinite
period at energy E=0, and bifurcations of numerous periodic orbits for E>0. The
spectrum of allowed ratios of periods associated with beta- and
gamma-vibrations exhibits an abrupt change around zero energy. These findings
explain anomalous bunching of quantum states in the E0 region, which
is responsible for the redistribution of levels between O(6) and U(5)
multiplets.Comment: 11 pages, 7 figures; continuation of nucl-th/050401
Vanishing Twist near Focus-Focus Points
We show that near a focus-focus point in a Liouville integrable Hamiltonian
system with two degrees of freedom lines of locally constant rotation number in
the image of the energy-momentum map are spirals determined by the eigenvalue
of the equilibrium. From this representation of the rotation number we derive
that the twist condition for the isoenergetic KAM condition vanishes on a curve
in the image of the energy-momentum map that is transversal to the line of
constant energy. In contrast to this we also show that the frequency map is
non-degenerate for every point in a neighborhood of a focus-focus point.Comment: 13 page
Planning the Future of U.S. Particle Physics (Snowmass 2013): Chapter 4: Cosmic Frontier
These reports present the results of the 2013 Community Summer Study of the
APS Division of Particles and Fields ("Snowmass 2013") on the future program of
particle physics in the U.S. Chapter 4, on the Cosmic Frontier, discusses the
program of research relevant to cosmology and the early universe. This area
includes the study of dark matter and the search for its particle nature, the
study of dark energy and inflation, and cosmic probes of fundamental
symmetries.Comment: 61 page
Maslov Indices and Monodromy
We prove that for a Hamiltonian system on a cotangent bundle that is
Liouville-integrable and has monodromy the vector of Maslov indices is an
eigenvector of the monodromy matrix with eigenvalue 1. As a corollary the
resulting restrictions on the monodromy matrix are derived.Comment: 6 page
Semiclassical analysis of Wigner -symbol
We analyze the asymptotics of the Wigner -symbol as a matrix element
connecting eigenfunctions of a pair of integrable systems, obtained by lifting
the problem of the addition of angular momenta into the space of Schwinger's
oscillators. A novel element is the appearance of compact Lagrangian manifolds
that are not tori, due to the fact that the observables defining the quantum
states are noncommuting. These manifolds can be quantized by generalized
Bohr-Sommerfeld rules and yield all the correct quantum numbers. The geometry
of the classical angular momentum vectors emerges in a clear manner. Efficient
methods for computing amplitude determinants in terms of Poisson brackets are
developed and illustrated.Comment: 7 figure file
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