3,743 research outputs found
Families of classical subgroup separable superintegrable systems
We describe a method for determining a complete set of integrals for a
classical Hamiltonian that separates in orthogonal subgroup coordinates. As
examples, we use it to determine complete sets of integrals, polynomial in the
momenta, for some families of generalized oscillator and Kepler-Coulomb
systems, hence demonstrating their superintegrability. The latter generalizes
recent results of Verrier and Evans, and Rodriguez, Tempesta and Winternitz.
Another example is given of a superintegrable system on a non-conformally flat
space.Comment: 9 page
Is the number of Photons a Classical Invariant?
We describe an apparent puzzle in classical electrodynamics and its
resolution. It is concerned with the Lorentz invariance of the classical analog
of the number of photons.Comment: Revised version, 3 figure
Chaos in a Relativistic 3-body Self-Gravitating System
We consider the 3-body problem in relativistic lineal gravity and obtain an
exact expression for its Hamiltonian and equations of motion. While
general-relativistic effects yield more tightly-bound orbits of higher
frequency compared to their non-relativistic counterparts, as energy increases
we find in the equal-mass case no evidence for either global chaos or a
breakdown from regular to chaotic motion, despite the high degree of
non-linearity in the system. We find numerical evidence for a countably
infinite class of non-chaotic orbits, yielding a fractal structure in the outer
regions of the Poincare plot.Comment: 9 pages, LaTex, 3 figures, final version to appear in Phys. Rev. Let
Stratigraphic Column of the Kope and Fairview Formations, Kentucky 445, Brent, Kentucky
The Upper Ordovician Kope Formation is exposed over a broad area of southwestern Ohio, southeastern Indiana, and northern Kentucky (Weir and others, 1984). Roadcuts along Ky. 445 near Brent (Figs. 2-3) and adjacent roadcuts along Interstate 275 expose a nearly complete section of the Kope Formation as well as the overlying Fairview Formation
Bohr-Sommerfeld Quantization of Periodic Orbits
We show, that the canonical invariant part of corrections to the
Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be
computed by the Bohr-Sommerfeld quantization rules, which usually apply for
integrable systems. We argue that the information content of the classical
action and stability can be used more effectively than in the usual treatment.
We demonstrate the improvement of precision on the example of the three disk
scattering system.Comment: revte
Classification of phase transitions and ensemble inequivalence, in systems with long range interactions
Systems with long range interactions in general are not additive, which can
lead to an inequivalence of the microcanonical and canonical ensembles. The
microcanonical ensemble may show richer behavior than the canonical one,
including negative specific heats and other non-common behaviors. We propose a
classification of microcanonical phase transitions, of their link to canonical
ones, and of the possible situations of ensemble inequivalence. We discuss
previously observed phase transitions and inequivalence in self-gravitating,
two-dimensional fluid dynamics and non-neutral plasmas. We note a number of
generic situations that have not yet been observed in such systems.Comment: 42 pages, 11 figures. Accepted in Journal of Statistical Physics.
Final versio
Light-Front Nuclear Physics: Mean Field Theory for Finite Nuclei
A light-front treatment for finite nuclei is developed from a relativistic
effective Lagrangian (QHD1) involving nucleons, scalar mesons and vector
mesons. We show that the necessary variational principle is a constrained one
which fixes the expectation value of the total momentum operator to be
the same as that for . This is the same as minimizing the sum of the total
momentum operators: . We obtain a new light-front version of the
equation that defines the single nucleon modes. The solutions of this equation
are approximately a non-trivial phase factor times certain solutions of the
usual equal-time Dirac equation. The ground state wave function is treated as a
meson-nucleon Fock state, and the meson fields are treated as expectation
values of field operators in that ground state. The resulting equations for
these expectation values are shown to be closely related to the usual meson
field equations. A new numerical technique to solve the self-consistent field
equations is introduced and applied to O and Ca. The computed
binding energies are essentially the same as for the usual equal-time theory.
The nucleon plus momentum distribution (probability for a nucleon to have a
given value of ) is obtained, and peaks for values of about seventy
percent of the nucleon mass. The mesonic component of the ground state wave
function is used to determine the scalar and vector meson momentum distribution
functions, with a result that the vector mesons carry about thirty percent of
the nuclear plus-momentum. The vector meson momentum distribution becomes more
concentrated at as increases.Comment: 36 pages, 2 figure
Nuclear medium modification of the F2 structure function
We study the nuclear effects in the electromagnetic structure function
F2(x,Q^2) in nuclei in the deep inelastic lepton nucleus scattering process by
taking into account Fermi motion, binding, pion and rho meson cloud
contributions. Calculations have been done in a local density approximation
using relativistic nuclear spectral functions which include nucleon
correlations for nuclear matter. The ratios over deuteron structure function
are obtained and compared with the recent JLAB results for light nuclei with
special attention to the slope of the x distributions. This magnitude shows a
non trivial A dependence and it is insensitive to possible normalization
uncertainties. The results have also been compared with some of the older
experiments using intermediate mass nuclei.Comment: 19 pages, 8 figures. This version matches accepted version to be
published in Nuclear Physics
Mixing Quantum and Classical Mechanics
Using a group theoretical approach we derive an equation of motion for a
mixed quantum-classical system. The quantum-classical bracket entering the
equation preserves the Lie algebra structure of quantum and classical
mechanics: The bracket is antisymmetric and satisfies the Jacobi identity, and,
therefore, leads to a natural description of interaction between quantum and
classical degrees of freedom. We apply the formalism to coupled quantum and
classical oscillators and show how various approximations, such as the
mean-field and the multiconfiguration mean-field approaches, can be obtained
from the quantum-classical equation of motion.Comment: 31 pages, LaTeX2
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