Geometric approach to chaos in the classical dynamics of abelian lattice gauge theory

A Riemannian geometrization of dynamics is used to study chaoticity in the classical Hamiltonian dynamics of a U(1) lattice gauge theory. This approach allows one to obtain analytical estimates of the largest Lyapunov exponent in terms of time averages of geometric quantities. These estimates are compared with the results of numerical simulations, and turn out to be very close to the values extrapolated for very large lattice sizes even when the geometric quantities are computed using small lattices. The scaling of the Lyapunov exponent with the energy density is found to be well described by a quadratic power law.Comment: REVTeX, 9 pages, 4 PostScript figures include

Geometric Approach to Lyapunov Analysis in Hamiltonian Dynamics

As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of the Hamiltonian function. To separate out these two directions and to apply Lyapunov analysis effectively in directions for which Lyapunov exponents are not trivial, a geometric method is proposed for natural Hamiltonian systems, in particular. In this geometric method, Hamiltonian flows of a natural Hamiltonian system are regarded as geodesic flows on the cotangent bundle of a Riemannian manifold with a suitable metric. Stability/instability of the geodesic flows is then analyzed by linearized equations of motion which are related to the Jacobi equations on the Riemannian manifold. On some geometric setting on the cotangent bundle, it is shown that along a geodesic flow in question, there exist Lyapunov vectors such that two of them are in the two marginal directions and the others orthogonal to the marginal directions. It is also pointed out that Lyapunov vectors with such properties can not be obtained in general by the usual method which uses linearized Hamilton's equations of motion. Furthermore, it is observed from numerical calculation for a model system that Lyapunov exponents calculated in both methods, geometric and usual, coincide with each other, independently of the choice of the methods.Comment: 22 pages, 14 figures, REVTeX

Relaxation of classical many-body hamiltonians in one dimension

The relaxation of Fourier modes of hamiltonian chains close to equilibrium is studied in the framework of a simple mode-coupling theory. Explicit estimates of the dependence of relevant time scales on the energy density (or temperature) and on the wavenumber of the initial excitation are given. They are in agreement with previous numerical findings on the approach to equilibrium and turn out to be also useful in the qualitative interpretation of them. The theory is compared with molecular dynamics results in the case of the quartic Fermi-Pasta-Ulam potential.Comment: 9 pag. 6 figs. To appear in Phys.Rev.

On the mean-field spherical model

Exact solutions are obtained for the mean-field spherical model, with or without an external magnetic field, for any finite or infinite number N of degrees of freedom, both in the microcanonical and in the canonical ensemble. The canonical result allows for an exact discussion of the loci of the Fisher zeros of the canonical partition function. The microcanonical entropy is found to be nonanalytic for arbitrary finite N. The mean-field spherical model of finite size N is shown to be equivalent to a mixed isovector/isotensor sigma-model on a lattice of two sites. Partial equivalence of statistical ensembles is observed for the mean-field spherical model in the thermodynamic limit. A discussion of the topology of certain state space submanifolds yields insights into the relation of these topological quantities to the thermodynamic behavior of the system in the presence of ensemble nonequivalence.Comment: 21 pages, 5 figure

Young stars in the periphery of the Large Magellanic Cloud

Despite their close proximity, the complex interplay between the two Magellanic Clouds, the Milky Way, and the resulting tidal features, is still poorly understood. Recent studies have shown that the Large Magellanic Cloud (LMC) has a very extended disk strikingly perturbed in its outskirts. We search for recent star formation in the far outskirts of the LMC, out to ~30 degrees from its center. We have collected intermediate-resolution spectra of thirty-one young star candidates in the periphery of the LMC and measured their radial velocity, stellar parameters, distance and age. Our measurements confirm membership to the LMC of six targets, for which the radial velocity and distance values match well those of the Cloud. These objects are all young (10-50 Myr), main-sequence stars projected between 7 and 13 degrees from the center of the parent galaxy. We compare the velocities of our stars with those of a disk model, and find that our stars have low to moderate velocity differences with the disk model predictions, indicating that they were formed in situ. Our study demonstrates that recent star formation occurred in the far periphery of the LMC, where thus far only old objects were known. The spatial configuration of these newly-formed stars appears ring-like with a radius of 12 kpc, and a displacement of 2.6 kpc from the LMC's center. This structure, if real, would be suggestive of a star-formation episode triggered by an off-center collision between the Small Magellanic Cloud and the LMC's disk.Comment: Accepted for publication in MNRA