13,851 research outputs found
The Hodge Conjecture for general Prym varieties
The space of Hodge cycles of the general Prym variety is proved to be
generated by its Neron-Severi group.Comment: LaTeX-fil
The Arbitrary Trajectory Quantization Method
The arbitrary trajectory quantization method (ATQM) is a time dependent
approach to quasiclassical quantization based on the approximate dual
relationship that exists between the quantum energy spectra and classical
periodic orbits. It has recently been shown however, that, for polygonal
billiards, the periodicity criterion must be relaxed to include closed
almost-periodic (CAP) orbit families in this relationship. In light of this
result, we reinvestigate the ATQM and show that at finite energies, a
smoothened quasiclassical kernel corresponds to the modified formula that
includes CAP families while the delta function kernel corresponding to the
periodic orbit formula is recovered at high energies. Several clarifications
are also provided.Comment: revtex, ps figure
The CWKB Method of Particle Production in Periodic Potential
In this work we study the particle production in time dependent periodic
potential using the method of complex time WKB (CWKB) approximation. In the
inflationary cosmology at the end of inflationary stage, the potential becomes
time dependent as well as periodic. Reheating occurs due to particle production
by the oscillating inflaton field. Using CWKB we obtain almost identical
results on catastrophic particle production as obtained by others.Comment: 17 pages, latex, 2 figure
A kinetic Ising model study of dynamical correlations in confined fluids: Emergence of both fast and slow time scales
Experiments and computer simulation studies have revealed existence of rich
dynamics in the orientational relaxation of molecules in confined systems such
as water in reverse micelles, cyclodextrin cavities and nano-tubes. Here we
introduce a novel finite length one dimensional Ising model to investigate the
propagation and the annihilation of dynamical correlations in finite systems
and to understand the intriguing shortening of the orientational relaxation
time that has been reported for small sized reverse micelles. In our finite
sized model, the two spins at the two end cells are oriented in the opposite
directions, to mimic the effects of surface that in real system fixes water
orientation in the opposite directions. This produces opposite polarizations to
propagate inside from the surface and to produce bulk-like condition at the
centre. This model can be solved analytically for short chains. For long chains
we solve the model numerically with Glauber spin flip dynamics (and also with
Metropolis single-spin flip Monte Carlo algorithm). We show that model nicely
reproduces many of the features observed in experiments. Due to the destructive
interference among correlations that propagate from the surface to the core,
one of the rotational relaxation time components decays faster than the bulk.
In general, the relaxation of spins is non-exponential due to the interplay
between various interactions. In the limit of strong coupling between the spins
or in the limit of low temperature, the nature of relaxation of the spins
undergoes a qualitative change with the emergence of a homogeneous dynamics
where decay is predominantly exponential, again in agreement with experiments.Comment: 27 pages, 8 figure
Periodic Orbits in Polygonal Billiards
We review some properties of periodic orbit families in polygonal billiards
and discuss in particular a sum rule that they obey. In addition, we provide
algorithms to determine periodic orbit families and present numerical results
that shed new light on the proliferation law and its variation with the genus
of the invariant surface. Finally, we deal with correlations in the length
spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure
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