2,487 research outputs found
Deformations of Calogero-Moser Systems
Recent results are surveyed pertaining to the complete integrability of some
novel n-particle models in dimension one. These models generalize the
Calogero-Moser systems related to classical root systems. Quantization leads to
difference operators instead of differential operators.Comment: 4 pages, Latex (version 2.09), talk given at NEEDS '93, Gallipoli,
Ital
Long-Time Asymptotics of the Toda Lattice for Decaying Initial Data Revisited
The purpose of this article is to give a streamlined and self-contained
treatment of the long-time asymptotics of the Toda lattice for decaying initial
data in the soliton and in the similarity region via the method of nonlinear
steepest descent.Comment: 41 page
Angular distribution of photoluminescence as a probe of Bose Condensation of trapped excitons
Recent experiments on two-dimensional exciton systems have shown the excitons
collect in shallow in-plane traps. We find that Bose condensation in a trap
results in a dramatic change of the exciton photoluminescence (PL) angular
distribution. The long-range coherence of the condensed state gives rise to a
sharply focussed peak of radiation in the direction normal to the plane. By
comparing the PL profile with and without Bose Condensation we provide a simple
diagnostic for the existence of a Bose condensate. The PL peak has strong
temperature dependence due to the thermal order parameter phase fluctuations
across the system. The angular PL distribution can also be used for imaging
vortices in the trapped condensate. Vortex phase spatial variation leads to
destructive interference of PL radiation in certain directions, creating nodes
in the PL distribution that imprint the vortex configuration.Comment: 4 pages, 3 figure
Two-dimensional metric and tetrad gravities as constrained second order systems
Using the Gitman-Lyakhovich-Tyutin generalization of the Ostrogradsky method
for analyzing singular systems, we consider the Hamiltonian formulation of
metric and tetrad gravities in two-dimensional Riemannian spacetime treating
them as constrained higher-derivative theories. The algebraic structure of the
Poisson brackets of the constraints and the corresponding gauge transformations
are investigated in both cases.Comment: replaced with revised version published in
Mod.Phys.Lett.A22:17-28,200
Comments on ``A note on first-order formalism and odd-derivative actions'' by S. Deser
We argue that the obstacles to having a first-order formalism for
odd-derivative actions presented in a pedagogical note by Deser are based on
examples which are not first-order forms of the original actions. The general
derivation of an equivalent first-order form of the original second-order
action is illustrated using the example of topologically massive
electrodynamics (TME). The correct first-order formulations of the TME model
keep intact the gauge invariance presented in its second-order form
demonstrating that the gauge invariance is not lost in the Ostrogradsky
process.Comment: 6 pages, references are adde
Examining the Bidirectional Relationship Between Entrepreneurship and Economic Growth: Is Entrepreneurship Endogenous?
Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems
We work out finite-dimensional integral formulae for the scalar product of
genus one states of the group Chern-Simons theory with insertions of Wilson
lines. Assuming convergence of the integrals, we show that unitarity of the
elliptic Knizhnik-Zamolodchikov-Bernard connection with respect to the scalar
product of CS states is closely related to the Bethe Ansatz for the commuting
Hamiltonians building up the connection and quantizing the quadratic
Hamiltonians of the elliptic Hitchin system.Comment: 24 pages, latex fil
The Fermi-Pasta-Ulam recurrence and related phenomena for 1D shallow-water waves in a finite basin
In this work, different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are
simulated numerically for fully nonlinear "one-dimensional" potential water
waves in a finite-depth flume between two vertical walls. In such systems, the
FPU recurrence is closely related to the dynamics of coherent structures
approximately corresponding to solitons of the integrable Boussinesq system. A
simplest periodic solution of the Boussinesq model, describing a single soliton
between the walls, is presented in an analytical form in terms of the elliptic
Jacobi functions. In the numerical experiments, it is observed that depending
on a number of solitons in the flume and their parameters, the FPU recurrence
can occur in a simple or complicated manner, or be practically absent. For
comparison, the nonlinear dynamics of potential water waves over nonuniform
beds is simulated, with initial states taken in the form of several pairs of
colliding solitons. With a mild-slope bed profile, a typical phenomenon in the
course of evolution is appearance of relatively high (rogue) waves, while for
random, relatively short-correlated bed profiles it is either appearance of
tall waves, or formation of sharp crests at moderate-height waves.Comment: revtex4, 10 pages, 33 figure
Exact solutions for a class of integrable Henon-Heiles-type systems
We study the exact solutions of a class of integrable Henon-Heiles-type
systems (according to the analysis of Bountis et al. (1982)). These solutions
are expressed in terms of two-dimensional Kleinian functions. Special periodic
solutions are expressed in terms of the well-known Weierstrass function. We
extend some of our results to a generalized Henon-Heiles-type system with n+1
degrees of freedom.Comment: RevTeX4-1, 13 pages, Submitted to J. Math. Phy
Fermions, Skyrmions and the 3-Sphere
This paper investigates a background charge one Skyrme field chirally coupled
to light fermions on the 3-sphere. The Dirac equation for the system commutes
with a generalised angular momentum or grand spin. It can be solved explicitly
for a Skyrme configuration given by the hedgehog form. The energy spectrum and
degeneracies are derived for all values of the grand spin. Solutions for
non-zero grand spin are each characterised by a set of four polynomials. The
paper also discusses the energy of the Dirac sea using zeta function
regularization.Comment: 19 pages, 2 figure
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