562 research outputs found
On the structure of the B\"acklund transformations for the relativistic lattices
The B\"acklund transformations for the relativistic lattices of the Toda type
and their discrete analogues can be obtained as the composition of two duality
transformations. The condition of invariance under this composition allows to
distinguish effectively the integrable cases. Iterations of the B\"acklund
transformations can be described in the terms of nonrelativistic lattices of
the Toda type. Several multifield generalizations are presented
On the one class of hyperbolic systems
The classification problem is solved for some type of nonlinear lattices. These lattices are closely related to the lattices of Ruijsenaars-Toda type and define the Bäcklund auto-transformations for the class of two-component hyperbolic systems
Higher Dimensional Classical W-Algebras
Classical -algebras in higher dimensions are constructed. This is achieved
by generalizing the classical Gel'fand-Dickey brackets to the commutative limit
of the ring of classical pseudodifferential operators in arbitrary dimension.
These -algebras are the Poisson structures associated with a higher
dimensional version of the Khokhlov-Zabolotskaya hierarchy (dispersionless
KP-hierarchy). The two dimensional case is worked out explicitly and it is
shown that the role of Diff is taken by the algebra of generators of
local diffeomorphisms in two dimensions.Comment: 22 pages, Plain TeX, KUL-TF-92/19, US-FT/6-9
Gaussian queues in light and heavy traffic
In this paper we investigate Gaussian queues in the light-traffic and in the
heavy-traffic regime. The setting considered is that of a centered Gaussian
process with stationary increments and variance
function , equipped with a deterministic drift ,
reflected at 0: We
study the resulting stationary workload process
in the limiting regimes (heavy
traffic) and (light traffic). The primary contribution is that we
show for both limiting regimes that, under mild regularity conditions on the
variance function, there exists a normalizing function such that
converges to a non-trivial
limit in
Anisotropic flows from initial state of a fast nucleus
We analyze azimuthal anisotropy in heavy ion collisions related to the
reaction plane in terms of standard reggeon approach and find that it is
nonzero even when the final state interaction is switched off. This effect can
be interpreted in terms of partonic structure of colliding nuclei. We use
Feynman diagram analysis to describe details of this mechanism. Main
qualitative features of the appropriate azimuthal correlations are discussed.Comment: 16 pages, 11 figures. This paper is an extended version of a talk
given at Session of Nuclear Physics Division of Russian Academy of Sciences
in November 200
A One-Parameter Family of Hamiltonian Structures for the KP Hierarchy and a Continuous Deformation of the Nonlinear \W_{\rm KP} Algebra
The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson
structures obtained from a generalized Adler map in the space of formal
pseudodifferential symbols with noninteger powers. The resulting \W-algebra
is a one-parameter deformation of \W_{\rm KP} admitting a central extension
for generic values of the parameter, reducing naturally to \W_n for special
values of the parameter, and contracting to the centrally extended
\W_{1+\infty}, \W_\infty and further truncations. In the classical limit,
all algebras in the one-parameter family are equivalent and isomorphic to
\w_{\rm KP}. The reduction induced by setting the spin-one field to zero
yields a one-parameter deformation of \widehat{\W}_\infty which contracts to
a new nonlinear algebra of the \W_\infty-type.Comment: 31 pages, compressed uuencoded .dvi file, BONN-HE-92/20, US-FT-7/92,
KUL-TF-92/20. [version just replaced was truncated by some mailer
Coherent J/psi production - a novel feature at LHC?
Energy dependence of heavy quarkonia production in hadron-nucleus collisions
is studied in the framework of the Glauber-Gribov theory. We emphasize a change
in the space-time picture of heavy-quark state production on nuclei with
energy. Longitudinally ordered scattering of a heavy-quark system takes place
at low energies, while with increasing energy it transforms to a coherent
scattering of projectile partons on the nuclear target. The characteristic
energy scale for this transition depends on masses and rapidities of produced
particles. For J/psi, produced in the central rapidity region, the transition
happens at RHIC energies. The parameter-free calculation of J/psi in dAu
collisions is in good agreement with recent RHIC data. We use distributions of
gluons in nuclei to predict suppression of heavy quarkonia at LHC.Comment: 13 pages, 4 figures; experimental data and reference included,
conclusions unchanged; to appear in Phys. Lett.
Non-Local Matrix Generalizations of W-Algebras
There is a standard way to define two symplectic (hamiltonian) structures,
the first and second Gelfand-Dikii brackets, on the space of ordinary linear
differential operators of order , . In this paper, I consider in detail the case where the are
-matrix-valued functions, with particular emphasis on the (more
interesting) second Gelfand-Dikii bracket. Of particular interest is the
reduction to the symplectic submanifold . This reduction gives rise to
matrix generalizations of (the classical version of) the {\it non-linear}
-algebras, called -algebras. The non-commutativity of the
matrices leads to {\it non-local} terms in these -algebras. I show
that these algebras contain a conformal Virasoro subalgebra and that
combinations of the can be formed that are -matrices of
conformally primary fields of spin , in analogy with the scalar case .
In general however, the -algebras have a much richer structure than
the -algebras as can be seen on the examples of the {\it non-linear} and
{\it non-local} Poisson brackets of any two matrix elements of or
which I work out explicitly for all and . A matrix Miura transformation
is derived, mapping these complicated second Gelfand-Dikii brackets of the
to a set of much simpler Poisson brackets, providing the analogue of the
free-field realization of the -algebras.Comment: 43 pages, a reference and a remark on the conformal properties for
adde
Current Distribution in the Three-Dimensional Random Resistor Network at the Percolation Threshold
We study the multifractal properties of the current distribution of the
three-dimensional random resistor network at the percolation threshold. For
lattices ranging in size from to we measure the second, fourth and
sixth moments of the current distribution, finding {\it e.g.\/} that
where is the conductivity exponent and is the
correlation length exponent.Comment: 10 pages, latex, 8 figures in separate uuencoded fil
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