2,121 research outputs found
Explicit solutions of the classical Calogero & Sutherland systems for any root system
Explicit solutions of the classical Calogero (rational with/without harmonic
confining potential) and Sutherland (trigonometric potential) systems is
obtained by diagonalisation of certain matrices of simple time evolution. The
method works for Calogero & Sutherland systems based on any root system. It
generalises the well-known results by Olshanetsky and Perelomov for the A type
root systems. Explicit solutions of the (rational and trigonometric) higher
Hamiltonian flows of the integrable hierarchy can be readily obtained in a
similar way for those based on the classical root systems.Comment: 18 pages, LaTeX, no figur
Water resources of the island of Kahoolawe, Hawaii : preliminary findings
Water-Resources Investigations Report 89-420
Volume preserving multidimensional integrable systems and Nambu--Poisson geometry
In this paper we study generalized classes of volume preserving
multidimensional integrable systems via Nambu--Poisson mechanics. These
integrable systems belong to the same class of dispersionless KP type equation.
Hence they bear a close resemblance to the self dual Einstein equation. All
these dispersionless KP and dToda type equations can be studied via twistor
geometry, by using the method of Gindikin's pencil of two forms. Following this
approach we study the twistor construction of our volume preserving systems
DMRG and periodic boundary conditions: a quantum information perspective
We introduce a picture to analyze the density matrix renormalization group
(DMRG) numerical method from a quantum information perspective. This leads us
to introduce some modifications for problems with periodic boundary conditions
in which the results are dramatically improved. The picture also explains some
features of the method in terms of entanglement and teleportation.Comment: 4 page
-analogue of modified KP hierarchy and its quasi-classical limit
A -analogue of the tau function of the modified KP hierarchy is defined by
a change of independent variables. This tau function satisfies a system of
bilinear -difference equations. These bilinear equations are translated to
the language of wave functions, which turn out to satisfy a system of linear
-difference equations. These linear -difference equations are used to
formulate the Lax formalism and the description of quasi-classical limit. These
results can be generalized to a -analogue of the Toda hierarchy. The results
on the -analogue of the Toda hierarchy might have an application to the
random partition calculus in gauge theories and topological strings.Comment: latex2e, a4 paper 15 pages, no figure; (v2) a few references are
adde
SDiff(2) Toda equation -- hierarchy, function, and symmetries
A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda
equation, is shown to have a Lax formalism and an infinite hierarchy of higher
flows. The Lax formalism is very similar to the case of the self-dual vacuum
Einstein equation and its hyper-K\"ahler version, however now based upon a
symplectic structure and the group SDiff(2) of area preserving diffeomorphisms
on a cylinder . An analogue of the Toda lattice tau function is
introduced. The existence of hidden SDiff(2) symmetries are derived from a
Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function
turn out to have commutator anomalies, hence give a representation of a central
extension of the SDiff(2) algebra.Comment: 16 pages (``vanilla.sty" is attatched to the end of this file after
``\bye" command
Toda Lattice Hierarchy and Generalized String Equations
String equations of the -th generalized Kontsevich model and the
compactified string theory are re-examined in the language of the Toda
lattice hierarchy. As opposed to a hypothesis postulated in the literature, the
generalized Kontsevich model at does not coincide with the
string theory at self-dual radius. A broader family of solutions of the Toda
lattice hierarchy including these models are constructed, and shown to satisfy
generalized string equations. The status of a variety of string
models is discussed in this new framework.Comment: 35pages, LaTeX Errors are corrected in Eqs. (2.21), (2.36), (2.33),
(3.3), (5.10), (6.1), sentences after (3.19) and theorem 5. A few references
are update
Dispersionless integrable equations as coisotropic deformations. Extensions and reductions
Interpretation of dispersionless integrable hierarchies as equations of
coisotropic deformations for certain algebras and other algebraic structures
like Jordan triple systInterpretation of dispersionless integrable hierarchies
as equations of coisotropic deformations for certain algebras and other
algebraic structures like Jordan triple systems is discussed. Several
generalizations are considered. Stationary reductions of the dispersionless
integrable equations are shown to be connected with the dynamical systems on
the plane completely integrable on a fixed energy level. ems is discussed.
Several generalizations are considered. Stationary reductions of the
dispersionless integrable equations are shown to be connected with the
dynamical systems on the plane completely integrable on a fixed energy level.Comment: 21 pages, misprints correcte
Critical Point of a Symmetric Vertex Model
We study a symmetric vertex model, that allows 10 vertex configurations, by
use of the corner transfer matrix renormalization group (CTMRG), a variant of
DMRG. The model has a critical point that belongs to the Ising universality
class.Comment: 2 pages, 6 figures, short not
- âŠ