1,393 research outputs found
Integrable Systems for Particles with Internal Degrees of Freedom
We show that a class of models for particles with internal degrees of freedom
are integrable. These systems are basically generalizations of the models of
Calogero and Sutherland. The proofs of integrability are based on a recently
developed exchange operator formalism. We calculate the wave-functions for the
Calogero-like models and find the ground-state wave-function for a
Calogero-like model in a position dependent magnetic field. This last model
might have some relevance for matrix models of open strings.Comment: 10 pages, UVA-92-04, CU-TP-56
Periodic motions galore: How to modify nonlinear evolution equations so that they feature a lot of periodic solutions
A simple trick is illustrated, whereby nonlinear evolution equations can be
modified so that they feature a lot - or, in some cases, only -- periodic
solutions. Several examples (ODEs and PDEs) are exhibited.Comment: arxiv version is already officia
Multidimensional Calogero systems from matrix models
We show that a particular many-matrix model gives rise, upon hamiltonian
reduction, to a multidimensional version of the Calogero-Sutherland model and
its spin generalizations. Some simple solutions of these models are
demonstrated by solving the corresponding matrix equations. A connection of
this model to the dimensional reduction of Yang-Mills theories to
(0+1)-dimensions is pointed out. In particular, it is shown that the low-energy
dynamics of D0-branes in sectors with nontrivial fermion content is that of
spin-Calogero particles.Comment: 12 pages, no figures, plain tex, phyzzx macr
Generalized Calogero models through reductions by discrete symmetries
We construct generalizations of the Calogero-Sutherland-Moser system by
appropriately reducing a classical Calogero model by a subset of its discrete
symmetries. Such reductions reproduce all known variants of these systems,
including some recently obtained generalizations of the spin-Sutherland model,
and lead to further generalizations of the elliptic model involving spins with
SU(n) non-invariant couplings.Comment: 14 pages, LaTeX, no figure
Generalized Calogero-Sutherland systems from many-matrix models
We construct generalizations of the Calogero-Sutherland-Moser system by
appropriately reducing a model involving many unitary matrices. The resulting
systems consist of particles on the circle with internal degrees of freedom,
coupled through modifications of the inverse-square potential. The coupling
involves SU(M) non-invariant (anti)ferromagnetic interactions of the internal
degrees of freedom. The systems are shown to be integrable and the spectrum and
wavefunctions of the quantum version are derived.Comment: 8 pages, LaTeX, no figure
Goldfish geodesics and Hamiltonian reduction of matrix dynamics
We relate free vector dynamics to the eigenvalue motion of a time-dependent
real-symmetric NxN matrix, and give a geodesic interpretation to Ruijsenaars
Schneider models.Comment: 8 page
Exact Spectrum of SU(n) Spin Chain with Inverse-Square Exchange
The spectrum and partition function of a model consisting of SU(n) spins
positioned at the equilibrium positions of a classical Calogero model and
interacting through inverse-square exchange are derived. The energy levels are
equidistant and have a high degree of degeneracy, with several SU(n) multiplets
belonging to the same energy eigenspace. The partition function takes the form
of a q-deformed polynomial. This leads to a description of the system by means
of an effective parafermionic hamiltonian, and to a classification of the
states in terms of "modules" consisting of base-n strings of integers.Comment: 12 pages, CERN-TH-7040/9
Goldfishing by gauge theory
A new solvable many-body problem of goldfish type is identified and used to
revisit the connection among two different approaches to solvable dynamical
systems. An isochronous variant of this model is identified and investigated.
Alternative versions of these models are presented. The behavior of the
alternative isochronous model near its equilibrium configurations is
investigated, and a remarkable Diophantine result, as well as related
Diophantine conjectures, are thereby obtained.Comment: 22 page
Exchange Operator Formalism for Integrable Systems of Particles
We formulate one dimensional many-body integrable systems in terms of a new
set of phase space variables involving exchange operators. The hamiltonian in
these variables assumes a decoupled form. This greatly simplifies the
derivation of the conserved charges and the proof of their commutativity at the
quantum level.Comment: 8 page
Crossover from Fermi Liquid to Non-Fermi Liquid Behavior in a Solvable One-Dimensional Model
We consider a quantum moany-body problem in one-dimension described by a
Jastrow type, characterized by an exponent and a parameter .
We show that with increasing , the Fermi Liquid state (
crosses over to non-Fermi liquid states, characterized by effective
"temperature".Comment: 8pp. late
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