arXiv subjects

Alexios P. Polychronakos

Publications and source records attributed to Alexios P. Polychronakos.

82 records · Page 5Linked to original sources

arXiv1995

Probabilities and Path-Integral Realization of Exclusion Statistics

A microscopic formulation of Haldane's exclusions statistics is given in terms of a priori occupation probabilities of states. It is shown that negative probabilities are always necessary to reproduce fractional statistics. Based on this formulation, a path-integral realization for systems with exclusion statistics is derived. This has the advantage of being generalizable to interacting systems, and can be used as the starting point for further generalizations of statistics. As a byproduct, the vanishing of the heat capacity at zero temperature for exclusion statistics systems is proved.

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arXiv1994

Density Correlation Functions in Calogero Sutherland Models

Using arguments from two dimensional Yang-Mills theory and the collective coordinate formulation of the Calogero-Sutherland model, we conjecture the dynamical density correlation function for coupling $l$ and $1/l$, where $l$ is an integer. We present overwhelming evidence that the conjecture is indeed correct.

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arXiv1993

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.

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arXiv1993

Interacting Fermion Systems from Two Dimensional QCD

We consider two dimensional U(N) QCD on the cylinder with a timelike Wilson line in an arbitrary representation. We show that the theory is equivalent to N fermions with internal degrees of freedom which interact among themselves with a generalized Sutherland-type interaction. By evaluating the expectation value of the Wilson line in the original theory we explicitly find the spectrum and degeneracies of these particle systems.

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arXiv1993

Equivalence of Two Dimensional QCD and the $c=1$ Matrix Model

We consider two dimensional QCD with the spatial dimension compactified to a circle. We show that the states in the theory consist of interacting strings that wind around the circle and derive the Hamiltonian for this theory in the large $N$ limit, complete with interactions. Mapping the winding states into momentum states, we express this Hamiltonian in terms of a continuous field. For a $U(N)$ gauge group with a background source of Wilson loops, we recover the collective field Hamiltonian found by Das and Jevicki for the $c=1$ matrix model, except the spatial coordinate is on a circle. We then proceed to show that two dimensional QCD with a $U(N)$ gauge group can be reduced to a one- dimensional unitary matrix model and is hence equivalent to a theory of $N$ free nonrelativistic fermions on a circle. A similar result is true for the group $SU(N)$, but the fermions must be modded out by the center of mass coordinate.

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arXiv1992

Lattice Integrable Systems of Haldane-Shastry Type

We present a new lattice integrable system in one dimension of the Haldane-Shastry type. It consists of spins positioned at the static equilibrium positions of particles in a corresponding classical Calogero system and interacting through an exchange term with strength inversely proportional to the square of their distance. We achieve this by viewing the Haldane-Shastry system as a high-interaction limit of the Sutherland system of particles with internal degrees of freedom and identifying the same limit in a corresponding Calogero system. The commuting integrals of motion of this system are found using the exchange operator formalism.

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arXiv1992

Schrodinger Equation for Particle with Friction

A new quantum mechanical wave equation describing a particle with frictional forces is derived. It depends on a parameter $α$ whose range is determined by the coefficient of friction $γ$, that is, $0 \leq α\leq γ$. For one extreme value of this parameter, $α= 0$, we recover Kostin's equation. For the other extreme value, $α= γ$, we obtain an equation in which friction manifests in "magnetic" type terms. It further exhibits breakdown of translational invariance, manifesting through a symmetry breaking parameter $β$, as well as localized stationary states in the absence of external potentials. Other physical properties of this new class of equations are also discussed.

hep-th↗

arXiv1992

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.

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arXiv1992

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.

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arXiv1991

New Integrable Systems from Unitary Matrix Models

We show that the one dimensional unitary matrix model with potential of the form $a U + b U^2 + h.c.$ is integrable. By reduction to the dynamics of the eigenvalues, we establish the integrability of a system of particles in one space dimension in an external potential of the form $a \cos (x+α) + b \cos ( 2x +β)$ and interacting through two-body potentials of the inverse sine square type. This system constitutes a generalization of the Sutherland model in the presence of external potentials. The positive-definite matrix model, obtained by analytic continuation, is also integrable, which leads to the integrability of a system of particles in hyperbolic potentials interacting through two-body potentials of the inverse hypebolic sine square type.

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