Classical Many-particle Clusters in Two Dimensions

We report on a study of a classical, finite system of confined particles in two dimensions with a two-body repulsive interaction. We first develop a simple analytical method to obtain equilibrium configurations and energies for few particles. When the confinement is harmonic, we prove that the first transition from a single shell occurs when the number of particles changes from five to six. The shell structure in the case of an arbitrary number of particles is shown to be independent of the strength of the interaction but dependent only on its functional form. It is also independent of the magnetic field strength when included. We further study the effect of the functional form of the confinement potential on the shell structure. Finally we report some interesting results when a three-body interaction is included, albeit in a particular model.Comment: Minor corrections, a few references added. To appear in J. Phys: Condensed Matte

The Bloch-Okounkov correlation functions of classical type

Bloch and Okounkov introduced an n-point correlation function on the infinite wedge space and found an elegant closed formula in terms of theta functions. This function has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, etc, and it can also be interpreted as correlation functions on integrable gl_\infty-modules of level one. Such gl_\infty-correlation functions at higher levels were then calculated by Cheng and Wang. In this paper, generalizing the type A results, we formulate and determine the n-point correlation functions in the sense of Bloch-Okounkov on integrable modules over classical Lie subalgebras of gl_\infty of type B,C,D at arbitrary levels. As byproducts, we obtain new q-dimension formulas for integrable modules of type B,C,D and some fermionic type q-identities.Comment: v2, very minor changes, Latex, 41 pages, to appear in Commun. Math. Phy

Homogeneous Loop Quantum Cosmology: The Role of the Spin Connection

Homogeneous cosmological models with non-vanishing intrinsic curvature require a special treatment when they are quantized with loop quantum cosmological methods. Guidance from the full theory which is lost in this context can be replaced by two criteria for an acceptable quantization, admissibility of a continuum approximation and local stability. A quantization of the corresponding Hamiltonian constraints is presented and shown to lead to a locally stable, non-singular evolution compatible with almost classical behavior at large volume. As an application, the Bianchi IX model and its modified behavior close to its classical singularity is explored.Comment: revtex4, 36 pages, 10 figures. In version 2 the introduction is expanded, section III E is added and a paragraph on relevance of results is added in the conclusions. Refs updated, results unchanged. To appear in Class. Quant. Gravit

The Bloch-Okounkov correlation functions, a classical half-integral case

Bloch and Okounkov's correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of \hgl_\infty-modules of level one. Recent works have calculated these character functions for higher levels for \hgl_\infty and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type $D$ of half-integral levels and as a byproduct, obtain $q$-dimension formulas for integral modules of type $D$ at half-integral level.Comment: v2: minor changes to the introduction; accepted for publication in Letters in Mathematical Physic

Dual Resonance Model Solves the Yang-Baxter Equation

The duality of dual resonance models is shown to imply that the four point string correlation function solves the Yang-Baxter equation. A reduction of transfer matrices to $A_l$ symmetry is described by a restriction of the KP $\tau$ function to Toda molecules.Comment: 10 pages, LaTe

Spin current and magneto-electric effect in non-collinear magnets

A new microscopic mechanism of the magneto-electric (ME) effect based on the spin supercurrent is theoretically presented for non-collinear magnets. The close analogy between the superconductors (charge current) and magnets (spin current) is drawn to derive the distribution of the spin supercurrent and the resultant electric polarization. Application to the spiral spin structure is discussed.Comment: 5 pages, 2 figure

Coherent Backscattering of Ultracold Atoms

We report on the direct observation of coherent backscattering (CBS) of ultracold atoms, in a quasi-two-dimensional configuration. Launching atoms with a well-defined momentum in a laser speckle disordered potential, we follow the progressive build up of the momentum scattering pattern, consisting of a ring associated with multiple elastic scattering, and the CBS peak in the backward direction. Monitoring the depletion of the initial momentum component and the formation of the angular ring profile allows us to determine microscopic transport quantities. The time resolved evolution of the CBS peak is studied and is found a fair agreement with predictions, at long times as well as at short times. The observation of CBS can be considered a direct signature of coherence in quantum transport of particles in disordered media. It is responsible for the so called weak localization phenomenon, which is the precursor of Anderson localization.Comment: 5 pages, 4 figure

Exact finite-size spectrum for the multi-channel Kondo model and Kac-Moody fusion rules

The finite-size spectrum for the multi-channel Kondo model is derived analytically from the exact solution, by mapping the nontrivial Z$_{n}$ part of the Kondo scattering into that for the RSOS model coupled with the impurity. The analysis is performed for the case of $n-2S=1$, where $n$ is the number of channel and $S$ is the impurity spin. The result obtained is in accordance with the Kac-Moody fusion hypothesis proposed by Affleck and Ludwig.Comment: RevTex, 4 page

Consistency Conditions for Fundamentally Discrete Theories

The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to ensure that the numerical solutions can reliably be used as approximations to solutions of the differential equation. There are, however, also systems where a difference equation is deemed to be fundamental, mainly in the context of quantum gravity. Since difference equations in general are harder to solve analytically than differential equations, it can be helpful to introduce an approximating differential equation as a continuum approximation. In this paper implications of this change in view point are analyzed to derive the conditions that the difference equation should satisfy. The difference equation in such a situation cannot be chosen freely but must be derived from a fundamental theory. Thus, the conditions for a discrete formulation can be translated into conditions for acceptable quantizations. In the main example, loop quantum cosmology, we show that the conditions are restrictive and serve as a selection criterion among possible quantization choices.Comment: 33 page

Higher spin vertex models with domain wall boundary conditions

We derive determinant expressions for the partition functions of spin-k/2 vertex models on a finite square lattice with domain wall boundary conditions.Comment: 14 pages, 12 figures. Minor corrections. Version to appear in JSTA