Schur Polynomials and The Yang-Baxter Equation

We describe a parametrized Yang-Baxter equation with nonabelian parameter group. That is, we show that there is an injective map \({g \mapsto R (g)}\) from \({ \rm{GL}(2, \mathbb{C}) \times \rm{GL}(1, \mathbb{C})}\) to End \({(V \otimes V)}\) , where V is a two-dimensional vector space such that if \({g, h \in G}\) then R ₁₂(g)R ₁₃(gh) R ₂₃(h) = R ₂₃(h) R ₁₃(gh)R ₁₂(g). Here R _{i j} denotes R applied to the i, j components of \({V \otimes V \otimes V}\) . The image of this map consists of matrices whose nonzero coefficients a ₁, a ₂, b ₁, b ₂, c ₁, c ₂ are the Boltzmann weights for the non-field-free six-vertex model, constrained to satisfy a ₁ a ₂ + b ₁ b ₂ ? c ₁ c ₂ = 0. This is the exact center of the disordered regime, and is contained within the free fermionic eight-vertex models of Fan and Wu. As an application, we show that with boundary conditions corresponding to integer partitions λ, the six-vertex model is exactly solvable and equal to a Schur polynomial s _λ times a deformation of the Weyl denominator. This generalizes and gives a new proof of results of Tokuyama and Hamel and King.     

Explicit formulas for the waldspurger and bessel models

This paper studies certain models of irreducible admissible representations of the split special orthogonal group SO(2n+1) over a nonarchimedean local field. Ifn=1, these models were considered by Waldspurger. Ifn=2, they were considered by Novodvorsky and Piatetski-Shapiro, who called them Bessel models. In the works of these authors, uniqueness of the models is established; in this paper functional equations and explicit formulas for them are obtained. As a global application, the Bessel period of the Eisenstein series on SO(2n+1) formed with a cuspidal automorphic representation π on GL(n) is computed—it is shown to be a product of L-series. This generalizes work of Böcherer and Mizumoto forn=2 and base field ?, and puts it in a representation-theoretic context. In an appendix by M. Furusawa, a new Rankin-Selberg integral is given for the standardL-function on SO(2n+1)×GL(n). The local analysis of the integral is carried out using the formulas of the paper.     

Influence of electron exchange and correlation on the stopping power for slow ions in metals

The exchange and correlations between free electrons in metals are shown always to increase electronic stopping power for slow ions. The stopping power is expressed analytically for theoretical evaluations. This expression was used to calculate stopping powers for slow protons in Al and Ag. A better agreement with experimental data is noticed.     

The Eikonal-SVEAS analytic closed forms for single-photon superradiance

Using the Slowly Varying Envelope Approximation in Space and the Eikonal Approximation, we obtain closed-form analytic expressions for the single-photon superradiance from a spherical cloud of two-level atoms in the scalar photon theory. The value 0.171, calculated in this approximation for the value of the maximum probability of secondary excited states, agrees with those obtained from the eigenmode analysis method and from the Debye-refined method.     

Deviations of the lepton mapping matrix from the Harrison-Perkins- Scott form

We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott （HPS） form. These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector. The perturbing matrix is assumed to be purely imaginary （thus maximally T-violating） and to have a strength in energy scale no greater （but perhaps smaller） than the muon mass. As we shall show, it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than O（（mμ/mτ）^2） ≈ 3.5 ×10^-3 from their HPS values. Assuming that （mμ/mτ）^2 can be neglected, we derive two simple constraints on the four parameters θ12,θ23, θ31, and δ of the mapping matrix. These constraints are independent of the details of the imaginary T-violating perturbation of the charged lepton mass matrix. We also show that the e and μ parts of the mapping matrix have a definite form governed by two parameters α and β; any deviation of order mμ/mτ can be accommodated by adjusting these two parameters.     

Time-dependent directionality of cooperative emission after short pulse excitation

Cooperative emission from a sphere of N two-level atoms excited by a short pulse is shown to have a time-dependent angular distribution, with the possibility of reversal in the dominant direction of emission. This is a result of the different values of the frequency shifts and decay rates associated with the various collective eigenmodes of the atomic system obtained in a scalar photon model.     

Convergent iterative solutions of Schroedinger equation for a generalized double well potential

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with a generalized double well potential . The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameter a are discussed.