The spin chains originating from large-N conformal gauge theories are of a special kind: The Hamiltonian is not invariant under the symmetry algebra, it is rather a part of it. This leads to interesting properties within the asymptotic Bethe ansatz. Here we study an S-matrix with u(1|1) symmetry which arises in a long-range spin chain with fundamental spins of su(2|1).

We use the LSZ reduction theorem and interpolating fields, alongwith the heavy quark effective theory, to investigate the structure of the BetheSalpeter amplitude for heavy hadrons. We show how a simple form of this amplitude, used extensively in heavy hadron decay calculations, follows naturally upto O(1/M) from these field theoretic considerations. Accepted for publication in Physics Letters B

We obtain, using the Birman-Schwinger method, upper limits on the total number of bound states and on the number of l-wave bound states of the semirelativistic spinless Salpeter equation. We also obtain a simple condition, in the ultrarelativistic case (m = 0), for the existence of at least one l-wave bound states: C(l, p/(p− 1)) ∫∞ 0 dr r p−1 |V −(r)|p ≥ 1, where C(l, p/(p− 1)) is a known func...

This note is a review of rigged configurations and the Bethe Ansatz. In the first part, we focus on the algebraic Bethe Ansatz for the spin 1/2 XXX model and explain how rigged configurations label the solutions of the Bethe equations. This yields the bijection between rigged configurations and crystal paths/Young tableaux of Kerov, Kirillov and Reshetikhin. In the second part, we discuss a gen...

The Bethe–Salpeter equations for the light-quark composite systems, qq̄, are written in terms of spectral integrals. For the qq̄-mesons characterized by the mass M , spin J and radial quantum number n, the equations are presented for the following (n,M2)trajectories: πJ , ηJ , aJ , fJ , ρJ , ωJ , hJ and bJ .

We present a new derivation of the spectral gap of the totally asymmetric exclusion process on a half-filled ring of size L by using the Bethe Ansatz. We show that, in the large L limit, the Bethe equations reduce to a simple transcendental equation involving the polylogarithm, a classical special function. By solving that equation, the gap and the dynamical exponent are readily obtained. Our m...

We examine the use of distributions in numerical treatments of Anderson localisation and supply evidence that treating exponential localisation on Bethe lattices recovers the overall picture known from hypercubic lattices in 3d.

We consider Schrödinger operator −∆+V in R (d ≥ 2) with smooth periodic potential V and prove that there are only finitely many gaps in its spectrum. Dedicated to the memory of B.M.Levitan

A random tiling of rectangles and triangles displaying a decagonal phase is solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square triangle and the octagonal rectangle triangle tiling an exact expression for the maximum of the entropy is found.

We investigate some properties of Bethe–Salpeter wave functions in integrable models. In particular we illustrate the application of the operator product expansion in determining the short distance behavior. The energy dependence of the potentials obtained from such wave functions is studied, and further we discuss the (limited) phenomenological significance of zero–energy potentials.