Nonsingular integral equation for two-body scattering and applications in two and three dimensions

Abstract

We introduce a new nonsingular scattering integral equation, which is suitable for the investigation of the total (also off-shell) transition matrix in arbitrary dimension n )2. In particular, the low-energy properties are derived and lead, in connection with spin-polarized atomic hydrogen H $, to the low-temperature behavior of two-and three-body surface processes. In addition, for three dimensions the method leads in a natural way to a separable approximation to the T matrix for all energies, with the possibility of formulating a procedure for optimizing this approximation. To show the practicability of the equation we also present numerical results for both n =2 and n = 3.

Cold bosons in optical lattices

“…The same form (2.138) can be derived from the definition [106,107] of the superfluid fraction 139) applicable to equilibrium systems. Here the grand potential for the moving system is 140) and the free energy for that system is…”

“…The latter, for a general nonuniform system, can be represented as On the other hand, the two-body scattering matrix can be defined as a solution of a Lippman-Schwinger equation [138,139], which, in the limit of weak interactions, results in the total anomalous average (2.180) evaluated in the same weak-coupling limit [140][141][142].…”

Nonuniversal Equation of State of the Two-Dimensional Bose Gas

“…Given the inter-atomic potentialṼ (q), the corresponding 2D scattering length a s is obtained calculating the s-wave phase shift δ 0 (q) that is related to a s by the expression [13,[34][35][36][37][38] …”

The influence of the Kosterlitz-Thouless transition on the decay of spin-polarized atomic hydrogen

“…Using a Jastrow-like approximation [5] for the initial-state wavefunction in the recombination matrix element we find for the rate constant in the normal phase…”