Some recent developments in n-particle scattering theory

J. M. Combes

Ralf Der

Abstract Ladder summation techniques are applied to the recently developed c‐number diagram expansion for kinetic equations describing the relaxation of quantum fluids. By way of the resummation, the kinetic equations are reformulated in terms of a T‐matrix which describes the scattering of two particles influenced by the remaining particles of the system via the particle statistics (Bose or Fermi). At sufficiently high temperatures (Maxwell‐Boltzmann statistics), the T‐matrix introduced coincides with the usual T‐matrix of conventional two‐body scattering theory in free space. In low‐temperature Fermi systems, the T‐matrix differs from the reaction matrix of the Brueckner‐Goldstone theory because the “healing” property of the two‐body wave function does not obtain.

Paul G. Federbush

Mark S. Hillery, Edgar Feldman

We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through the graph, to the other. The particle propagates freely on the half lines but is scattered at each vertex in the original graph. The probability of starting on one line and reaching the other after n steps can be expressed in terms of the transmission amplitude for the graph. An example is presented. Classical random walks on graphs can be used to construct algorithms that solve 2-SAT, graph connectivity problems, and for finding satsifying assignments for Boolean functions. A hope is that recently defined quantum walks will prove similarly useful in the development of quantum algorithms. In fact, it has recently been shown that it is possible to use a quantum walk to perform a search on the hypercube faster than can be done classically [1]. In this problem

L. D. Faddeev, S. P. Merkuriev

G. Bencze, C. Chandler

A time-dependent multichannel nonrelativistic quantum scattering theory is established for systems which contain identical particles. The symmetry properties of the theory are rooted in the abstract algebraic relationships between permutations. The formalism of second quantization is thus avoided. Appropriate wave and scattering operators are defined, including those for systems with long range (e.g., Coulomb) interactions. A correctly symmetrized dynamical equation for the symmetric form of the transition operator is derived and used to develop an optical potential formalism.NUCLEAR REACTIONS Nonrelativistic multichannel scattering theory for identical particles, wave and scattering operators, dynamical equations, optical potentials.