Multiparticle Landau-Zener problem

Abstract

We propose a simple ansatz that allows to generate new exactly solvable multi-state Landau-Zener models. It is based on a system of two decoupled two-level atoms whose levels vary with time and cross at some moments. Then we consider multiparticle systems with Heisenberg equations for annihilation operators having similar structure with Shrödinger equation for amplitudes in multistate Landau-Zener models and show that the corresponding Shrödinger equation in multiparticle sector belongs to the multistate Landau-Zener class. This observation allows to generate new exactly solvable models from already known ones. We discuss possible applications of the new solutions in the problem of the driven charge transport in quantum dots.