Multiparticle Landau-Zener problem

TL;DR

This paper introduces a method to generate new exactly solvable multi-state Landau-Zener models using an ansatz based on two decoupled two-level systems, with applications in quantum dot charge transport.

Contribution

It presents a novel ansatz that enables the creation of new exactly solvable multi-state Landau-Zener models from known solutions.

Findings

New exactly solvable models derived from existing ones.

Application potential in driven charge transport in quantum dots.

Framework linking multiparticle systems to multistate Landau-Zener class.

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 Shr\"odinger equation for amplitudes in multistate Landau-Zener models and show that the corresponding Shr\"odinger 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.