A large class of solvable multistate Landau-Zener models and quantum integrability

TL;DR

This paper introduces a new class of exactly solvable multistate Landau-Zener models with arbitrary states, revealing their quantum integrability and providing explicit transition probabilities, thus advancing the understanding of time-dependent quantum systems.

Contribution

It presents a novel class of solvable MLZ models with arbitrary states, demonstrating their quantum integrability and analytical solutions for transition probabilities.

Findings

Exact solutions for transition probabilities in models with N≥4 states

Identification of multiple energy crossing points at different times

Connection between solvable MLZ models and quantum integrability

Abstract

The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians. Within the multistate Landau-Zener (MLZ) theory, however, there has been a successful alternative approach to identify and solve complex time-dependent models. Here we compare both methods by applying them to a new class of exactly solvable MLZ models. This class contains systems with an arbitrary number $N\ge 4$ of interacting states and shows a quickly growing with $N$ number of exact adiabatic energy crossing points, which appear at different moments of time. At each $N$, transition probabilities in these systems can be found analytically and exactly but complexity and variety of solutions in this class also grow with $N$ quickly. We illustrate how common features of solvable MLZ systems appear from quantum integrability and develop an approach to further classification of solvable MLZ problems.