Multitime Landau-Zener model: classification of solvable Hamiltonians

TL;DR

This paper classifies solvable multitime Landau-Zener models, identifying independent families of solutions for systems with multiple states, and discusses their scattering matrices, enriching the understanding of multistate quantum dynamics.

Contribution

It introduces a systematic classification method for solvable multitime Landau-Zener models and analyzes their scattering matrices, expanding the theoretical framework for multistate quantum systems.

Findings

Classification of all independent families for given number of states

Proof of absence of certain interaction types in solvable models

Detailed characterization of scattering matrices within solvable families

Abstract

We discuss a class of models that generalize the two-state Landau-Zener (LZ) Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum mechanical evolution can be understood in great detail. Here, we present an approach to classify such solvable models, namely, to identify all their independent families for a given number $N$ of interacting states and prove the absence of such families for some types of interactions. We also discuss how, within a solvable family, one can classify the scattering matrices, i.e., the system's dynamics. Due to the possibility of such a detailed classification, the multitime Landau-Zener (MTLZ) model defines a useful special function of theoretical physics.