Multitime Landau-Zener model: classification of solvable Hamiltonians

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.

arXiv commentVersion published on Journal of Physics A: Mathematical and Theoretical

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• Derivation of the Landau-Zener formula via functional equations
• Effect of decay of the final states on the probabilities of the Landau-Zener transitions in multistate non-integrable models
• Graph-theoretical search for integrable multistate Landau-Zener models