Integrability in the multistate Landau-Zener model with time-quadratic commuting operators

TL;DR

This paper explores the prevalence of time-quadratic commuting operators in multistate Landau-Zener models, revealing their role in constraining scattering parameters and enabling exact transition probability calculations.

Contribution

It demonstrates that time-quadratic operators are common in MLZ models and introduces new solvable systems based on these operators.

Findings

Time-quadratic operators are more common than previously thought in MLZ models.

Constraints from these operators allow for asymptotically exact transition probability expressions.

New fully solvable MLZ systems are identified.

Abstract

Exactly solvable multistate Landau-Zener (MLZ) models are associated with families of operators that commute with the MLZ Hamiltonians and depend on time linearly. There can also be operators that satisfy the integrability conditions with the MLZ Hamiltonians but depend on time quadratically. We show that, among the MLZ systems, such time-quadratic operators are much more common. We demonstrate then that such operators generally lead to constraints on the independent variables that parametrize the scattering matrix. We show how such constraints lead to asymptotically exact expressions for the transition probabilities in the adiabatic limit of a three-level MLZ model. New fully solvable MLZ systems are also found.