Landau-Zener Transitions in Chains

TL;DR

This paper derives exact transition probabilities for specific multistate Landau-Zener models and explores their implications for quantum phase transitions, revealing symmetries and scaling behaviors supported by numerical simulations.

Contribution

It provides the first exact solutions for certain multistate Landau-Zener models and uncovers a symmetry property applicable to a broad class of such models.

Findings

Exact transition probabilities for two multistate LZ models

Demonstration of scaling behavior in particle statistics during phase transitions

Identification of a symmetry property in multistate LZ models

Abstract

We determine transition probabilities in two exactly solvable multistate Landau-Zener (LZ) models and discuss applications of our results to the theory of dynamic passage through a phase transition in the dissipationless quantum mechanical regime. In particular, we show that statistics of particles in a new phase demonstrate scaling behavior. Our results also reveal a symmetry that we claim is a property of a large class of multistate LZ models, whose explicit solutions are not presently known. We support our arguments by direct numerical simulations.