Duality in Landau-Zener-Stueckelberg potential curve crossing

TL;DR

This paper explores the duality in Landau-Zener-Stueckelberg potential crossings, developing a perturbation theory applicable in both weak and strong interaction regimes, and analyzing effects on quantum coherence.

Contribution

It introduces a duality-based perturbation approach for potential curve crossings and explains the Landau-Zener formula without Stokes phenomena, revealing a topological kink-like object.

Findings

Perturbation theory valid in both weak and strong limits.

Landau-Zener formula accurately described without Stokes phenomena.

Potential curve crossing suppresses quantum coherence similar to dissipation.

Abstract

It is pointed out that there exists an interesting strong and weak duality in the Landau-Zener-Stueckelberg potential curve crossing. A reliable perturbation theory can thus be formulated in the both limits of weak and strong interactions. It is shown that main characteristics of the potential crossing phenomena such as the Landau-Zener formula including its numerical coefficient are well-described by simple (time-independent) perturbation theory without referring to Stokes phenomena. A kink-like topological object appears in the ``magnetic'' picture, which is responsible for the absence of the coupling constant in the prefactor of the Landau-Zener formula. It is also shown that quantum coherence in a double well potential is generally suppressed by the effect of potential curve crossing, which is analogous to the effect of Ohmic dissipation on quantum coherence.