Landau-Zener-St\"uckelberg-Majorana dynamics of magnetized quarkonia

TL;DR

This paper studies how charmonia, a type of magnetized hadron, undergo nonadiabatic transitions in time-dependent magnetic fields, revealing complex dynamics like Landau-Zener transitions and interference effects.

Contribution

It introduces a multi-channel Landau-Zener model for charmonia in magnetic fields and analyzes their real-time transition dynamics under various magnetic field profiles.

Findings

Nonadiabatic transitions significantly affect state occupation probabilities.

Landau-Zener and St"uckelberg interference phenomena are observed.

Results guide future lattice simulations of magnetized hadron dynamics.

Abstract

The mass spectrum of hadrons in magnetic fields features avoided level-crossing structures arising from the mixing of spin eigenstates. In this work, we investigate the impact of level-crossing dynamics of charmonia subjected to time-dependent magnetic fields, where we particularly focus on the occupation probabilities of two or more states as they undergo transitions at avoided crossings. Using a static spectrum of charmonia in magnetic fields, we construct a multi-channel Landau-Zener Hamiltonian. Within this framework, we analyze the time evolution under several representative magnetic-field profiles, including linear ramps and Gaussian decays corresponding to single-passage dynamics, as well as Gaussian pulses realizing double-passage dynamics, and compute the occupation probabilities over a wide range of sweep rates and initial conditions. Our results show that nonadiabatic dynamics, including Landau-Zener transitions and St\"uckelberg interference, strongly influences the occupation probabilities of charmonia. These findings provide new insights into the real-time dynamics of magnetized hadrons and offer useful guidance for future lattice simulation studies.