Berry Phase for Systems with Angular Momenta in Electric and Magnetic Fields

TL;DR

This paper explores the Berry phase in systems with two angular momenta under electric and magnetic fields, demonstrating its robustness across diverse quantum systems and suggesting new avenues for experimental and theoretical research.

Contribution

It extends the understanding of Berry phase to various angular momentum systems, highlighting its geometric nature and potential for future studies with electric fields.

Findings

Berry phase is robust across different angular momentum systems.

Time varying magnetic fields induce a consistent geometric phase.

Potential for new studies with electric fields is indicated.

Abstract

The Berry phase for a variety of systems comprising of two angular momenta is discussed. These include the electron and proton in the ground state of the hydrogen atom (taking into account the hyperfine interaction), the positronium atom, the spin and orbital angular momenta of a single electron, muon capture by the deuteron in an external magnetic field, etc. Though the time scales involved, the underlying intrinsic Hamiltonians are quite different, as also the possible experimental probes, the geometric nature of the results for the Berry phase due to a time varying externally imposed magnetic field is found to be quite robust. Some indications are also put forward as to the possible interesting studies with time varying electric fields. The objective of this work is an attempt to broaden the scope of such studies in both the experimental and theoretical directions.