Time Reversal Symmetry for Classical, Nonrelativistic Quantum and Spin Systems in Presence of Magnetic Fields

TL;DR

This paper extends classical results on time reversal symmetry to nonrelativistic quantum and spin systems in magnetic fields, showing that certain symmetries and reciprocal relations hold without additional conditions.

Contribution

It demonstrates that time reversal invariance persists in quantum and spin systems under magnetic fields, generalizing classical results without needing Casimir modifications.

Findings

Time reversal symmetry holds in quantum systems with magnetic fields.

Spin-field interaction does not break time reversal invariance.

Onsager reciprocal relations are derived without Casimir modifications.

Abstract

We extend to quantum mechanical systems results previously obtained for classical mechanical systems, concerning time reversibility in presence of a magnetic field. As in the classical case, results like the Onsager reciprocal relations are consequently obtained, without recourse to the Casimir modification. The quantum systems treated here are nonrelativistic, and are described by the Schr{\"o}dinger equation or the Pauli equation. In particular, we prove that the spin-field interaction does not break the time reversal invariance (TRI) of the dynamics, and that it does not require additional conditions for such a symmetry to hold, compared to the spinless cases.