Time evolution of spin singlet in static homogeneous exchange and magnetic fields

TL;DR

This paper investigates how static homogeneous exchange and magnetic fields influence the time evolution of the spin singlet state of two electrons using a rotation-invariant approach, with implications for superconductivity and spin chemistry.

Contribution

It introduces a rotation-invariant method to analyze the spin singlet, revealing the form of the interaction Hamiltonian and its time evolution under external fields.

Findings

Derived a generalized spin singlet representation based on invariance principles.

Showed the form of the interaction Hamiltonian with external fields.

Applied results to ferromagnetic superconductors and spin chemistry.

Abstract

Within the framework of an idealized theoretical model, we study the effect of external static homogeneous exchange and magnetic field on the spin part of the singlet wave function of two electrons. We begin by revising the traditional (text- book) approach to the spin singlet. Basing our own approach solely on the property of invariance under rotations of the coordinate system and using the theory of spinor in- variants, we derive a generalized representation of the spin singlet whose main feature is that the spins are in mutually time-reversed states. We show that exactly this fea- ture predetermines the actual form of the Hamiltonian of interaction with the external field and stipulates time evolution of the singlet. Some applications of these results to the theory of superconductivity and spin chemistry are presented. In particular, it is shown that the case of ferromagnetic superconductors constitutes a good illustration of the validity of our quantum-mechanical consideration.