Quantum-mechanical equation for spectroscopic transitions in ordered ferroelectric and ferromagnetic chains

TL;DR

This paper develops a quantum-mechanical framework for describing spectroscopic transitions in ordered ferroelectric and ferromagnetic chains, deriving a Lorentz-invariant Landau-Lifshitz equation and applying it to experimental optical data.

Contribution

It introduces a quaternion-based, Lorentz-invariant quantum equation for spectroscopic transitions in ordered chains, linking theory with experimental spin measurements.

Findings

First optical measurement of spin S=1/2 for spin-Peierls solitons in carbon chains.

Derived ratio of imaginary to real components of complex charge as approximately 100.

Established a quaternionic, Lorentz-invariant form of the Landau-Lifshitz equation.

Abstract

Transition operator method is proposed for description of the dynamics of spectroscopic transitions. Quantum-mechanical analogue of Landau-Lifshitz equation has been derived for the system representing itself the periodical ferroelectrically (ferromagnetically) ordered chain of $N$ equivalent elements, interacting with external oscillating electromagnetic field. Landau-Lifshitz equation was represented in Lorentz invariant form by using Hilbert space over the ring of quaternions. It has been shown, that spin vector can be considered to be quaternion vector of the state of the system studied. From comparison with experiment for the first time from pure optical measurements the value of spin $S = 1/2$ for optically active centers - spin-Peierls solitons in carbon chains - has been obtained. The ratio of imagine to real components of complex charge is evaluated for given centers to be $\frac{g}{e} \approx (1.1 - 1.3)10^{2}$.