Dynamic equations for three different qudits in a magnetic field

TL;DR

This paper derives a comprehensive set of dynamic equations for three magnetic qudits in a time-dependent magnetic field, facilitating analysis of their quantum behavior using algebraic structures.

Contribution

It introduces a novel method for deriving closed-form equations for qudit systems in arbitrary magnetic fields, including calculations of algebraic structure constants.

Findings

Derived equations for local Bloch vectors and spin correlations

Presented an algorithm for equation derivation

Calculated structure constants for su(2S+1) algebra

Abstract

A closed system of equations for the local Bloch vectors and spin correlation functions of three magnetic qudits, which are in an arbitrary, time-dependent, external magnetic field, is obtained using decomplexification of the Liouville-von Neumann equation. The algorithm of the derivation of the dynamic equations is presented. In the basis convenient for the important physical applications structure constants of algebra su(2S+1) are calculated.