On the Generalized Bloch Precession Equations

TL;DR

This paper generalizes the classical Bloch equations to include higher-rank polarization tensors in arbitrary multipole fields, simplifying their derivation through a specialized bra-ket notation.

Contribution

It introduces a unified framework for the evolution of polarization tensors of various ranks, extending the applicability of Bloch equations to complex multipole fields.

Findings

Derived generalized Bloch equations for higher-rank tensors

Simplified derivation using bra-ket notation

Applicable to arbitrary multipole magnetic fields

Abstract

The Bloch equations, which describe spin precession and relaxation in external magnetic fields, can be generalized to include the evolution of polarization tensors of various ranks in arbitrary multipole fields. The derivation of these generalized Bloch equations can be considerably simplified by using a particular bra-ket notation for irreducible tensors.