Derivation of a time dependent Schr\"odinger equation as quantum mechanical Landau-Lifshitz-Bloch equation

TL;DR

This paper derives a quantum mechanical version of the Landau-Lifshitz-Bloch equation, resulting in a time-dependent Schrödinger equation with relaxation terms, supported by analytical proofs and simulations.

Contribution

It introduces a novel derivation of a relaxation-inclusive Schrödinger equation from classical magnetization dynamics equations.

Findings

Derivation of a quantum Landau-Lifshitz-Bloch type Schrödinger equation

Analytical proofs confirming the equation's correctness

Computer simulations demonstrating applicability

Abstract

The derivation of the time dependent Schr\"odinger equation with transversal and longitudinal relaxation, as the quantum mechanical analog of the classical Landau-Lifshitz-Bloch equation, has been described. Starting from the classical Landau-Lifshitz-Bloch equation the transition to quantum mechanics has been performed and the corresponding von-Neumann equation deduced. In a second step the time Schr\"odinger equation has been derived. Analytical proofs and computer simulations show the correctness and applicability of the derived Schr\"odinger equation.