Quantum Boltzmann equation for fermions: An attempt to calculate the NMR relaxation and decoherence times using quantum field theory techniques

TL;DR

This paper employs the quantum Boltzmann equation and quantum field theory techniques to analyze nucleon density matrix evolution, aiming to compute NMR relaxation and decoherence times.

Contribution

It introduces a quantum field theory-based approach to derive the quantum Boltzmann equation for nucleons and applies it to calculate NMR relaxation and decoherence times.

Findings

Derived Bloch equations for nucleons in magnetic fields.

Calculated longitudinal and transverse relaxation times.

Demonstrated the use of forward scattering and collision terms.

Abstract

Extracting macroscopic properties of a system from microscopic interactions has always been an interesting topic with the most diverse applications. Here, we use the quantum Boltzmann equation to investigate the density matrix evolution of a system of nucleons. Using the quantum field theory tools for constructing the density matrix operators and calculating the interactions is the main advantage of this equation. The right-hand side of this equation involves forward scattering and usual collision terms. As examples of application, we calculate the standard Bloch equations for the nucleon system in the presence of a constant and an oscillating magnetic field from the forward scattering term. We find the longitudinal and transverse (decoherence) relaxation times from the collision term by considering the nucleon-nucleon scattering.