Abstract
An open quantum system refers to a system, which is in turn coupled to an environment that can describe time irreversible dynamics through which the system evolves toward the thermal equilibrium state. We present a quantum mechanically rigorous theory in order to help an analysis of spectra obtained from the advanced nuclear magnetic resonance (NMR) and muon spin rotation, relaxation or resonance ($\mu$SR) techniques. Our approach is based on the numerically "exact" hierarchical equations of motion (HEOM) approach, which allows us to study the reduced system dynamics for non-perturbative and non-Markovian system-bath interactions at finite temperature even under strong time-dependent perturbations. We demonstrate the present theory to analyze $\mu$SR and low-field NMR spectra, as an extension of the Kubo-Toyabe theory focusing on the effects of temperature and anisotropy of a local magnetic field, to help further the development of these experimental means.
Highlights
For the analysis of nuclear magnetic resonance (NMR) and ESR spectroscopies, the quantum master equation or the Redfield theory has been developed to describe the effects of the longitudinal and transversal relaxations characterized by the time constants T1 and T2 .1,2) the stochastic theory has been employed to describe the effects of the inhomogeneous dephasing characterized by the time decay constant T2y in the fast modulation limit.3) Owing to the advent of experimental techniques that include NMR and ESR, spin dynamics are investigated under extreme physical conditions, such as quantum computing, where the quantum nature of an environment plays an essential role.4,5) such existing theories are insufficient to investigate the complex motion of a spin system
We present a quantum mechanically rigorous theory in order to help the analysis of spectra obtained from the advanced nuclear magnetic resonance (NMR) and muon spin rotation, relaxation or resonance techniques
We demonstrate the present theory to analyze μSR and low-field NMR spectra, as an extension of the Kubo–Toyabe theory focusing on the effects of temperature and anisotropy of a local magnetic field on spectra, to help further the development of these experimental means
Summary
For the analysis of NMR and ESR spectroscopies, the quantum master equation or the Redfield theory has been developed to describe the effects of the longitudinal and transversal relaxations characterized by the time constants T1 and T2 .1,2) the stochastic theory has been employed to describe the effects of the inhomogeneous dephasing characterized by the time decay constant T2y in the fast modulation limit.3) Owing to the advent of experimental techniques that include NMR and ESR, spin dynamics are investigated under extreme physical conditions, such as quantum computing, where the quantum nature of an environment plays an essential role.4,5) such existing theories are insufficient to investigate the complex motion of a spin system This is true for zero- to ultralow-field. In 1966, Kubo and Toyabe developed the spin relaxation theory for NMR in zero or weak external magnetic field comparable to the local field from a stochastic approach.11) Such a low-field measurement was realized by μSR spectroscopy, and since the Kubo–Toyabe theory has been employed to analyze the long-time behavior of the μSR spectrum to probe a local environment of materials.).
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