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arXiv:0810.3540 · Journal of Statistical Physics

A Resonance Theory for Open Quantum Systems with Time-Dependent Dynamics

Marco Merkli, Shannon Starr

Published Nov 10, 2008• 4 citations
arXivHTMLPDF
DOI
10.1007/s10955-008-9645-5

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An open quantum system is a system 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 the analysis of spectra obtained from the advanced nuclear magnetic resonance (NMR) and muon spin rotation, relaxation or resonance (μSR) 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 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.
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Understanding quantum many-body systems with long-range or infinite-range interactions is of relevance across a broad set of physical disciplines, including quantum optics, nuclear magnetic resonance and nuclear physics. From a theoretical viewpoint, these systems are appealing since they can be efficiently studied with numerics, and in the thermodynamic limit are expected to be governed by mean-field equations of motion. Over the past years the capabilities to experimentally create long-range interacting systems have dramatically improved permitting their control in space and time. This allows to induce and explore a plethora of nonequilibrium dynamical phases, including time-crystals and even chaotic regimes. However, establishing the emergence of these phases from numerical simulations turns out to be surprisingly challenging. This difficulty led to the assertion that mean-field theory may not be applicable to time-dependent infinite-range interacting systems. Here, we rigorously prove that mean-field theory in fact exactly captures their dynamics, in the thermodynamic limit. We further provide bounds for finite-size effects and their dependence on the evolution time.