Trajectory Ensemble Methods Provide Single-Molecule Statistics for Quantum Dynamical Systems

Abstract

The emergence of experiments capable of probing quantum dynamics at the single-molecule level requires the development of new theoretical tools capable of simulating and analyzing these dynamics beyond an ensemble-averaged description. In this article, we present an efficient method for sampling and simulating the dynamics of the individual quantum systems that make up an ensemble and apply it to study the nonequilibrium dynamics of the ubiquitous spin-boson model. We generate an ensemble of single-system trajectories, and we analyze this trajectory ensemble using tools from classical statistical mechanics. Our results demonstrate that the dynamics of quantum coherence is highly heterogeneous at the single-system level due to variations in the initial bath configuration, which significantly affects the transient exchange of coherence between the system and its bath. We observe that single systems tend to retain coherence over time scales longer than that of the ensemble. We also compute a novel thermodynamic entanglement entropy that quantifies a thermodynamic driving force favoring system−bath entanglement.

A Semiclassical Framework for Mixed Quantum Classical Dynamics

“…Nonadiabatic dynamic processes, where nuclear motion is coupled to and drives transitions between electronic states, have been studied using a variety of SC-IVR methods. ,,,− ,− This is facilitated by the Meyer-Miller-Stock-Thoss (MMST) mapping , where discrete electronic state variables are mapped to continuous Cartesian electronic phase space variables that can undergo approximate time-evolution under a classical analog Hamiltonian. Using the MMST mapping, a nonadiabatic MQC-IVR expression can be derived to enable independent control over the extent of quantization of the nuclear and electronic degrees of freedom .…”

Perturbation theory under the truncated Wigner approximation reveals how system-environment entanglement formation drives quantum decoherence

“…[9][10][11][12][13][14][15][16][17] This would suggest implementation strategies akin to those found in natural light harvesting, where discrete quantum systems in the form of coupled chromophores experience an environment tailored to their functioning: the efficient dynamical localization of quantum excitations on an acceptor state. [18,19] Modeling the transient behavior of discrete quantum systems and their environments can provide mechanistic insight on how details of an initial state preparation and systemenvironment interactions impact their evolution, [20] while offering an opportunity to optimize function by engineering these factors. There has been an enormous effort in the development of efficient nonadiabatic quantum dynamics techniques that are capable of reliably modeling decoherence processes following preparation of an initial nonequilibrium state.…”

“…Instead, it only imposes that the initial environmental Wigner function be of a Gaussian form that encompasses both the thermal density and (shifted) wave packets, which may be utilized as a means to describe configurations of a single discrete quantum system. [20] For the harmonic environment model considered here, our framework provides a fully consistent avenue for deriving (nearly) analytical time-dependent expectation values of operators in the system and environment Hilbert space, including that of entanglement entropy.…”