A partially linearized spin-mapping approach for nonadiabatic dynamics. I. Derivation of the theory

Abstract

We present a new partially linearized mapping-based approach for approximating real-time quantum correlation functions in condensed-phase nonadiabatic systems, called spin-PLDM. Within a classical trajectory picture, partially linearized methods treat the electronic dynamics along forward and backward paths separately by explicitly evolving two sets of mapping variables. Unlike previously derived partially linearized methods based on the Meyer-Miller-Stock-Thoss mapping, spin-PLDM uses the Stratonovich-Weyl transform to describe the electronic dynamics for each path within the spin-mapping space; this automatically restricts the Cartesian mapping variables to lie on a hypersphere and means that the classical equations of motion can no longer propagate the mapping variables out of the physical subspace. The presence of a rigorously derived zero-point energy parameter also distinguishes spin-PLDM from other partially linearized approaches. These new features appear to give the method superior accuracy for computing dynamical observables of interest, when compared with other methods within the same class. The superior accuracy of spin-PLDM is demonstrated within this paper through application of the method to a wide range of spin-boson models, as well as to the Fenna-Matthews-Olsen complex.

arXiv comment15 pages, 5 figures

References in corpus (25)

• Efficient classical simulation of slightly entangled quantum computations
• Quantum entanglement in photosynthetic light harvesting complexes
• Mapping Variable Ring Polymer Molecular Dynamics: A Path-Integral Based Method for Nonadiabatic Processes
• Quantum-Classical Liouville Dynamics in the Mapping Basis
• Modified-scaled hierarchical equation of motion approach for the study of quantum coherence in photosynthetic complexes
• Mapping quantum-classical Liouville equation: projectors and trajectories
• Generalized spin mapping for quantum-classical dynamics
• Nonadiabatic Dynamics in Open Quantum-Classical Systems: Forward-Backward Trajectory Solution
• Spin-mapping approach for nonadiabatic molecular dynamics
• Generalized Quantum Master Equations In and Out of Equilibrium: When Can One Win?
• Approximate but Accurate Quantum Dynamics from the Mori Formalism: I. Nonequilibrium Dynamics
• On the identity of the identity operator in nonadiabatic linearized semiclassical dynamics
• Analysis of the Forward-Backward Trajectory Solution for the Mixed Quantum-Classical Liouville Equation
• Path-Integral Isomorphic Hamiltonian for Including Nuclear Quantum Effects in Non-adiabatic Dynamics
• Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations
• Coherent State Mapping Ring-Polymer Molecular Dynamics for Non-Adiabatic quantum propagations
• Improved population operators for multi-state nonadiabatic dynamics with the mixed quantum-classical mapping approach
• Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics
• Approximate but accurate quantum dynamics from the Mori formalism: II. Equilibrium correlation functions
• Ultra-Fast Relaxation, Decoherence and Localization of Photoexcited States in $\pi$-Conjugated Polymers: A TEBD Study
• A partially linearized spin-mapping approach for nonadiabatic dynamics. II. Analysis and comparison with related approaches
• SU(N)-symmetric quasi-probability distribution functions
• Investigating Photoinduced Proton Coupled Electron Transfer Reaction using Quasi Diabatic Dynamics Propagation
• Isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian with only 1-electron interactions
• Exciton Dissociation and Charge Separation at Donor-Acceptor Interfaces from Quantum-Classical Dynamics Simulations

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