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 condensedphase nonadiabatic systems, called the spin partially linearized density matrix (spin-PLDM) approach. 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 in this paper through application of the method to a wide range of spin-boson models as well as to the Fenna-Matthews-Olsen complex.

Path-integral approximations to quantum dynamics

“…Some calculations have used the surface-hopping technique to do this [139,146]. Another approach [147][148][149][150][151][152][153][154][155][156] is the use of mapping-variables [168,169] which has the advantage of making both the electronic and the nuclear degrees of freedom classical (at the price of requiring the use of projection operators). Recently, Chowdhury and Huo [70] have developed 'non-adiabatic Matsubara dynamics', which treats the mapping variables quantum mechanically and the nuclear coordinates by Matsubara dynamics.…”

Non-adiabatic Matsubara Dynamics and Non-adiabatic Ring Polymer Molecular Dynamics

“…If so, then non-adiabatic Matsubara will be a trajectory-based approach that can correctly describe electronic Rabi oscillations and preserve the QBD, a method that is currently lacking. 101 We hope that our current work provides a framework and a new paradigm for accurate non-adiabatic quantum dynamics approaches by interfacing the recent development in the field of mapping dynamics [such as new mapping representations [102][103][104][105][106] as well as new estimators (window functions 107,108 and the identity trick 109 )] with the development of accurate nuclear quantum dynamics in the field of path-integral dynamics [such as the Matsubara dynamics [69][70][71][72] and its approximations, including CMD, 40,73 RPMD, 43,44,73 mean-field Matsubara dynamics, 86 quasi-CMD 87 , Planetary model 70,88 , etc]. It allows one to borrow recent developments from each subfield, and facilitate the merger of both sub-fields for developing more accurate non-adiabatic quantum dynamics approaches.…”

Speeding up quantum dissipative dynamics of open systems with kernel methods

“…In addition to these methods, another popular approach is classical mapping-based approach (Meyer-Miller-Stock-Thoss mapping, [35][36][37][38][39] spin-based mapping 40,41 and so on), where system and surrounding environment dynamics is described by classical trajectories. Classical mapping-based approaches are more feasible but because of the classical description, they fail to properly describe the dynamics of the system especially at low temperature.…”