A Novel Class of Phase Space Representations for the Exact Population Dynamics of Two-State Quantum Systems and the Relation to Triangle Window Functions

Abstract

Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart. We use the constraint phase space developed in J. Chem. Phys. 2016, 145, 204105; 2019, 151, 024105 and J. Phys. Chem. Lett. 2021, 12, 2496-2501, non-covariant phase space functions, time-dependent weight functions, and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system. The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation. The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite. We also prove that the triangle window function approach, albeit proposed as a heuristic empirical model in J. Chem. Phys. 2016, 145, 144108, is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.

References in corpus (9)

• A Unified Theoretical Framework for Mapping Models for the Multi-State Hamiltonian
• Unified Formulation of Phase Space Mapping Approaches for Nonadiabatic Quantum Dynamics
• Negative Zero-Point-Energy Parameter in the Meyer-Miller Mapping Model for Nonadiabatic Dynamics
• Nonadiabatic Field on Quantum Phase Space: A Century after Ehrenfest
• Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics
• Performance Evaluation of the Symmetrical Quasi-Classical Dynamics Method based on Meyer-Miller Mapping Hamiltonian in the Treatment of Site-Exciton Models
• Nonadiabatic Field with Triangle Window Functions on Quantum Phase Space
• Isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian with only 1-electron interactions
• Initial Sampling in Symmetrical Quasiclassical Dynamics Based on Li-Miller Mapping Hamiltonian

Cited by in corpus (4)

• Nonadiabatic Field with Triangle Window Functions on Quantum Phase Space
• Nonadiabatic Field: A Conceptually Novel Approach for Nonadiabatic Quantum Molecular Dynamics
• Twin-Space Representation of Classical Mapping Model in the Constraint Phase Space Representation: Numerically Exact Approach to Open Quantum Systems
• Geometric Phase Effect in Thermodynamic Properties and in the Imaginary-Time Multi-Electronic-State Path Integral Formulation