Semiclassical Dynamics in Wigner Phase Space I : Adiabatic Hybrid Wigner Dynamics
arXiv:2405.20493 · doi:10.1063/5.0223185
Abstract
The Wigner phase space formulation of quantum mechanics is a complete framework for quantum dynamic calculations that elegantly highlights connections with classical dynamics. In this series of two articles, building upon previous efforts, we derive the full hierarchy of approximate semiclassical (SC) dynamic methods for adiabatic and non-adiabatic problems in Wigner phase space. In paper I, focusing on adiabatic single surface processes, we derive the well-known Double Herman-Kluk (DHK) approximation for real-time correlation functions in Wigner phase space, and connect it to the Linearized SC (LSC) approximation through a stationary phase approximation. We exploit this relationship to introduce a new hybrid SC method, termed Adiabatic Hybrid Wigner Dynamics (AHWD) that allows for a few important `system' degrees of freedom (dofs) to be treated at the DHK level, while treating the rest of the dofs (the `bath') at the LSC level. AHWD is shown to accurately capture quantum interference effects in models of coupled oscillators, and the decoherence of vibrational probability density of a model I Morse oscillator coupled to an Ohmic thermal bath. We show that AHWD significantly mitigates the sign-problem and employs a reduced dimensional prefactor bringing calculations of complex system-bath problems within the reach of SC methods. Paper II focuses on extending this hybrid SC dynamics to nonadiabatic processes.
References in corpus (41)
- Phase space representation of quantum dynamics
- Full dimensional (15D) quantum-dynamical simulation of the protonated water-dimer II: infrared spectrum and vibrational dynamics
- Dynamics and Infrared Spectroscopy of the Protonated Water Dimer
- Full dimensional (15D) quantum-dynamical simulation of the protonated water-dimer I: Hamiltonian setup and analysis of the ground vibrational state
- Chemical Reaction Rates from Ring Polymer Molecular Dynamics: Theory and Practical Applications
- Boltzmann-conserving classical dynamics in quantum time-correlation functions: Matsubara dynamics
- Quantum Dynamics of Vibrational Polariton Chemistry
- Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics
- Non-Markovian Dissipative Semiclassical Dynamics
- Semiclassical Theory of Coherence and Decoherence
- Quantum-Classical Correspondence via Liouville Dynamics: I. Integrable Systems and the Chaotic Spectral Decomposition
- Path-integral dynamics of water using curvilinear centroids
- Semiclassical propagator of the Wigner function
- The coupling of the hydrated proton to its first solvation shell
- Quantum-Classical Correspondence via Liouville Dynamics: II. Correspondence for Chaotic Hamiltonian Systems
- The Shape of the Electric Dipole Function Determines the Sub-Picosecond Dynamics of Anharmonic Vibrational Polaritons
- Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation
- The Importance of the Pre-exponential Factor in Semiclassical Molecular Dynamics
- Quantum dynamics using path integral coarse-graining
- Long-time and unitary properties of semiclassical initial value representations
- On the propagation of semiclassical Wigner functions
- Validating and Implementing Modified Filinov Phase Filtration in Semiclassical Dynamics
- Vibrational strong coupling in liquid water from cavity molecular dynamics
- Fast quasi-centroid molecular dynamics
- Semiclassical propagation of Wigner functions
- Dissociation dynamics of a diatomic molecule in an optical cavity
- Anharmonic quantum mechanical systems do not feature phase space trajectories
- Proton Tunneling in a Two-Dimensional Potential Energy Surface with a Non-linear System-Bath Interaction: Thermal Suppression of Reaction Rate
- Mean-field Matsubara dynamics: Analysis of path-integral curvature effects in rovibrational spectra
- Testing the quasicentroid molecular dynamics method on gas-phase ammonia
- A Semiclassical Framework for Mixed Quantum Classical Dynamics
- Semiclassical investigation of revival phenomena in one dimensional system
- Semiclassical dynamics in the mixed quantum-classical limit
- Quantum revival patterns from classical phase-space trajectories
- A Linearized Semiclassical dynamics study of the multi-quantum vibrational relaxation of NO scattering from a Au(111) Surface
- Fast quasi-centroid molecular dynamics for water and ice
- Non-Linear Correlation Functions and Zero-Point Energy Flow in Mixed Quantum-Classical Semiclassical Dynamics
- Comparison of Matsubara dynamics with exact quantum dynamics for an oscillator coupled to a dissipative bath
- Semiclassical Propagation: Hilbert Space vs. Wigner Representation
- Effective Markovian description of decoherence in bound systems
- Semiclassical Dynamics in Wigner Phase Space II : nonadiabatic Hybrid Wigner Dynamics