On Computing Spectral Densities from Classical, Semiclassical and Quantum Simulations

Abstract

The Caldeira-Leggett model provides a compact characterization of a thermal environment in terms of a spectral density function. This simplicity has led to a variety of numerically exact quantum methods for reduced density matrix propagation. When using these methods, a spectral density has to be computed from dynamical properties of system and environment, which is commonly done using classical molecular dynamics simulations. However, there are situations, where quantum effects could play a role. Therefore, we reformulate our recently developed Fourier method in order to enable spectral density calculations from semiclassical simulations which approximately consider quantum effects. We propose two possible protocols based on either correlation functions or expectation values. These protocols are tested for the linearized semiclassical initial-value representation (LSC-IVR), the thawed Gaussian wave packet dynamics (TGWD) and hybrid schemes combining the two with the more accurate Herman-Kluk (HK) formula. Surprisingly, spectral densities from the LSC-IVR method, based on a completely classical propagation, are extremely accurate whereas those from the single-trajectory TGWD are of poor quality in the anharmonic regime. The hybrid methods provide reasonable quality when the system is close to the classical regime, although, at finite temperature, the computation protocol from expectation values turns out to be more robust. If stronger quantum effects are observed, both hybrid methods turn out as too inaccurate.

arXiv comment29 pages, 5 figures

References in corpus (11)

• Non-Markovian Quantum State Diffusion
• Exact c-number Representation of Non-Markovian Quantum Dissipation
• Hierarchy of stochastic pure states for open quantum system dynamics
• Analytic Representations of Bath Correlation Functions for Ohmic and Superohmic Spectral Densities Using Simple Poles
• Simulating spin-boson dynamics with stochastic Liouville-von Neumann equations
• On-the-fly ab initio semiclassical dynamics: Identifying degrees of freedom essential for emission spectra of oligothiophenes
• Mixed Semiclassical Initial Value Representation Time-Averaging Propagator for Spectroscopic Calculations
• On the Applicability of the Caldeira-Leggett Model to Condensed Phase Vibrational Spectroscopy
• Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations
• Vibrational spectroscopy via the Caldeira-Leggett model with anharmonic system potentials
• Semiclassical Propagation: Hilbert Space vs. Wigner Representation

Cited by in corpus (3)

• Modeling intermolecular and intramolecular modes of liquid water using multiple heat baths: Machine learning approach
• On Hagedorn wavepackets associated with different Gaussians
• Complexified phase spaces, initial value representations, and the accuracy of semiclassical propagation