2018/04/24 by Fabian Gottwald, Sergei D. Ivanov, Oliver Kühn
Physics and Astronomy · #Advanced Chemical Physics Studies #Physics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Semiclassical physics #Spectroscopy and Quantum Chemical Studies #Statistical physics #physics.chem-ph
paper · pdf · doi:10.1063/1.5045293
29 pages, 5 figures
arxiv created 2018/04/24 · openalex publication_date 2019/02/27 · arxiv updated 2019/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Caldeira-Leggett model provides a compact characterization of a thermal environment in terms of a spectral density function, which has led to a variety of numerically exact quantum methods for reduced density matrix propagation. Since spectral densities are often computed from classical molecular dynamics simulations, we investigate in this paper whether quantum effects should be accounted for in the calculations. Therefore, we reformulate the recently developed Fourier method for spectral density calculations from semiclassical simulations which approximately allow for quantum effects. We propose two possible protocols based on either correlation functions or expectation values. These protocols are tested on a generic Calderra-Leggett model 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 formula. Surprisingly, spectral densities from the LSC-IVR method, which treats the dynamics completely classically, are found to be extremely accurate, even in the quantum regime, where this method does not give a correct description of the correlation functions and expectation values. In contrast, the TGWD method turns out as too inaccurate for spectral density calculations, and the hybrid schemes perform well only if the system is close to the classical regime. This implies that, if the bath has a Caldeira-Leggett form, spectral densities are insensitive to quantum effects and any effort to approximately account for them rather leads to errors. Hence, in this case, spectral densities can be computed from classical simulations and used in a reduced quantum simulation as well.