On computing spectral densities from classical, semiclassical, and quantum simulations.

Area of Science:

• Quantum chemistry
• Computational physics
• Chemical dynamics

Background:

• The Caldeira-Leggett model characterizes thermal environments using spectral density functions.
• This has enabled various quantum methods for reduced density matrix propagation.
• Spectral densities are often derived from classical molecular dynamics simulations.

Purpose of the Study:

• To investigate the necessity of including quantum effects in spectral density calculations.
• To reformulate the Fourier method for spectral density calculations from semiclassical simulations.
• To evaluate different protocols for incorporating approximate quantum effects.

Main Methods:

• Reformulation of the Fourier method for spectral density calculations.
• Proposal of two protocols: correlation functions and expectation values.
• Testing on Caldeira-Leggett model using linearized semiclassical initial-value representation (LSC-IVR), thawed Gaussian wave packet dynamics (TGWD), and hybrid schemes.

Main Results:

• LSC-IVR, a classical method, yielded highly accurate spectral densities even in the quantum regime.
• TGWD and hybrid schemes showed inaccuracies in spectral density calculations.
• Spectral densities were found to be insensitive to quantum effects in the Caldeira-Leggett model.

Conclusions:

• Classical simulations are sufficient for computing spectral densities in the Caldeira-Leggett model.
• Attempting to include approximate quantum effects can introduce errors.
• Computed spectral densities from classical simulations can be reliably used in reduced quantum simulations.