Quantum-classical path integral. I. Classical memory and weak quantum nonlocality.

Area of Science:

• Quantum Dynamics
• Chemical Physics
• Computational Chemistry

Background:

• Path integral methods describe quantum systems interacting with environments.
• Current quantum-(semi)classical path integral (QCPI) methods are computationally expensive due to non-local time couplings.
• Accurate simulation of quantum systems requires efficient handling of environmental interactions.

Purpose of the Study:

• To develop practical path integral methods for quantum systems coupled to classical environments.
• To analyze the nature of environmental effects on quantum systems.
• To enable large-scale simulations of quantum dynamics.

Main Methods:

• Approximating the polyatomic environment with classical trajectories.
• Developing a "classical path" limit of QCPI.
• Introducing an inexpensive random hop QCPI model for corrections.
• Iterative evaluation of the path integral to include quantum decoherence.
• Utilizing Monte Carlo methods for multidimensional phase space integrals.

Main Results:

• The classical path limit of QCPI effectively captures system decoherence via classical mechanisms.
• The random hop QCPI model provides small corrections for back-reaction effects.
• Iterative path integral evaluation allows for further inclusion of quantum decoherence.
• A smooth integrand facilitates Monte Carlo integration for phase space calculations.

Conclusions:

• The classical path approximation offers a computationally feasible approach for simulating quantum system dynamics with classical environments.
• This work provides a pathway towards more accurate and scalable simulations of quantum decoherence.
• The developed methods pave the way for efficient exploration of complex quantum-classical systems.