Extended hydrodynamic approach to quantum-classical nonequilibrium evolution. I. Theory.

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Computational chemistry

Background:

• Modeling quantum systems interacting with large classical environments is computationally challenging.
• Existing methods often struggle to capture the complex dynamics at the quantum-classical interface.
• Hydrodynamic representations offer a promising avenue for simplifying these systems.

Purpose of the Study:

• To develop a novel mixed quantum-classical formulation for quantum subsystems coupled to a classical N-particle environment.
• To derive exact quantum hydrodynamic equations for the system.
• To investigate various closure schemes for approximating the resulting hierarchy of equations.

Main Methods:

• Starting from the quantum Liouville equation for N-particle and reduced single-particle distributions.
• Deriving exact quantum hydrodynamic equations for momentum moments.
• Applying closure approximations: Grad-Hermite, Gaussian, and dynamical density functional theory.
• Taking the quantum-classical limit.

Main Results:

• Exact quantum hydrodynamic equations were derived for the single-particle distribution moments.
• The study successfully implemented and compared three distinct closure schemes.
• A mixed quantum-classical formulation consistent with prior work was recovered via the dynamical density functional theory approximation.

Conclusions:

• The developed mixed quantum-classical formulation provides a versatile framework for studying quantum-classical systems.
• The explored closure schemes offer different levels of approximation and applicability.
• This work advances the computational treatment of complex quantum-environment interactions.