Dynamics in the quantum/classical limit based on selective use of the quantum potential

Area of Science:

• Quantum mechanics and molecular dynamics simulations.

Background:

• The time-dependent Schrödinger equation describes quantum dynamics.
• The quantum potential, a non-local quantity, generates quantum mechanical features.
• Hybrid quantum/classical methods are needed for molecular systems with light and heavy nuclei.

Purpose of the Study:

• To define a classical limit of quantum dynamics by compensating the quantum potential.
• To develop a hybrid quantum/classical dynamics approach for molecular systems.
• To avoid Ehrenfest averaging in mixed quantum/classical methods.

Main Methods:

• Defining a classical limit via quantum potential compensation in the Schrödinger equation.
• Employing a trajectory-based form of the Schrödinger equation (Madelung, de Broglie, Bohm).
• Using selective inclusion of the quantum potential for "quantum" degrees of freedom.
• Applying conventional grid-based and approximate quantum-trajectory time propagation.
• Defining an approximate quantum force on spatial domains to prevent unphysical wavefunction coupling.

Main Results:

• The hybrid approach successfully examines the evolution of light/heavy systems in harmonic and double-well potentials.
• The method avoids unphysical coupling of wavefunction fragments across distinct classical channels.
• The quantum potential generates forces on both quantum and classical particles, accounting for backreaction.

Conclusions:

• The developed hybrid quantum/classical dynamics method provides a robust framework for simulating complex molecular systems.
• This approach accurately captures quantum effects in specific degrees of freedom while treating others classically.
• The backreaction of the quantum potential on classical particles is effectively modeled.