Ehrenfest dynamics with spontaneous localization.

Area of Science:

• Quantum dynamics
• Theoretical chemistry
• Computational physics

Background:

• Mixed quantum-classical methods are essential for simulating chemical processes.
• Existing methods often use ad hoc decoherence corrections, lacking physical rigor.
• There is a need for a consistent theoretical framework to address decoherence.

Purpose of the Study:

• To develop a decoherence-corrected extension of Ehrenfest dynamics.
• To provide a physically consistent alternative to current mixed quantum-classical methods.
• To establish a rigorous and extensible framework for quantum dynamics.

Main Methods:

• Propose Ehrenfest Dynamics with Spontaneous Localization (SLED), based on the Gisin-Percival quantum-state diffusion equation.
• The electronic wave function evolves stochastically in the adiabatic energy basis, leading to trajectory-level localization.
• The ensemble of trajectories reproduces Lindblad-type propagation of the reduced electronic density matrix, ensuring linearity, trace preservation, and complete positivity.

Main Results:

• SLED successfully reproduces electronic populations in benchmark simulations.
• The method captures essential features of coherence decay in Tully models and spin-boson Hamiltonians.
• Generalizing the localization kernel is identified as crucial for accurate electron-nucleus coupling treatment.

Conclusions:

• SLED provides a rigorous and extensible framework for mixed quantum-classical dynamics.
• It bridges the gap between mixed quantum-classical methods and open quantum system theory.
• Future work will focus on refining the localization kernel for improved accuracy.