Quantum Dynamics with the Quantum Trajectory-Guided Adaptable Gaussian Bases.

Area of Science:

• Quantum mechanics
• Computational chemistry
• Theoretical physics

Background:

• Describing quantum systems with anharmonic interactions is computationally expensive, scaling exponentially with system size.
• Efficient wave function representation is crucial, especially for high-dimensional systems with large-amplitude motion.
• Existing dynamic Gaussian basis methods face implementation challenges or may not adequately sample configuration space.

Purpose of the Study:

• To introduce a novel Quantum Trajectory-guided Adaptable Gaussian (QTAG) basis method.
• To develop an efficient and stable time propagator for QTAG dynamics.
• To overcome limitations of variational and classical dynamics approaches for Gaussian basis generation.

Main Methods:

• Utilizing quantum trajectory dynamics to continuously adapt Gaussian basis parameters (position, phase, width).
• Employing a time propagator with basis transformation via projections for enhanced efficiency and stability.
• Demonstrating the method's efficacy on standard computational tests and the ammonia inversion model.

Main Results:

• The QTAG method generates an efficient basis representation in configuration space by adapting to wave function evolution.
• The proposed time propagator ensures efficiency and stability in QTAG dynamics.
• Successful application to benchmark problems, including the ammonia inversion, validates the QTAG approach.

Conclusions:

• The QTAG method offers a computationally efficient alternative for representing quantum wave functions in complex systems.
• This approach bypasses the difficulties associated with traditional variational methods for Gaussian basis parameter optimization.
• The QTAG method provides a stable and efficient framework for simulating quantum dynamics, particularly for high-dimensional problems.