The partition-of-unity quantum (PUQ) method for wavepacket dynamics.

Area of Science:

• Quantum mechanics
• Computational chemistry
• Theoretical physics

Background:

• Accurate simulation of quantum wavepacket dynamics is crucial for understanding molecular processes.
• Traditional methods often struggle with high dimensionality and complex potentials, requiring significant computational resources.

Purpose of the Study:

• Introduce the Partition-of-Unity Quantum (PUQ) method for efficient and accurate wavepacket dynamics.
• Demonstrate the effectiveness of PUQ in handling complex quantum systems.

Main Methods:

• Construct a piecewise representation using local, overlapping nodes with compactly supported weight functions (Partition-of-Unity).
• Employ the Dirac-Frenkel variational principle for equations of motion and a Crank-Nicolson propagator for norm and energy conservation.
• Utilize local enrichment functions, including a normal mode variant (NM-PUQ), tailored to local physics.

Main Results:

• The bare PUQ method achieves high fidelity on a 2D coupled multi-well potential.
• Local enrichment significantly reduces node density, with NM-PUQ showing critical dependence on enrichment choice.
• Both PUQ variants achieve near-reference fidelity with substantially fewer degrees of freedom compared to global plane wave or SVD contraction methods.
• PUQ basis functions' compact support leads to sparse operator matrices scaling linearly with node count.

Conclusions:

• The Partition-of-Unity Quantum (PUQ) framework is an effective basis for quantum dynamics.
• PUQ offers a computationally efficient and accurate alternative for simulating complex wavepacket dynamics.
• The method's sparse nature and linear scaling hold promise for large-scale quantum simulations.