Computational Quantum Mechanics in Phase Space - An Attempt to Break the Curse of Dimensionality

Explore a conference talk on computational quantum mechanics in phase space, focusing on attempts to break the curse of dimensionality. Delve into recent progress in grid-based deterministic and particle-based stochastic methods for simulating high-dimensional Wigner quantum dynamics. Learn about the characteristic-spectral-mixed (CHASM) scheme, a massively parallel solver for evolving the Wigner-Coulomb system in 6-D phase space. Discover strategies to overcome the numerical sign problem in particle-based stochastic simulations, including the SPA (Stationary Phase Approximation) + SPADE (Sequential-clustering Particle Annihilation via Discrepancy Estimation) approach. Examine simulations of proton-electron couplings in 6-D and 12-D phase space, demonstrating the accuracy and efficiency of particle-based stochastic methods in high-dimensional quantum systems.