摘要:

The infamous numerical sign problem poses a fundamental obstacle to particle- based stochastic Wigner simulations in high-dimensional phase space. Although the existing particle annihilation (PA) via uniform mesh significantly alleviates the sign problem when dimensionality D <= 4, the mesh size grows dramatically when D >= 6 due to the curse of dimensionality and consequently makes the annihilation very inefficient. In this paper, we propose an adaptive PA algorithm, termed sequential-clustering particle annihilation via discrepancy estimation (SPADE), to overcome the sign problem. SPADE follows a divide-and-conquer strategy: adaptive clustering of particles via controlling their number-theoretic discrepancies and independent random matching in each cluster. The target is to alleviate the oversampling problem induced by the overpartitioning of phase space and to capture the nonclassicality of the Wigner function simultaneously. Combining SPADE with the variance reduction technique based on the stationary phase approximation, we attempt to simulate the proton-electron couplings in six- and 12-dimensional phase space. A thorough performance benchmark of SPADE is provided with the reference solutions in six-dimensional phase space produced by a characteristic-spectral-mixed scheme under a 733*803 uniform grid, which fully explores the limit of grid-based deterministic Wigner solvers.

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