So sánh phương pháp

	Path Integral Monte Carlo	Lý thuyết Hàm Mật độ
Lĩnh vực	Tính toán lượng tử	Tính toán lượng tử
Họ	Machine learning	Machine learning
Năm ra đời	1948	1965
Người khởi xướng	Richard Feynman	Walter Kohn
Loại	Stochastic simulation	Electronic structure method
Công trình gốc	Feynman, R. P. (1948). Space-time approach to non-relativistic quantum mechanics. Reviews of Modern Physics, 20, 367–387.	Kohn, W., Sham, L. J. (1965). Self-consistent equations including exchange and correlation effects. Physical Review, 140, A1133–A1138.
Tên gọi khác	PIMC, Feynman path integral	DFT, Kohn-Sham equations
Liên quan	3	4
Tóm tắt	Path Integral Monte Carlo (PIMC) is a computational method for calculating thermodynamic and structural properties of quantum systems using Feynman's path integral formulation. Developed rigorously by David Ceperley and colleagues in the 1990s, PIMC treats quantum particles as classical polymers in a higher-dimensional space, enabling efficient Monte Carlo sampling of quantum statistics.	Density Functional Theory (DFT) is a computational method for determining the properties of materials and molecules by modeling the ground state electron density. Developed by Walter Kohn and Lu Jeu Sham in the 1960s, DFT reduces the complexity of quantum chemistry from tracking individual electron coordinates to optimizing the total electron density, enabling efficient simulations of large molecular and condensed-matter systems.