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Explore quantum Monte Carlo methods as powerful numerical tools for solving many-body problems in Bose particle systems through this comprehensive lecture from a mathematical physics workshop. Learn how projective Monte-Carlo methods can solve the Schrödinger equation for many-body ground states at zero temperature, regardless of dimensionality, external fields, confining geometries, or interaction coupling strength. Discover the essential aspects of these numerical methods and examine their applications to challenging problems in ultracold atom physics where interaction and quantum fluctuation effects cannot be adequately treated using mean-field or perturbative approaches. Study specific applications including the equation of state of interacting Bose gases, dipolar systems in two spatial dimensions, and one-dimensional two-component Bose gases with contact interactions. Understand how quantum Monte-Carlo simulations reproduce exact results from the exactly solvable Lieb-Liniger model while providing extensions to broader classes of problems, demonstrating the method's accuracy and versatility in quantum many-body physics.
