BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shi Jin (Shanghai Jiao Tong University) DTSTART:20201012T130000Z DTEND:20201012T140000Z DTSTAMP:20260423T052644Z UID:SNPDEA/8 DESCRIPTION:Title: R andom Batch Methods for classical and quantum N-body problems\nby Shi Jin (Shanghai Jiao Tong University) as part of "Partial Differential Equat ions and Applications" Webinar\n\n\nAbstract\nWe first develop random batc h methods for classical interacting particle systems with large number of particles. These methods use small but random batches for particle intera ctions\, thus the computational cost is reduced from O(N^2) per time step to O(N)\, for a system with N particles with binary interactions. For one of the methods\, we give a particle number independent error estimate unde r some special interactions.\n\nThis method is also extended to quantum Mo nte-Carlo methods for N-body Schrodinger equation and will be shown to hav e significant gains in computational speed up over the classical Metropol is-Hastings algorithm and the Langevin dynamics based Euler-Maruyama metho d for statistical samplings of general distributions for interacting parti cles. \n\nFor quantum N-body Schrodinger equation\, we also obtain\, for pair-wise random interactions\, a convergence estimate for the Wigner tran sform of the single-particle reduced density matrix of the particle system at time t that is uniform in N > 1 and independent of the Planck constant \\hbar. To this goal we need to introduce a new metric specially tailored to handle at the same time the difficulties pertaining to the small \\hba r regime (classical limit)\, and those pertaining to the large N regime (m ean-field limit).\n\nThis talk is based on joint works with Lei Li\, Jian- Guo Liu\, Francois Golse\, Thierry Paul and Xiantao Li.\n LOCATION:https://researchseminars.org/talk/SNPDEA/8/ END:VEVENT END:VCALENDAR