Seminar Event Detail

Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, November 05, 2021
Location:  ZOOM East Hall (3:00 PM to 4:00 PM)

Title:  Efficient numerical algorithms for simulating quantum dynamics

Abstract:   I will describe a few algorithmic advances which reduce computational bottlenecks in simulations of quantum many-body dynamics. In time-dependent density functional theory (TDDFT), the many-body wavefunction is approximated using a collection of single-particle wavefunctions, which independently satisfy the Schrödinger equation and are coupled through an effective potential. I will introduce a high-order, FFT-based solver for free space (nonperiodic) problems in TDDFT which sidesteps the usual requirement of imposing artificial boundary conditions. Many-body Green's functions, which describe correlations between quantum observables, enable practical simulations beyond the effective one-body picture of TDDFT. The Green's functions satisfy history dependent Volterra integro-differential equations with kernel nonlinearities. I will outline efficient history integration algorithms which significantly extend feasible propagation times in both equilibrium and nonequilibrium calculations.


Speaker:  Jason Kaye
Institution:  Flatiron Institute

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