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Texas A&M University

Events for 09/27/2023 from all calendars

Numerical Analysis Seminar

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Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Dionisios Margetis, University of Maryland

Title: On a non-Hermitian formalism for many-body Boson quantum dynamics

Abstract: The last three decades have witnessed interesting advances in atomic physics. Notably, the first experimental observation of a single macroscopic quantum state in trapped atomic gases, known as the phenomenon of ``Bose-Einstein condensation’’, at extremely low temperatures was reported in 1995. Since then, the efforts of physicists to harness cold atomic gases have expanded considerably. An emergent and far-reaching advance is the highly precise manipulation of atoms by optical or magnetic means in laboratory settings. In this talk, I will discuss mathematical implications of a physically motivated model for a dilute gas of zero-spin particles (Bosons) with repulsive pairwise interactions at zero temperature. In particular, I will describe aspects of the excited many-body quantum states of this system by accounting for the scattering of atoms in pairs from the macroscopic state (condensate). Key in this formulation is a non-unitary transformation of a prototypical many-body Hamiltonian. This transformation makes use of the ``pair-excitation kernel'', a function that satisfies a nonlinear partial integro-differential equation. For stationary tates, I will present an existence theory for solutions to this equation in a variational framework. I will also discuss how this theory is intimately connected to the physically motivated concept of ``quasiparticles’’, or collective excitations, in the atomic gas. This is joint work with M. Grillakis (UMD) and S. Sorokanich (NIST).


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Time: 6:00PM - 7:00PM

Location: BLOC 302

Speaker: Suhan Zhong, Texas A&M University

Title: Distributionally Robust Optimization with Moment Ambiguity Sets

Abstract: In this talk, we introduce distributionally robust optimization when the ambiguity set is given by moments for the distributions. The objective and constraints are given by polynomials in decision variables. We reformulate the DRO with equivalent moment conic constraints. Under some general assumptions, we prove the DRO is equivalent to a linear optimization problem with moment and psd polynomial cones. A Moment-SOS relaxation method is proposed to solve it. Its asymptotic and finite convergence are shown under certain assumptions.