Numerical Analysis Seminar

Date: September 27, 2023

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).