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Nonlinear Schrodinger Equations and How Mathematicians Can Be Useful to Physicists

Speaker

Norbert J Mauser, University of Vienna

Time

2019.09.18 14:00-15:00

Venue

Room 306, No.5 Science Building

Abstract

Nonlinear Schrodinger equations (NLS) are an important class of dispersive (time dependent) Partial Differential Equations that arise, e.g., in nonlinear optics and quantum physics.We briefly discuss “derivations” of NLS, and the mathematical work on NLS as well as it’s impact on applications.We then focus on the Gross-Pitaevskii equation (GPE), a cubic NLS with confinement potential, that is the simplest model for (computer simulations of) Bose Einstein Condensates (BEC). We present the GPE and the interplay of mathematical-numerical modeling with the phases of BEC experiments.We further show extensions of the GPE (e.g. with quartic and quintic terms), including “temperature”, quantum noise, decoherence, etc. for dipolar, rotating BEC, e.g. “stochastic GPE”.The talk is ment for a broad audience of pure and applied mathematicians and physicists, including good undergraduate students.

Bio

N.J. Mauser studied mathematics, physics and astronomy at TU Wien and Univ. Wien, and did his PhD with P. Markowich. After Pre/Post-doc years at TU Berlin, CRS4 Cagliari, Univ. Nice, ENS Paris and Courant Inst. NYU he returned to Vienna as professor of mathematics at Univ. Wien. He works on (asymptotic) analysis, modeling, numerical methods and application of PDEs in quantum physics / materials, micromagnetism / semiconductors and cosmology, including ground breaking results on Wigner transform methods. He is director of the Wolfgang Pauli Institute and coordinator of large international interdisciplinary research training networks.