Workshop »Numerics, dynamics & physics«

Date and place

June 14th, 2024 @ KIT · Karlsruhe

Speakers

Scientific program

Friday, June 14th
14:00 Caroline Lasser · Observing Variational Gaussian Wave Packets
Abstract: We discuss time-dependent Schrödinger equations with smooth electric and magnetic potentials. We analyze time-dependent variational approximation with a single nonlinearly parametrized Gaussian wave packet. The derived error estimates are joint work with S. Burkhard, B. Dörich and M. Hochbruck: They generalize established results on accuracy with respect to the $L^2$-norm and strongly improve what has been known with respect to observable accuracy.
14:45 Kurt Busch · Atom-Surface Interactions: Theory and Computations
Abstract: When an atom is placed near a material body, it experiences quantum fluctuations of the electromagnetic field that are modified relative to those of vacuum. In turn, this leads to a number of quantum-fluctuation-induced effects that include modifications of spontaneous emission and near-field radiative transfer as well as the occurrence of fluctuation-induced forces such as Casimir, Casimir-Polder forces and quantum friction. The latter are of particular relevance for micro- and nano-electromechanical systems and atom-chips.
In this talk, a path from basic physical principles to reliable quantitative computations of atom-surface interactions will be sketched where the emphasis will be on the Casimir-Polder force. Highly symmetric systems with simple material models lend themselves to semi-analytical solutions where the evaluation of poorly converging series greatly benefit from recent advances in summation techniques based modified discrete Laguerre polynomials. Complex geometries and material models require advanced Maxwell solvers that are capable of addressing the various underlying length and time scales. In particular, it is demonstrated that Discontinuous-Galerkin Time-Domain Maxwell solvers facilitate accurate computations for systems at finite temperatures and for spatially nonlocal materials.
15:30 Break
16:00 Christian Lubich · Transient Dynamics Under Structured Perturbations: Bridging Unstructured and Structured Pseudospectra
Abstract: This talk is about numerics for problems of linear dynamics via nonlinear dynamics, with possible uses in physics. As is known, bounds of the resolvent of a matrix in the right complex half-plane yield bounds of solutions of homogeneous and inhomogeneous linear differential equations with this matrix. We ask two basic questions:
  • Up to which size of structured perturbations are the resolvent norms of the perturbed matrices within a given bound in the right complex half-plane?
  • For a given size of structured perturbations, what is the smallest common bound for the resolvent norms of the perturbed matrices in the right complex half-plane?
This is considered for general linear structures such as complex or real matrices with a given sparsity pattern or with restricted range and corange, or special classes such as Toeplitz matrices. Conceptually we combine unstructured and structured pseudospectra in a joint pseudospectrum, allowing for the use of resolvent bounds as with unstructured pseudospectra and for structured perturbations as with structured pseudospectra. The above questions are addressed by an algorithm which solves eigenvalue optimization problems via suitably discretized rank-1 matrix differential equations. Numerical experiments illustrate the behaviour of the algorithm. The talk is based on joint work with Nicola Guglielmi.
16:45
until 17:45		 Get-together

Contact

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