Wolfgang Pauli Institute (WPI) Vienna

Workshop on "Quantum dynamics and uncertainty Quantification"

Location: WPI, OMP 1, Seminar Room 08.135 Tue, 20. Jun - Thu, 22. Jun 17
Organisation(s)
WPI
Organiser(s)
Shi Jin (U. Madison & INS Shanghai)
Norbert J. Mauser (WPI c/o U.Wien)
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Talks in the framework of this event


Olof Runborg (Mathematik Institution, Stockholm) WPI, OMP 1, Seminar Room 08.135 Tue, 20. Jun 17, 10:00
Uncertainty Quantification for High Frequency Wave Propagation
We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest (QoI) related to the solution $u^\varepsilon$ and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. In the talk we will discuss how the rate of convergence for the stochastic collocation and the complexity of evaluating the QoI depend on the short wavelength $\varepsilon$. We find in particular that QoIs based on local averages of $\vert u^\varepsilon\vert ^2$ can give fast convergence rates, despite the fact that $u^\varepsilon$ is highly oscillatory in both physical and stochastic space.
  • Thematic program: Classical and Quantum Transport (2016/2017)
  • Event: Workshop on "Quantum dynamics and uncertainty Quantification" (2017)

Mohammed Lemou WPI, OMP 1, Seminar Room 08.135 Tue, 20. Jun 17, 15:30
"Averaging techniques and application to numerical methods for highly oscillatory Vlasov and Klein-Gordon models"
A brief description of averaging theory for highly-oscillatory problems will be first presented with an emphasis on the so-called classical and stroboscopic averaging methods. Then I will present two general strategies to construct efficient numerical schemes for a class of highly oscillatory PDEs: the so-obtained numerical schemes have a uniform accuracy with respect to the frequency. Two applications will be considered: the Vlasov kinetic equation with strong magnetic field and the Klein-Gordon equation in the non-relativistic regime.
  • Thematic program: Classical and Quantum Transport (2016/2017)
  • Event: Workshop on "Quantum dynamics and uncertainty Quantification" (2017)

Shi Jin (University of Wisconsin-Madison and Shanghai Jiao Tong University) WPI, OMP 1, Seminar Room 08.135 Wed, 21. Jun 17, 10:00
Semiclassical computational methods for oscillatory and uncertain quantum dynamics with band-crossings
Band-crossing is a quantum dynamical behavior that contributes to important physics and chemistry phenomena such as quantum tunneling, Berry connection, charge transfer, chemical reaction etc. In this talk, we will discuss some recent works in developing semiclassical methods for band-crossing in surface hopping. For such systems we will also introduce an nonlinear geometric optics method based "asymptotic-preserving" method that is accurate uniformly for all wave numbers, including the problem with random uncertain band gaps.
  • Thematic program: Classical and Quantum Transport (2016/2017)
  • Event: Workshop on "Quantum dynamics and uncertainty Quantification" (2017)

Olivier Pinaud (Colorado State University) WPI, OMP 1, Seminar Room 08.135 Wed, 21. Jun 17, 14:00
Waves in random media and applications
We will review some results concerning uncertainties in the derivation of kinetic equations from wave propagation in random media, that is modeled by a wave or a Schroedinger equation. Kinetic equations usually describe quadratic quantities in the wavefield such as the energy or wave-wave correlations, and can be used to solve some imaging problems in complex media.
  • Thematic program: Classical and Quantum Transport (2016/2017)
  • Event: Workshop on "Quantum dynamics and uncertainty Quantification" (2017)

François Golse WPI, OMP 1, Seminar Room 08.135 Thu, 22. Jun 17, 10:00
A convergence rate estimate for the semiclassical limit with Lipschitz continuous force field
We propose an explicit bound for the convergence rate in the semiclassical limit for the Schrödinger equation which holds for potentials with Lipschitz continuous gradient. This bound is based on an analogue of the Wasserstein metric used in optimal transportation, adapted to measuring the distance between a quantum and a classical density.
  • Thematic program: Classical and Quantum Transport (2016/2017)
  • Event: Workshop on "Quantum dynamics and uncertainty Quantification" (2017)

Yong Zhang WPI, OMP 1, Seminar Room 08.135 Thu, 22. Jun 17, 14:00
“Numerical methods/analysis for Schrödinger equations and micro-magnetism”
We present some mathematical methods occurring in the modeling and simulation of Nonlinear Schrödinger equations and nonlocal potentials. We focus on Gross-Pitaevskii equations describing Bose Einstein Condensates and stray field calculations in micro-magnetism.
  • Thematic program: Classical and Quantum Transport (2016/2017)
  • Event: Workshop on "Quantum dynamics and uncertainty Quantification" (2017)

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