Hosts: Prof. Dr. Marita Thomas (WIAS/FU), Prof. Dr. Frank Noé (FU)
Location: !!! Attention !!!, this term it will take place in Freie Universität Berlin, Institut für Mathematik, Arnimallee 7, Room: 031, 14195 Berlin-Dahlem
Time: The seminar takes place on Thursday at 4:00 pm
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16:00 Priyanka Maity, TU Ilmenau
14:00 - 20:00 International Women in Mathematics Day Arnimallee 22, Gr. Hörsaal (room B.001)
Monday, 16.05.2022 !!!
14:00 William A. Eaton, National instutute of Health NIH, Bethesda, Maryland USA
Ascension Day (Public holiday)
14:00-16:00 !!! Alberto Lanconelli, University of Bologna
Using Gaussian stochastic analysis to solve a chemical diffusion master equation
Abstract: We propose a novel method to solve a chemical diffusion master equation of birth and death type. This is an infinite system of Fokker-Planck equations where the different components are coupled by reaction dynamics similar in form to a chemical master equation. This system was proposed in a recent paper by M. J. del Razo et al. for modelling the probabilistic evolution of chemical reaction kinetics associated with spatial diffusion of individual particles. Using some basic tools and ideas from infinite dimensional Gaussian analysis we are able to reformulate the aforementioned infinite system of Fokker-Planck equations as a single evolution equation solved by a generalized stochastic process and written in terms of Malliavin derivatives and differential second quantization operators. Via this alternative representation we link certain finite dimensional projections of the solution of the original problem to the solution of a single partial differential equations of Ornstein-Uhlenbeck type containing as many variables as the dimension of the aforementioned projection space. Our approach resembles and to some extents generalizes the classical generating function method utilized for solving certain chemical master equations.
This hybrid event will also be broadcast via Zoom. The meeting link will be posted here: https://www.mi.fu-berlin.de/en/math/groups/ag-comp-stat-phys/events/lanconelli.html one day in advance.
16:00 Feliks Nüske, MPI Magdeburg
Koopman Analysis of Quantum Systems
Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Most applications of Koopman theory have been concerned with classical dynamical systems driven by ordinary or stochastic differential equations. In this presentation, we will first compare the ground-state transformation and Nelson's stochastic mechanics, thereby demonstrating that data-driven methods developed for the approximation of the Koopman operator can be used to analyze quantum physics problems. Moreover, we exploit the relationship between Schrödinger operators and stochastic control problems to show that modern data-driven methods for stochastic control can be used to solve the stationary or imaginary-time Schrödinger equation. Our findings open up a new avenue towards solving Schrödinger's equation using recently developed tools from data science.
If you are not able to attend in person, please follow this link: https://riceuniversity.zoom.us/j/95245308776?pwd=akZKd1JJbTRuODdvNXdLTzd4R2xQQT09