Paul Bergold
PDEs in Mixed Quantum-Classical Dynamics and the Koopmon Method abstract
Abstract:
To alleviate the computational cost associated with fully quantum dynamics, a novel mixed quantum-classical (MQC) particle method – the Koopmon method – has recently been introduced [1]. Unlike conventional MQC models, which often suffer from inconsistencies such as violations of Heisenberg’s principle, this new approach resolves these issues by blending Koopman’s formulation of classical mechanics on Hilbert spaces with tools from symplectic geometry.The resulting continuum model, which can be regarded as a correction to the Ehrenfest PDE, retains both a variational and a Hamiltonian structure, while its nonlinear character calls for suitable closure schemes. Exploiting the underlying action principle, we introduce a regularization procedure that enables a singular-solution ansatz, thereby defining the trajectories of computational particles – the so-called Koopmons.Numerical experiments demonstrate the capability of the Koopmon method to reproduce nonadiabatic quantum-classical transitions and to capture Rashba-type spin dynamics in quantum nanowire systems. We conclude by proposing a novel strategy for a hybrid Ehrenfest–Koopman implementation that integrates the advantages of both approaches.[1] Bauer, W.; Bergold, P.; Gay-Balmaz, F., and Tronci, C. Koopmon trajectories in nonadiabatic quantum-classical dynamics. SIAM Multiscale Model. Simul., 22(4):1365-1401 (2024)[2] Gay-Balmaz, F.; Tronci, C. Evolution of hybrid quantum-classical wavefunctions. Phys. D 440, 133450 (2022)[3] Gay-Balmaz, F.; Tronci, C. Koopman wavefunctions and classical states in hybrid quantum-classical dynamics. J. Geom. Mech. 14, n. 4, 559-596 (2022)
10:15 • EP Lausanne, BCH 3118
Bo\'az Klartag (The Weizmann Institute of Science)
CANCELLED: Isoperimetric inequalities in high-dimensional convex sets
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Dr. Stefano Rossi (ETH Zürich)
Quasineutral limit for the relativistic Vlasov--Maxwell system abstract
Abstract:
<p>I will present a recent result concerning the quasineutral limit for the relativistic Vlasov--Maxwell system, a fundamental model in plasma physics. The quasineutral limit describes the regime in which the Debye length — the characteristic scale of charge separation — becomes negligible compared to the macroscopic scale of the plasma, so that the plasma behaves as if it were electrically neutral. While this singular limit has been extensively studied in the electrostatic case (i.e., the Vlasov--Poisson system), the full electromagnetic setting introduces new difficulties due to the coupling with Maxwell’s equations and the presence of a magnetic field, which give rise to additional oscillatory phenomena. I will explain how, in this context, one can rigorously establish strong convergence to a limiting electron magnetohydrodynamics (e-MHD) system, and clarify the precise sense in which this limit holds. This is based on a joint work with A. Gagnebin, M. Iacobelli, and A. Rege.</p>
16:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Walter Gander
The first algorithms to compute the SVD abstract
Abstract:
The singular values of a matrix A can be computed as the square roots of the eigenvalues of the matrix A^T A. However, the calculation of A^T A in finite arithmetic seriously violates the smaller singular values. Therefore the pioneers Gene Golub, William Kahan and Christian Reinsch constructed new algorithms which compute the singular values directly from A without forming A^T A. We describe the first algorithm proposed by Golub/Kahan 1965. Then we discuss the two algorithms by Golub-Businger 1967 and by Reinsch 1967 which were developed independently at the same time. The current algorithm used in all software packages is the one of Reinsch. We explain why the algorithm of Reinsch appeared in ``Handbook of Automatic Computation\'\' under joint authorship with G.H. Golub
16:15 • Université de Genève, Conseil Général 7-9, Room 1-05
Razvan-Octavian Radu (Princeton University)
Desingularization of V-states abstract
Abstract:
<p>V-states are uniformly rotating vortex patch solutions to the 2D Euler equations. Namely, the vorticity is given by the characteristic function of a domain which rotates around the origin with constant angular velocity. Examples of V-states include Kirchhoff ellipses and m-fold symmetric patches which bifurcate from the disk. I will describe how, for any V-state satisfying a certain non-degeneracy condition, there exist smooth rigidly rotating solutions to the 2D Euler equations approximating it arbitrarily well in the natural Hölder spaces. I will then argue that all but countably many Kirchhoff ellipses, as well as all m-fold symmetric V-states near the disk satisfy this non-degeneracy.</p>
17:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.2
Andi Bodnariu (Stockholm University)
Time inconsistent control and stopping problems, blowing up intensities and rates abstract
Abstract:
The goal of this talk is to present recent results in the field of time-inconsistent stopping and control problems driven by stochastic differential equations. The talk considers the weak equilibrium approach. While solving these problems interesting novel type of strategies appear that are not present in the time consistent version. In particular for time-inconsistent stopping problems, a class of mixed (i.e., randomized) stopping times based on a local time construction of the stopping intensity appears. The counterpart for singular time-inconsistent control problems is given by a control which results in an absolutely continuous rate that creates an inaccessible boundary. Additionally, can be shown that the classical solution approach to these problems used in the time-consistent version (pure stopping times with no mixing and reflection for the SSC) does not always result in an equilibrium making these type of novel strategies necessary. This creates further insight into the strategy space that should be considered in order to prove general existence of equilibria, which is an open problem for most time-inconsistent problems.
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43