Quantum trajectories, quantum potential, superoscillations: Madelung, de Broglie, Newton

Date

Mar 24, 2025

Time

4:30 PM - 5:30 PM

Speaker

Prof. Michael Berry

Affiliation

University of Bristol

Series

MPI-PKS Kolloquium

Language

en

Main Topic

Physik

Other Topics

Physik

Description

The wave counterparts of classical particle paths and geometrical-optics rays are families of trajectories – patterns of streamlines – modified by a ‘quantum potential’. Wave interference corresponds to undulations in these trajectories, as envisaged by Isaac Newton. Streamline patterns are dominated by singularities at wave vortices and stagnation points. The local momentum (phase gradient of the wave), can exceed the values classically allowed. Regions of such ‘superoscillations’ are bounded by manifolds where the quantum potential is zero. Some classical ‘curl forces’ – not the gradient of a potential – are associated with Hamiltonians (dispersion relations) anisotropic in momentum components, with unusual group velocity field singularities, and eigenfunctions with unfamiliar classical counterparts. For simple dispersion relations, some singularities coincide; for general cases, they are separate.

Last modified: Mar 9, 2025, 7:39:30 AM