Berlin 2024 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 7: Poster (joint session MP/QI)

MP 7.5: Poster

Tuesday, March 19, 2024, 11:00–13:00, Poster B

Particle dynamics on quantum membranes — •Lars Meschede, Benjamin Schwager, and Jamal Berakdar — Martin-Luther-Universität Halle-Wittenberg

We are working on an approach for an effective description of particles confined to a thin tubular neighborhood of a curved, dynamical, lower-dimensional submanifold (e.g. membranes). In addition to the well-known geometric potential due to confinement to a static submanifold, the dynamical degrees of freedom give rise to new effective, dynamical scalar and vector potentials. The coupling of the particles to the underlying space itself allows the transfer of energy and momentum to the manifold. In the case of membranes, the coupled dynamics of the particles and the membrane can be described by a (quantum) field theory of two interacting fields, which also yields an equation governing the membrane dynamics in the presence of particles confined to it. This setup can be seen as an elastic field analog of an electromagnetic cavity. If one considers the non-relativistic case, the Lagrangian and the necessity of the existence of a new effective vector potential follow from the invariance requirement under Galilean transformations. An additional coupling of the particles to the external electromagnetic field allows radiative excitations of vibrational modes of the membrane. This approach could be of interest for the description of the long-wavelength coupled electron-membrane dynamics on flexible 2D structures.

Keywords: Quantum dynamics; 2D systems; Quantum geometry; Dimensional reduction; Electron-Phonon coupling