Numerical Evaluation of the Casimir-Polder Interaction at Finite Temperature

Explore the intricacies of the Casimir-Polder interaction at finite temperature in this 21-minute conference talk by Bettina Beverungen at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the world of thermal and quantum fluctuations, examining their role in quantum electrodynamics and the emergence of forces between neutral objects. Learn about a novel numerical scheme using the finite-element-based discontinuous Galerkin time-domain (DGTD) method for calculating Casimir-Polder interactions in various setups, including nonlocal materials and finite temperatures. Discover practical examples illustrating the flexibility and validity of this approach, from the basics of atom-surface interactions to advanced topics like zero-temperature Casimir-Polder force near a wedge. Gain insights into the limits of analytical calculations and the power of numerical simulations in understanding these fundamental physical phenomena.

Intro
An atom in front of a surface
Practical relevance
The limits of (semi-)analytical calculations
Numerical approaches to Casimir calculations
The discontinuous Galerkin time domain method
An example including dispersion and dissipation
The semi-analytical reference solution
Distance dependence of the Casimir-Polder interaction
The Casimir-Polder interaction energy
An intuitive interpretation of the Green tensor
From frequency domain to time domain
Numerical simulation of the dipole field
Postprocessing
Putting it all together
Reminder: Rubidium atom in front of a gold halfspace
Numerical simulation vs. reference solution
Convergence study
Beyond planar geometries
Zero-temperature Casimir-Polder force near a wedge
Summary