Casimir forces are microscopic forces created by fluctuations in the electromagnetic field. They allow geckos to stick to walls and are relevant in nano-devices like cellphone gyroscopes. It was recently shown that Casimir forces can be used to create contactless nano-engines that can potentially avoid friction and wear. However, all forces must be in a delicate balance to create stable configurations that allow engine operation without contact among its parts. Can this be achieved using Casimir’s forces?
There is an interesting theorem regarding this question. The famous Earnshaw’s theorem,
formulated in 1848, forbids the arrangement of stable configurations based on electrostatic forces. This theorem does not apply to magnetostatics, which is the key to several technological applications such as ion traps and levitated trains. We have recently found some indications that a special type of material, called non-reciprocal materials, may violate Earnshaw’s theorem and allow for the creation of stable configuration and levitation. In this project, we will numerically test this hypothesis to determine if non-reciprocal systems comply with or violate Earnshaw’s theorem. f non-reciprocal materials do not comply with Earnshaw’s theorem, exciting possibilities for various applications can be opened, such as levitation, trapping, and the creation of contactless nano-engines, beginning with this project..
Prerequisites: Basic programming skills in any language (python, mathematica, matlab, etc) and basic quantum mechanics
References:
Gelbwaser-Klimovsky, D., Graham, N., Kardar, M., & Krüger, M. (2022). Equilibrium forces on nonreciprocal materials. Physical Review B, 106(11), 115106.
Gelbwaser-Klimovsky, D., Graham, N., Kardar, M., & Krüger, M. (2021). Near field propulsion forces from nonreciprocal media. Physical Review Letters, 126(17), 170401.
