Interfaces beyond the elastic approximation

The framework of disordered elastic systems is widely used to describe the physics of very diverse systems with typical scales ranging from nanometers to kilometers. However, this approach has the limitation that is only applicable to univalued and smooth interfaces, thus inducing uncontrolled approximations. Solving interface dynamics and statics in more realistic systems beyond the elastic approximation is still a largely open theoretical/analytical problem. We propose to address this problem by analyzing a Ginzburg-Landau model that allows us to extend the theory of disordered elastic systems. We show the connection of our approach with the disordered elastic systems theory [1]. In addition, we show how through this connection it is possible to explain otherwise not-understood experimental results in ferromagnetic interfaces [2]. Our approach also allows us to unravel properties of migrating epithelial rat cells-fronts, by treating its boundaries as interfaces moving in a disordered landscape [3].
[1] N. Caballero, E. Agoritsas, V. Lecomte, T.Giamarchi. PRB 102, 104204 (2020)
[2] N.Caballero. arXiv:2009.14205 (cond-mat).
[3] G. Rapin*, N. Caballero*, I. Gaponenko, B. Ziegler, A. Rawleigh, E. Moriggi, T. Giamarchi, S. A. Brown, P. Paruch. https://doi.org/10.1101/2020.10.26.354878