Programme

O.23 -- Oral, VCTP-50

Date: Thursday, 7 August 2025

Time: 11:10 - 11:35

Emergence of the Liouvillian Skin Effect in Driven – Dissipative Ultracold Atom Systems

Roland Crisopher F. Caballar (1,2,3)

(1) Department of Mathematics and Physics, College of Science, University of Santo Tomas, (2) Research Center for Natural and Applied Sciences, University of Santo Tomas, (3) The Graduate School, University of Santo Tomas

Topological insulators have been shown to exhibit the Liouvillian skin effect ([1], [2]), whereby dynamically stable edge states with zero energy emerge at the boundaries of the system due to the non-Hermiticity of the Hamiltonian describing the system. The importance of this Liouvillian skin effect manifests itself in, among other things, the relaxation time of dissipative quantum systems [3], whereby it is shown that the relaxation time, or the timescale over which the system achieves its steady state, is inversely proportional to the magnitude of the largest eigenvalue corresponding to these anomalous zero-energy edge states. We investigate whether this is indeed the case in a driven-dissipative ultracold atom system described in Ref. [4], which consists of a gas of ultracold atoms trapped in an array of harmonic potentials. We show that, under certain conditions, the Liouvillian skin effect will manifest itself in this system, and we derive the explicit form of the eigenvalues corresponding to these anomalous zero – energy edge states that are the hallmark of the Liouvillian skin effect. From this, we then obtain the relaxation time for the system, and compare the calculated relaxation time with the time obtained numerical simulations showing how the system evolves over time to its steady state.

Presenter: Caballar F. Roland Cristopher