Week 02.12.2024 – 08.12.2024

In this talk, I first give a very general overview of the concept of MBL (many-body localization). Then I introduce the so-called quantum sun model (aka avalanche model/ quantum grain model). Then  I discuss the significance of this model in the MBL community. Afterwards, I present our result which is proof of the localization and Poisson stat. for this model in certain range of parameters. Finally,  I give some rough ideas about the proof: we first prove the result for the "free model" (sum of free disordered spin z), then we show that the interacting model is sufficiently "similar" to the free model by controlling the ratio of "in-resonance" levels. This is joint work with Wojciech De Roeck.

Time crystals are many-body systems that spontaneously break time-translation symmetry, and thus exhibit long-range spatiotemporal order and robust periodic motion. Recent results have demonstrated how to build time-crystal phases in driven diffusive fluids, based on a particular class of symmetry-breaking dynamical phase transitions present in their rare event statistics. A main tool in this idea is the application of an external packing field coupled to density fluctuations, that triggers an instability to a time-crystal phase. In this seminar we will explore the connection between time crystals, rare events and dynamical phase transitions. We will also describe how to exploit this packing-field mechanism to engineer and control on demand programmable continuous time crystals characterized by an arbitrary number of rotating condensates, which can be further enhanced with higher-order modes. We will elucidate the underlying critical point, as well as general properties of the traveling condensates, illustrating our findings in various paradigmatic driven diffusive systems. Overall, these results demonstrate the versatility and broad possibilities of this promising route to time crystals.