One of the fundamental concepts in statistical mechanics is the notion of ergodicity, which is closely related to the lack of memory of a system. In quantum mechanics, it is observed that the interactions redistribute the available

energy and enable thermalization [1]. Under some conditions, however, an external drive can inhibit ergodicity [3–5]. In this case, the system looses the ability to explore all the available states [6–10] and keeps memory of the initial state. In this talk, I will discuss a model where ergodic behavior is broken due to integrability. The reduced dynamics of such as system is given by a time-local master equation with time-periodic rates. Due to the time-periodicity of the master equation, the dynamical map is divisible at discrete times, which is referred to as Floquet stroboscopic divisibility [11]. I will illustrate general theory by studying an oscillator coupled to both non-Markovian and Markovian baths. In this example, if one prepares the system in a cat state, the environment induces stroboscopic revivals of the cat after its death. Our theory may have profound implications in entropy production in non-equilibrium systems.

[1] M. Srednicki, Phys. Rev. E 50, 888 (1994).

[2] A. Lazarides, A. Das, and R. Moessner, Phys. Rev. Lett. 115, 030402 (2015).

[3] S. Restrepo, J. Cerrillo, V. M. Bastidas, D. G. Angelakis, and T. Brandes, Phys. Rev. Lett. 117, 250401 (2016).

[4] A. Eckardt, Rev. Mod. Phys. 89, 011004 (2017).

[5] V. M. Bastidas, B. Renoust, Kae Nemoto, W. J. Munro, arXiv:1807.00080 (2018).

[6] D. Basko, I. Aleiner, B. Altshuler, Ann. Phys. 321, 1126 (2006).

[7] R. Nandkishore, D. A. Huse, Annu. Rev. Condens. Matter Phys. 6, 15 (2015).

[8] E. Altman, R. Vosk, Annu. Rev. Condens. Matter Phys. 6, 383 (2015).

[9] M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, I. Bloch, Science

349, 842 (2015).

[10] P. Roushan, C. Neill, J. Tangpanitanon, V. M. Bastidas, A. Megrant, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A.

Dunsworth, A. Fowler, B. Foxen, M. Giustina, E. Jeffrey, J. Kelly, E. Lucero, J. Mutus,1 M. Neeley, C. Quintana, D. Sank,

A. Vainsencher, J. Wenner, T. White, H. Neven, D. G. Angelakis, J. Martinis, Science 358, 1175 (2017).

[11] V. M. Bastidas, T. H. Kyaw, J. Tangpanitanon, G. Romero, L.-C. Kwek, D. G. Angelakis, New J. Phys. 20, 093004 (2018).