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## Typicality and unconventional equilibrium states of an embedded quantum system.

### Grégoire Ithier (Royal Holloway, London, UK)

In recent years, the progress in quantum engineering has provided new tools for simulating the dynamics of truly isolated quantum systems. These systems, made of trapped ions or cold atoms[1], can be prepared in a global pure state and their level of isolation is such that they evolve unitarily according to the Schrödinger equation. Surprisingly, despite being at all times in a pure quantum state, they display signatures of a local equilibration which can be in strong disagreement with the predictions of statistical physics [2]. These experimental facts are clearly questioning what kind of statistical description is relevant for isolated many body quantum systems.

In this talk, I will present our recent results on a theoretical model dedicated to this problem. This model considers a quantum system coupled to a large quantum environment, and introduces some randomness at the level of the interaction Hamiltonian. We then demonstrate that the system has a typical dynamics for several classes of random interactions and most importantly for arbitrary system, environment, and global initial state [3]. In other words, the microscopic structure of interaction Hamiltonians does not matter and reduced density matrices have a self-averaging property.

These results have two important consequences: first they can explain the absence of sensitivity to microscopic details of processes like e.g. thermalization. Second they provide the rigorous ground for an averaging procedure over random interactions which can be used for analytical non perturbative calculations performed with full generality i.e. for arbitrary system, environment, and initial state.

We apply this technique to calculate analytically the stationary state at long times of the system and find a new thermodynamical ensemble more general than the microcanonical one [4].

- [1] C. Gross and I. Bloch,
*Quantum simulations with ultracold atoms in optical lattices*, Science**357,**6355, pp. 995-1001 (2017) - [2] M. Schreiber et al,
*Observation of many-body localization of interacting fermions in a quasirandom optical lattice*, Science**349**, 6250, pp. 842-845 (2015) - [3] G. Ithier and F. Benaych-Georges,
*Dynamical typicality of embedded quantum systems*, Phys. Rev. A**96**, 012108 (2017) - [4] G. Ithier, S. Ascroft, and F. Benaych-Georges,
*Typical equilibrium state of an embedded quantum system*, Phys. Rev. E**96**, 060102(R) (2017)