Title: Quantum collision models

Abstract: A collision model (or repeated-interactions model or conveyor-belt model) is a simple theoretical framework in which a system S undergoes successive interactions (“collisions”) with the subunits of a large environment [1-4]. Currently, quantum collision models are being used more and more in research areas such as open quantum systems theory (especially non-Markovian dynamics [5]), quantum thermodynamics [6], quantum optics [7] and, in some respects, even quantum gravity [8].
Here, starting from a few historical notes, we will present a general introduction to quantum collision models. In particular, we will discuss: their tight connection with the concept of CP-divisibility (CP standing for “completely positive”) and weak quantum measurements; the issue of their continuous-time limit; the possibility to derive the Lindblad master equation with no approximations; the different ways to modify their basic definition so as to introduce memory effects; the possibility of deriving well-defined non-Markovian master equations; their relationship with the input-output formalism of quantum optics.

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[6] P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Phys. Rev. X 7, 021003 (2017).
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[8] N. Altamirano, P. Corona-Ugalde, R. Mann, and M. A. Zych, New J. Phys. 19, 013035 (2017).

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