Simon Andréys

2018
- The Open Quantum Brownian Motion and continual measurement of observables , in preparation (pdf)
  This article is a mathematical analysis of the Open Quantum Brownian Motion. This object was introduced by Bauer, Bernard and Tilloy as the limit of a family of Open Quantum Random Walks on the discrete line. We prove the convergence for the three possible description of this object: the quantum trajectory following a Belavkin equation, the unitary evolution on the Fock space following a quantum Langevin equation, and the Lindbladian evolution. We introduce a very general framework for the continual measurement of non-demolition observables, which is applied to the measurement of the position of the Open Quantum Brownian Motion, and we probe some questions related to the convergence of processes in this context.

Repeated interaction processes in the continuous-time limit, applied to quadratic fermionic systems , submitted arXiv:1903.08223
We study a class of Lindblad equation on finite-dimensional fermionic systems. The model is obtained as the continuous-time limit of a repeated interaction process between fermionic systems with quadratic Hamiltonians, a setup already used by Platini and Karevski for the one-dimensional XY model. We prove a necessary and sufficient condition for the convergence to a unique stationary state, which is similar to the Kalman criterion in control theory. Several examples are treated, including a spin chain with interactions at both ends.

2016
- Simon Andreys, Philippe Jaming. Zak Transform and non-uniqueness in an extension of Pauli’s phase retrieval problem. Analysis Mathematica, Springer Verlag, 2016, 42, pp.185-201 arXiv:1501.03905
  We wrote this article during my M1 internship at the IMB (Bordeaux). Its concerns the phase retrieval problem for the fractionnal Fourier transform. It is loosely related to my current research, since it can be interpreted as a problem on states in quantum mechanics.

(Feb. 2019) Cambridge, CQIF seminar. Energy exchanges in open quantum systems, applied to quasi-free fermions.

(May 2018) Toulouse, workshop on quantum functionnal inequalities. Presentation of the article : "Hypercontractivity of quasi-free quantum semigroups" (Temme, Pastawski, Kastoryano, 2014).

(October 2017), Toulon, Doctoriades. Entropic fluctuations for quasi-free fermionic semigroups.

(October 2016), Angers, Rencontres doctorales Lebesgue. Convergence of quantum trajectories.

(May 2016), Toulouse, meeting of the MISTEQ project. Entropic fluctuations for quasi-free fermionic dynamical systems.