# Dr. C. Pellegrini

# Contact Details

####
School of Physics and National Institute for Theoretical Physics

University of KwaZulu-Natal

Private Bag X54001, Durban 4000

South Africa
e-mail: pelleg[at]math.univ-lyon1.fr

phone: +27 719194086

University of KwaZulu-Natal

Private Bag X54001, Durban 4000

South Africa

e-mail: pelleg[at]math.univ-lyon1.fr

phone: +27 719194086

# Title and Diploma

####
- Doctor in Mathematics, thesis supported at Institut Camille jordan (23th June 2008)

Mention: Congratulations of the jury.
- Agregation de Mathematiques: rang 15
- I won the
**prize of the best French thesis 2008** of the foundation EADS in the section "Mathematics and Interactions"

Mention: Congratulations of the jury.

**prize of the best French thesis 2008**of the foundation EADS in the section "Mathematics and Interactions"Let see my Cv in French [pdf.file].

Let see my Cv in English [pdf.file]

# Research Interest

####
- Probability Theory, Stochastic Differential Equations, Stochastic Convergence
- Quantum Probability Theory
- Quantum open systems Theory
- Quantum Trajectory theory, Stochastic Schrödinger equations

My research activities are the interface of Probability Theory and Quantum Mechanics. In particular, I study the stochastic differential equation approach of "Quantum Trajectories" in Open Quantum System. Quantum trajectories are solutions of "Stochastic Schödinger Equations" which are non-classical SDEs. My work concerns the existence and uniqueness problem of the solutions. I have also justify these stochastic models from the discrete approach of "Quantum Repeated Measurements".

Currently, I work on non-Markovian approach of stochastic Schrödinger equations. In this framework, the equations are expressed in an integro-differential way. In particular, it concerns non-markovian stochastic processes driven by colored noise (Ornstein Uhlenbeck, non white Gaussian process, fractionnal Brownian motion).

# Articles

- Existence, Uniqueness and Approximation of a Stochastic Schrödinger Equation: the Diffusive case (2008):

The Annals of Probability 2008, Vol. 36, No. 6, 2332–2353
- Poisson and Diffusion Approximations of Stochastic Master Equations with Control (under corrections).
- Existence, Uniqueness and Approximation of a Stochastic Schrödinger Equation: the Poisson case (submitted).
- Markov Chain Approximations of Jump-Diffusion Quantum trajectories (submitted).
- Random repeated Quantum Interactions and Random Invariant States (with Ion Nechita) (submitted).
- Non Markovian Quantum Repeated Interactions and Measurements (with Francesco Petruccione) (submitted)
- Return to Equilibrium and Heat Bath in Quantum Trajectory Theory (with Stephane Attal) (preprint)
- Stochastic Master Equations for Heat Baths (with Stephane Attal) (preprint).
- Random Quantum Trajectories in Random Environment (with Ion Nechita) (preprint).

The Annals of Probability 2008, Vol. 36, No. 6, 2332–2353