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

Title and Diploma

• Doctor in Mathematics, thesis supported at Institut Camille jordan (23th June 2008) 
  Mention: Congratulations of the jury.

  [pdf.file of my thesis]

• 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"

  [link to the site]

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

1. Existence, Uniqueness and Approximation of a Stochastic Schrödinger Equation: the Diffusive case (2008):
   The Annals of Probability 2008, Vol. 36, No. 6, 2332–2353

   [pdf.file]

2. Poisson and Diffusion Approximations of Stochastic Master Equations with Control (under corrections).

   [pdf.file]

3. Existence, Uniqueness and Approximation of a Stochastic Schrödinger Equation: the Poisson case (submitted).

   [pdf.file]

4. Markov Chain Approximations of Jump-Diffusion Quantum trajectories (submitted).

   [pdf.file]

5. Random repeated Quantum Interactions and Random Invariant States (with Ion Nechita) (submitted).

   [pdf.file]

6. Non Markovian Quantum Repeated Interactions and Measurements (with Francesco Petruccione) (submitted)

   [pdf.file]

7. Return to Equilibrium and Heat Bath in Quantum Trajectory Theory (with Stephane Attal) (preprint)
8. Stochastic Master Equations for Heat Baths (with Stephane Attal) (preprint).
9. Random Quantum Trajectories in Random Environment (with Ion Nechita) (preprint).