microNM · Microscopic derivation of non Markovian dynamics

Technology is moving in the direction of producing smaller and faster devices. The time scales at which the near future devices will operate, are such that the physical processes involved are foreseeable to be described in terms of non Markovian dynamics, i.e. dynamics displaying memory terms.Recently a strong interest on non Markovian dynamics is also grown in biology, in particular concerning the study of energy transfer and light harvesting in the photosynthesis process.So far, only phenomenological models have been proposed to describe non Markovian dynamics, but a microscopic derivation of non Markovian dynamics is still lacking. Our project aims at filling this gap.Aim of the research project is to give a microscopic derivation of non Markovian dynamics and to understand the nature of their memory terms. Such a goal will be achieved through the following three objectives:1) Classical microscopic derivation of non Markovian dynamics. We will study a classical particle coupled to an environment of harmonic oscillators.2) Quantum microscopic derivation of non Markovian dynamics. Once the classical model is understood, we will study the corresponding quantum one.3) Comparison of the results of previous objectives with known phenomenological models. We will be able to give a microscopic derivation of the microscopic parameters entering these models.We use advanced mathematical tools to analyze the properties of physical systems, which so far were studied only phenomenologically.The training objectives of the project are fully focused on mathematical aspects:- Acquire a solid knowledge on stochastic calculus and stochastic differential equations.- Study integro-differential equations and their properties.- Learn methods of statistical physics.- Study functional analysis tools, weak topologies and function spaces.As we will show, the applicant and the host institution profiles are perfectly matching with the project.