Chiara Saffirio receives an ERC Starting Grant

30 Aug 2022

Chiara Saffirio (UniBas) has received an ERC Starting Grant for the project: Advances in effective evolution equations for classical and quantum systems (AEQUA).

Summary of the project:

A major question in non-equilibrium statistical mechanics concerns the rigorous derivation of effective macroscopic equations from the microscopic laws of classical and quantum mechanics. Due to the high number of degrees of freedom, this is usually an extremely challenging task. AEQUA aims at addressing the aforementioned question in the framework of the kinetic theory of gases. Its purpose is twofold: on the one hand contributing to the resolution of longstanding open questions, such as the emergence of irreversibility from a microscopic time-reversible dynamics; on the other hand developing innovative mathematical methods originating from bridging different branches of mathematical physics and analysis, namely classical and quantum many-body systems, kinetic theories and PDEs.

AEQUA has four main goals: (a) the derivation of the Vlasov-Poisson Eq. with Coulomb and gravitational interactions from the many-body quantum dynamics; (b) the derivation of the Vlasov-Poisson Eq. from Newtonian mechanics in the mean-field regime; (c) the derivation of the quantum Boltzmann Eq. from a system of many interacting fermions in the weak-coupling limit; (d) the derivation of the classical Boltzmann Eq. from a system of many classical particles taking into account the boundary conditions.

The new developed methods will offer a completely new perspective on the derivation of kinetic equations and shed light on the derivation of the Boltzmann Eq. for long times, which is a topic of primary interest for mathematicians, theoretical physicists and philosophers of science. The key idea underlying the proposed novel techniques is to establish analogies between classical and quantum objects, between the many-body dynamics and its corresponding effective equation. We plan to push further the frontiers of second quantization methods developed in recent years and to build a classical analogue, thus avoiding conventional methods such as the BBGKY hierarchy.

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