Inspired by previous works by Kramer & Saraceno and Shi & Rabitz, this talk exploits symmetry methods for the variational formulation of different problems in physics and chemistry. First, I will use symmetry methods to provide new variational principles for the description of mixed quantum states, in various pictures including Schrödinger, Heisenberg, Dirac (interaction) and Wigner-Moyal. Then, after discussing Ehrenfest's mean-field model, I will modify its symmetry properties to provide a new variational principle for expectation value dynamics in general situations. Upon moving to the Hamiltonian approach, this construction provides a complete dynamical splitting between expectation values and quantum deviations. As we shall see, specializing to Gaussian states yields energy conserving variants of previous models from the chemistry literature. In the last part of the talk, I will discuss some of the geometric features emerging in coupled classical-quantum dynamics.
Cesare obtained a Laurea in Nuclear Engineering in May 2004 at the Politecnico di Torino (Italy). Then, after spending two years (06/2003 – 05/2005) at CERN (Switzerland) working on microwave electronics under the direction of Ugo Amaldi (also at TU München and TERA Foundation), he moved to the Theoretical Division (in the former Plasma Theory Group) of the Los Alamos National Lab (LANL, USA), where he visited Giovanni Lapenta (now at KU Leuven, Belgium) for several months. In 10/2005, Cesare entered a PhD program at Imperial College, under the direction of Darryl Holm. In his thesis, he worked on geometric analogies between kinetic theory and porous media equations to model the aggregation of ferromagnetic nanoparticles. Between 2006 and 2007, he also spent two summers at LANL, working with Bruce Carlsten in the former International, Space & Response Division (High Power Electrodynamics Group). In 09/2008, Cesare joined the Mathematics Section of EPF Lausanne (Switzerland) as a research assistant in Tudor Ratiu’s group (Geometric Analysis). Since 01/2012, he is Lecturer (Assistant Professor) in the Department of Mathematics of the University of Surrey and have visited several institutions in Europe and North America.