Giovanni Ciccotti: "Do we have a consistent non-adiabatic quantum-classical mechanics?"

Professor Giovanni Ciccotti
National Institute of Nuclear Physics, University of Rome "La Sapienza", Italy

Do we have a consistent non-adiabatic quantum-classical mechanics?

In this talk, we briefly describe an approach to mixed Quantum-Classical Statistical Dynamics based on the Wigner-Liouville formulation of quantum mechanics. We try to identify a consistent mixed Quantum-Classical Statistical Mechanics (QCSM) coming, in the usual way, from an underlying mixed Quantum-Classical Dynamics, which generates the time evolution of the given system, and is derived, under controlled approximations, from a set of formal prescriptions, comparable to the laws of quantum or classical mechanics.

We find unpleasant inconsistencies since our dynamics violates e.g. Jacobi identity and the disease seems incurable.

Recently Vladimir Kisil has proposed new equations found by generalizing the Heisenberg group formulation of quantum mechanics. In our attempt to understand the new quantum-classical dynamics, we have reconstructed and analyzed the derivation, finding that, in a suitable representation, the supposedly quantum-classical equations of motion clearly show their purely classical nature. Although not all paths to QCSM have been explored, we begin to suspect, behind those negative results, a no-go theorem.