Quantum-Classical Hybrid Dynamics

Dipartimento di Fisica "Enrico Fermi"
Universita di Pisa
Largo Pontecorvo 3
I-56127 Pisa, Italia

Quantum mechanics is beset with well known problems, intrinsic ones such as the measurement problem with collapse or reduction of the wave function, besides unresolved conceptual difficulties when applied to gravity. This has led to speculations that quantum mechanics might be to an underlying dynamics what hydrodynamics is to molecular or atomic physics. Thus quantum theory would appropriately describe phenomena that "emerge" only at sufficiently large length scales.

Here we discuss a framework which allows to couple directly deterministic classical and quantum mechanical degrees of freedom, which may be a useful step towards "emergent quantum mechanics". - Quite independently of the present motivation, however, the topic of such "hybrids" has a long and mixed history, dating back to Jauch's early remarks, taken up by Sudarshan and collaborators, and intermittently producing various no-go theorems. Besides, it is relevant for the consistency of "semiclassical quantum gravity", of the Born-Oppenheimer approximation, of mean field theory, and, last not least, for macroscopic classical operations in control of quantum computational protocols.

Our approach is based on phase space and a formal structure that consistently generalizes familiar Poisson and commutator brackets and the algebra of observables. It allows for a path integral version incorporating the classical dynamical degrees of freedom. Various interesting questions are brought up by this, for example, concerning quantum-classical backreaction, classically induced decoherence, deviations from Born's rule, etc. Last not least, our approach might offer possibilities for further generalization, such as incorporating deterministic degrees of freedom pertaining to fundamental cellular automata.

Vita:
I received a Phd from the University of Frankfurt (1985), following studies of
physics, mathematics, and biophysics at Universities of Giessen and Bonn. -
Postdoctoral positions in Berkeley, Helsinki, and several years spent at CERN.
Professorships in Bremen, Regensburg, and Tucson (Arizona), tenure at
Universidade Federal do Rio de Janeiro (1997). Affiliated with Universita di
Pisa since 2004. - Numerous fellowships, notably Heisenberg Fellow Award (DFG,
Germany) for studies of quantum transport phenomena in gauge theories. Organizer
of the biannual DICE conferences in Italy since 2002 and of conferences on high
energy density matter in Brazil. - Present interests include: decoherence (which
I proposed in 1994 as entropy source in high-energy collisions), entanglement,
the quantum-classical border, and the emergence of quantum mechanics from
dynamics beneath.