Quantum Chaos: An answer to the Boltzmann-Loschmidt controversy?.

HORACIO M. PASTAWSKI; GONZALO USAJ; PATRICIA R. LEVSTEIN

Contemporary Problems of Condensed Matter Physics

NOVA Scientific Publishing

Lugar: New York; Año: 2001; p. 203 - 233

We revive the long standing Boltzmann-Loschmidt polemic which confronts irreversible.Thermodynamics with reversible Mechanics. While this is solved within classical physics by the theory of Chaos, until now, there is no quantum de¯nition of dynamical chaos. A nice possibility o®ered by NMR is to invert the direction of time (quantum Loschmidt daemon) in a many-body spin system. The e±ciency of this reversion M(tR ) decays with the elapsed time tR before reversal, with a characteristic irreversibility time ¿Á . What controls this time? By changing the time scales of the system in several ways, we observe cases where ¿Á is determined by the reversible spin-spin interactions. A natural de¯nition of quantum chaos in our experimental context is the instability of dynamical quantum correlations with respect to in¯nitesimal perturbations in the Hamiltonian. Therefore, our whole set of experiments indicates that there is quantum chaos intrinsic to the many-body spin dynamics in the thermodynamic limit. It manifests as an instability towards perturbations (decoherence) with a ¿Á independent on how small the interaction with the environment is. We also argue that ¡ ln[M(tR )] represents a measure of the increasing entropy. This new evidence in support to Boltzmann´s physical insight also serves as a landmark to direct the theoretical and experimental work in the new ¯eld of quantum chaos.