Advances in Mathematical Physics
Volume 2012 (2012), Article ID 731602, 16 pages
Research Article

On the Existence and Robustness of Steady Position-Momentum Correlations for Time-Dependent Quadratic Systems

Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Universit√° del Salento and INFN, Sezione di Lecce, 73100 Lecce, Italy

Received 17 October 2011; Revised 10 January 2012; Accepted 13 February 2012

Academic Editor: Ricardo Weder

Copyright © 2012 M. Gianfreda and G. Landolfi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We discuss conditions giving rise to stationary position-momentum correlations among quantum states in the Fock and coherent basis associated with the natural invariant for the one-dimensional time-dependent quadratic Hamiltonian operators such as the Kanai-Caldirola Hamiltonian. We also discuss some basic features such as quantum decoherence of the wave functions resulting from the corresponding quantum dynamics of these systems that exhibit no timedependence in their quantum correlations. In particular, steady statistical momentum averages are seen over well-defined time intervals in the evolution of a linear superposition of the basis states of modified exponentially damped mass systems.