UNCERTAINTY RELATION AND NONDISPERSIVE STATES IN FINITE QUANTUM-MECHANICS

In this letter, we provide evidence for a classical sector of states i n the Hilbert space of Finite Quantum Mechanics (FQM). We construct a subset of states whose the minimum bound of position-momentum uncertai nty (equivalent to an effective h) vanishes. The classical regime, con trary to standard Quantum Mechanical Systems of particles and fields, but also of strings and branes appears in short distances of the order of the lattice spacing. For Linear quantum maps of long periods, we o bserve that time evolution leads to fast decorrelation of the wave pac kets, phenomenon similar to the behavior of wave packets in 'tHooft an d Susskind holographic picture. Moreoever, we construct explicitly a n on-dispersive basis of states in accordance with 'tHooft's arguments a bout the deterministic behavior of FQM. (C) 1997 Elsevier Science B.V.