Uncertainty relation and non-dispersive states in Finite Quantum Mechanics

Details Uncertainty relation and non-dispersive states in Finite Quantum Mechanics Uncertainty relation and non-dispersive states in Finite Quantum Mechanics

1997-06-23

arxiv.org/abs/hep-th/9706156v2

Phys.Lett. B412 (1997) 35-41

Physics

High Energy Physics

High Energy Physics - Theory

Latex file, 16pages, 3 ps-figures, version to appear in Phys.Lett.B

Scientific paper

10.1016/S0370-2693(97)01061-7

In this letter, we provide evidence for a classical sector of states in the Hilbert space of Finite Quantum Mechanics (FQM). We construct a subset of states whose the minimum bound of position -momentum uncertainty (equivalent to an effective $\hbar$) vanishes. The classical regime, contrary 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 observe that time evolution leads to fast decorrelation of the wave packets, phenomenon similar to the behavior of wave packets in t' Hooft and Susskind holographic picture. Moreoever, we construct explicitly a non - dispersive basis of states in accordance with t' Hooft's arguments about the deterministic behavior of FQM.

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