Europhys. Lett.
Volume 66, Number 5, June 2004
Page(s) 638 - 644
Section General
Published online 01 May 2004
Europhys. Lett., 66 (5) , pp. 638-644 (2004)
DOI: 10.1209/epl/i2004-10023-y

Random maps in physical systems

L. Trujillo1, 2, 3, J. J. Suárez3 and J. A. González2, 3

1  PMMH (CNRS UMR 7636), ESPCI - 10 rue Vauquelin, 75231 Paris Cedex 05, France
2  International Centre for Theoretical Physics (ICTP) - Trieste, Italy
3  Centro de Física, IVIC - A.P. 21827, Caracas 1020-A, Venezuela

(Received 12 January 2004; accepted in final form 25 March 2004)

We show that functions of type Xn=P[Zn], where P[t] is a periodic function and Z is a generic real number, can produce sequences such that any string of values $X_s,
X_{s+1},\ldots,X_{s+m}$ is deterministically independent of past and future values. There are no correlations between any values of the sequence. We show that this kind of dynamics can be generated using a recently constructed optical device composed of several Mach-Zehnder interferometers. Quasiperiodic signals can be transformed into random dynamics using nonlinear circuits. We present the results of real experiments with nonlinear circuits that simulate exponential and sine functions.

05.45.-a - Nonlinear dynamics and nonlinear dynamical systems.
42.65.Sf - Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics.
05.45.Vx - Communication using chaos.

© EDP Sciences 2004