Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 7: Statistical physics II (general)

DY 7.11: Talk

Tuesday, March 24, 2009, 12:30–12:45, HÜL 386

Reproduction of the collective behavior of the Hamiltonian Mean Field Model by means of a single forced oscillator — •Angelo Facchini^1,2 and Stefano Ruffo³ — ¹Center for the Study of Complex Systems, University of Siena, Italy — ²Department of Information Engineering, University of Siena, Italy — ³Dipartimento di Energetica ”S. Stecco”, University of Florence, INFN and CSDC, Italy

We force a single oscillator with the x and y components of the magnetization computed by integrating an N particles Hamiltonian Mean Field model (Phys. Rev. E, 52, 2361). The equations of motion read x=M_x(t)sin(x)−M_y(t)cos(x), where M_x(t) and M_y(t) are computed step by step and the energy is set to U=0.3. We show that the motion of the particle is statistically equivalent to the motion of the N particles cluster, and that the memory effect (Comm. Nonlin. Sc. and Num. Methods, 13, 868) observed in the life-time of the cluster is also found in the phase of the driven particle. Furthermore, we test the consistency of the single oscillator phase with that of the cluster by driving with M_x,y(t) a system of N uncoupled oscillators whose initial conditions correspond to those of the equilibrium state of the HMF model.