Scaling of dynamical properties of the Fermi–Ulam accelerator

Denis Gouvêa Ladeira and Jafferson Kamphorst Leal da Silva

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 23, 5707-5715

Abstract: We investigate numerically the chaotic sea of the complete Fermi–Ulam model (FUM) and of its simplified version (SFUM). We perform a scaling analysis near the integrable to non-integrable transition to describe the average energy as function of time t and as function of iteration (or collision) number n. When t is employed as independent variable, the exponents of FUM and SFUM are different. However, when n is used, the exponents are the same for both FUM and SFUM. In the collision number analysis, we present analytical arguments supporting the values of the exponents related to the control paramenter and to the initial velocity. We describe also how the scaling exponents obtained by using t as independent variable are related to the ones obtained with n. In contrast to SFUM, the average energy in FUM saturates for long times. We discuss the origin of the observed differences and similarities between FUM and its simplified version.

Keywords: Fermi model; Chaos; Scaling (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:23:p:5707-5715

DOI: 10.1016/j.physa.2008.06.013

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