Bead, Hoop, and Spring as a Classical Spontaneous Symmetry Breaking Problem

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dc.creatorOchoa, Fredy
dc.creatorClavijo, Jorge
dc.date2005-06-27
dc.date.accessioned2026-07-07T06:31:14Z
dc.date.available2026-07-07T06:31:14Z
dc.descriptionWe describe a simple mechanical system that involves Spontaneous Symmetry Breaking. The system consists of two beads constrained to slide along a hoop and attached each other through a spring. When the hoop rotates about a fixed axis, the spring-beads system will change its equilibrium position as a function of the angular velocity. The system shows two different regions of symmetry separated by a critical point analogous to a second order transition. The competitive balance between the rotational diynamics and the interaction of the spring causes an Spontaneous Symmetry Breaking just as the balance between temperature and the spin interaction causes a transition in a ferromagnetic system. In addition, the gravitational potential act as an external force that causes explicit symmetry breaking and a feature of first-order transition. Near the transition point, the system exhibits a universal critical behavior where the changes of the parameter of order is described by the critical exponent beta =1/2 and the susceptibility by gamma =1. We also found a chaotic behavior near the critical point. Through a demostrative device we perform some qualitative observations that describe important features of the system.
dc.description7 pages, 2 tables, 30 figures, LaTeX2e
dc.identifierhttps://arxiv.org/abs/physics/0506195
dc.identifierhttp://arxiv.org/abs/physics/0506195
dc.identifierEur. J. Phys. 27 (2006) 1277-1288
dc.identifierdoi:10.1088/0143-0807/27/6/002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98548
dc.subjectPhysics Education
dc.subjectGeneral Physics
dc.titleBead, Hoop, and Spring as a Classical Spontaneous Symmetry Breaking Problem
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