Limit Cycles in Effective Theories

Limit cycles in quantum theories.

Renormalization group limit cycles and more chaotic behavior may be commonplace for quantum Hamiltonians requiring renormalization, in contrast to experience based on classical models with critical behavior, where fixed points are far more common. We discuss the simplest quantum model Hamiltonian identified so far that exhibits a renormalization group with both limit cycle and chaotic behavior....

Central and Local Limit Theories in Markov Dependent Random Variables

Effective Field Theories in the Large N Limit

Various effective field theories in four dimensions are shown to have exact non-trivial solutions in the limit as the number N of fields of some type becomes large. These include extended versions of the U(N) Gross–Neveu model, the non-linear O(N) σ-model, and the CP model. Although these models are not renormalizable in the usual sense, the infinite number of coupling types allows a complete c...

Identifiability and Limit Cycles

The report discusses when the non-linear dynamic equations of a non-linear system in a limit-cycle can be determined from measured data. The minimal order needed for this turns out to be the minimal dimension in which the stable orbit of the system does not intersect itself. This is illustrated with a fourth order spiking neuron model, which is identified using a non-linear second order differe...

Friction generated limit cycles

This paper treats limit cycles caused by friction. The goal has been to explain phenomena that have been observed experimentally in mechatronic systems. Experiments have shown that oscillations of qualitatively different types can be obtained simply by changing controller specifications. Stiction is important in some cases but not in others. Necessary conditions for limit cycle are given for th...