Limit Cycles in Quantum 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

Laser Theory for Optomechanics: Limit Cycles in the Quantum Regime

Niels Lörch, Jiang Qian, Aashish Clerk, Florian Marquardt, and Klemens Hammerer Institut für Gravitationsphysik, Leibniz Universität Hannover and Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Callinstraße 38, 30167 Hannover, Germany Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany Arnold Sommerfeld Center for Theoret...

Quantum phase transitions in spin systems and the high temperature limit of continuum quantum field theories

We study the finite temperature crossovers in the vicinity of a zero temperature quantum phase transition. The universal crossover functions are observables of a continuum quantum field theory. Particular attention is focussed on the high temperature limit of the continuum field theory, the socalled “quantum-critical” region. Basic features of crossovers are illustrated by a simple solvable mod...

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...