Regular and Chaotic Time Evolution in Spin Clusters

Srivastava, Niraj; Kaufman, Charles; Müller, Gerhard

doi:10.1051/jphyscol:19888733

Cited by 1 publication

(2 citation statements)

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“…If it weren't for the slow convergence of the time averages along chaotic trajectories due to low-flux cantori [18][19][20], the entire chaotic region would be represented by a single isolated point in the constant-energy section of the invariant-surface. In the full ( M 2 x , M 2 z , E)-space, the points associated with chaotic regions form string-like objects.…”

Section: B Nonanalytic Invariantsmentioning

confidence: 99%

“…The present paper is, in fact, the fourth part of our study of the dynamics of integrable and nonintegrable spin clusters. In the first three parts, the focus was, respectively, on the following properties of classical 2-spin clusters: integrability criteria and analytic structure of invariants [17]; geometric structure of analytic and nonanalytic invariants [18]; time-dependent correlation functions and spectral properties [19,20].…”

Section: Introductionmentioning

confidence: 99%

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Quantum and classical spin clusters: disappearance of quantum numbers and Hamiltonian chaos

Srivastava

Müller

1990

Z. Physik B - Condensed Matter

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We present a direct link between manifestations of classical Hamiltonian chaos and quantum nonintegrability effects as they occur in quantum invariants. In integrable classical Hamiltonian systems, analytic invariants (integrals of the motion) can be constructed numerically by means of time averages of dynamical variables over phase-space trajectories, whereas in near-integrable models such time averages yield nonanalytic invariants with qualitatively different properties. Translated into quantum mechanics, the invariants obtained from time averages of dynamical variables in energy eigenstates provide a topographical map of the plane of quantized actions (quantum numbers) with properties which again depend sensitively on whether or not the classical integrability condition is satisfied. The most conspicuous indicator of quantum chaos is the disappearance of quantum numbers, a phenomenon directly related to the breakdown of invariant tori in the classical phase flow. All results are for a system consisting of two exchange-coupled spins with biaxial exchange and single-site anisotropy, a system with a nontrivial integrability condition.

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Section: B Nonanalytic Invariantsmentioning

confidence: 99%