Chaos in spin clusters: Quantum invariants and level statistics

Srivastava, Niraj; Kaufman, Charles; Müller, Gerhard

doi:10.1063/1.345907

Cited by 15 publications

(8 citation statements)

References 8 publications

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“…In a single subspace, the distribution P (ΔE) of nearest level spacings ΔE typically follows Poisson or Wigner statistics depending on whether the classical system is completely integrable or completely chaotic [19]. For the present system, this has been confirmed qualitatively by Srivastava et al [17]. In the following, a different quantity is studied, namely, the nearest-level spacing of levels contained in different subspaces.…”

Section: Nearest Level Spacings and Quasi-degeneraciessupporting

confidence: 60%

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Quasi-degeneracies in a 2-spin system: symmetry aspects and a perturbational approach to tunnel splitting

Schatzer

Breymann

Thomas

1996

Z. Phys. B - Condensed Matter

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A large number of energy levels in different invariant subspaces of the anisotropic XY-model are quasidegenerate in a wide parameter range, i.e., their spacing is much smaller than the mean level spacing of the system. These quasi-degeneracies can be interpreted in two ways: (i) as tunnel splitting, (ii) as weak level splitting related to a parametric point of exact degeneracy. Starting from the second interpretation we calculate the tunnel splitting by use of perturbative methods.

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Section: Nearest Level Spacings and Quasi-degeneraciessupporting

confidence: 60%

“…In the following, we confine ourselves to the case of spins of the same length, s 1 = s 2 = s, which has been studied extensively in [15][16][17]. Thus, the total Hilbert space of dimension (2s + 1) 2 is the direct product H s ⊗ H s of two identical one-spin spaces.…”

Section: The Anisotropic Xy -Modelmentioning

confidence: 99%

Quasi-degeneracies in a 2-spin system: symmetry aspects and a perturbational approach to tunnel splitting

Schatzer

Breymann

Thomas

1996

Z. Phys. B - Condensed Matter

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“…The method is not rigorously quantitative, but, in analogy to the Poincaré section method in classical mechanics [27], it enables a qualitative distinction between regular and chaotic motion. Regular and chaotic dynamics are inferred from the regular and chaotic form of particular spectral lattices [26,[28][29][30]. The method was recently applied to the geometric collective model, which is closely related to the IBM (see Ref.…”

Section: Signatures Of Intrinsic Regularitymentioning

confidence: 99%

Occurrence of high-lying rotational bands in the interacting boson model

2010

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We observe an adiabatic separation of collective rotations built upon a subset of intrinsic vibrational states within the interacting boson model (IBM) in the parameter domains corresponding to axially deformed ground state. The effect is not limited only to the low-lying states and closely follows the variation of quantum and classical measures of regularity. It leads to the existence of rotational bands even close to the highest accessible energies in specific regions within the IBM symmetry triangle. We propose a more general effect of regular intrinsic dynamics on the adiabatic separation of intrinsic and collective motion.

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“…Existing quantum chaos studies of the spinboson model have focused primarily on properties of the flow in the classical phase space and on quantum mechanical representations thereof (coherent-state representation, Husimi distributions [3,4,5], dynamics of level occupation probabilities [1], and energy-level statistics [6,7,8]. The purpose of this study, which is based on the methods of analysis introduced in [9,10,11] for a two-spin system, is the investigation of nonintegrability effects in quantum invariants of the spin-boson model and their implications for the level statistics. The spin-boson Hamiltonian considered in this work reads :…”

Section: Introductionmentioning

confidence: 99%

Incipience of quantum chaos in the spin-boson model

Cibils

Cuche

Müller

1995

Z. Physik B - Condensed Matter

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The peculiar spectral properties of the spin-boson model make it suitable for an investigation of quantum nonintegrability effects and level statistics from a new perspective. For fixed spin quantum number s, its energy spectrum consists of 2s + 1 sequences of levels with no upper bound. These sequences are identified and labelled consecutively by means of a quantum invariant calculated from the time average of a non-stationary operator. For integrable cases, level repulsion (on the energy axis) is limited to states within each sequence. From the observed spectral properties, we infer a series of s-dependent level-spacing distributions. They converge towards a Poisson distribution for s → ∞. For nonintegrable cases, level repulsion becomes a universal phenomenon, but the amount of repulsion between two states decreases with increasing separation (in label) of the two sequences to which they belong. For small s, the quantum nonintegrability effects are compelling but not at all chaotic. Nevertheless, they contain all the ingredients necessary to produce the symptoms commonly described as indicators of quantum chaos. In this model, we can observe quantum chaos in the making under very controllable conditions.

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Chaos in spin clusters: Quantum invariants and level statistics

Abstract: . Chaos in spin clusters: quantum invariants and level statistics.

Cited by 15 publications

References 8 publications

Quasi-degeneracies in a 2-spin system: symmetry aspects and a perturbational approach to tunnel splitting

Quasi-degeneracies in a 2-spin system: symmetry aspects and a perturbational approach to tunnel splitting

Occurrence of high-lying rotational bands in the interacting boson model

Incipience of quantum chaos in the spin-boson model

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