Incipience of quantum chaos in the Jahn-Teller model

Majerníková, E.; Shpyrko, S.

doi:10.1103/physreve.73.066215

Cited by 18 publications

(86 citation statements)

References 54 publications

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“…By using a combination of Rashba spin-orbit coupling, and deformed trap and a Zeeman field we find parameter regimes where the Wigner (4) and the Brody (5) distributions may be realized. While the Brody distribution has been discussed in the context of the JahnTeller model previously [51], the fourth order Wigner (4) was not observed as far as we can tell.…”

Section: Two Dimensionscontrasting

confidence: 61%

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Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Marchukov¹,

Volosniev²,

Fedorov³

et al. 2014

J. Phys. B: At. Mol. Opt. Phys.

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We compute single-particle energy spectra for a one-body hamiltonian consisting of a twodimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner distributions. The Brody and Wigner distributions characterize irregular motion and help identify quantum chaotic systems. We present a special choices of deformation and spin-orbit strengths without the Zeeman term which provide a fair reproduction of the fourth-power repelling Wigner distribution. By adding the Zeeman field we can reproduce a Brody distribution, which is known to describe a transition between the Poisson and linear Wigner distributions.

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Section: Two Dimensionscontrasting

confidence: 61%

“…In Ref. [51] these deviations are analyzed using distributions different from Wigner (2). The results presented below also go beyond the Poisson (1) and Wigner (2) distributions.…”

Section: Two Dimensionsmentioning

confidence: 99%

Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Marchukov¹,

Volosniev²,

Fedorov³

et al. 2014

J. Phys. B: At. Mol. Opt. Phys.

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“…The examples of numerical solutions to gCM equations are shown in Figures 1, 2 for three sets of variables (x n , p n , V mn ) involved. The solutions for energy levels not close to artificial interval boundaries locally effectively reproduce the numerical solutions for energy levels as functions of α obtained via the diagonalisation of the Hamiltonian matrix (7) (see [11], Fig.1). There the exact level spectrum is illustrated for two different domains introduced as "oscillating" and "kink-lattice" domains of the spectrum.…”

Section: In This Equation Esupporting

confidence: 59%

“…Probabilistic considerations enable determination of a measure of stochasticity within this irregular and highly non-universal model, in the context of earlier analyses of the nearest level spacing probability distributions [11]. Besides the numerical analysis we shall apply an alternative approach of level dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Level-dynamic approach to the excited spectra of the Jahn-Teller model – kink-train lattice and ‘glassy’ quantum phase

Majerníková

Shpyrko

2008

Eur. Phys. J. B

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Abstract. The dynamics of excited phonon spectra of the E ⊗ e Jahn-Teller (hereafter, JT) model mapped onto the generalized Calogero-Moser (gCM) gas of pseudoparticles implies a complex interplay between nonlinearity and fluctuations of quasiparticle trajectories. A broad crossover appears in a pseudotime (interaction strength) between the initial oscillator region and the nonlinear region of the kink-train lattice as a superlattice of the kink-antikink gCM trajectories. The local nonlinear fluctuations, nuclei (droplets) of the growing kink phase arise at the crossover, forming a new intermediate droplet "glassy" phase as a precursor of the kink phase. The "glassy" phase is related to a broad maximum in the entropy of the probability distributions of pseudoparticle accelerations, or level curvatures. The kink-train lattice phase with multiple kink-antikink collisions is stabilised by long-range correlations when approaching a semiclassical limit. A series of bifurcations of nearest-level spacings were recognised as signatures of pre-chaotic behaviour at the quantum level in the kink phase. Statistical characteristics can be seen to confirm the coexistence within all of the spectra of both regularity and chaoticity to a varying extent (nonuniversality). Regions are observed within which one of the phases is dominant.PACS. 31.30.-i Corrections to electronic structure -63.22.+m Phonons or vibrational states in lowdimensional structures and nanoscale materials -05.45.-a Nonlinear dynamics and chaos -34.10.+x General theories and models of atomic and molecular collisions and interactions

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Quantum chaos, localized states and clustering in excited spectra of Jahn–Teller models

Majerníková

Shpyrko

2007

Journal of Molecular Structure

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We studied complex spectra of spin-two boson systems represented by E⊗e and E⊗(b1 +b2) Jahn-Teller models. For E⊗e, at particular rotation quantum numbers we found a coexistence of up to three regions of the spectra, (i) the dimerized region of long-range ordered (extended) pairs of oscillating levels, (ii) the short-range ordered (localized) "kink lattice" of avoiding levels, and (iii) the intermediate region of kink nucleation with variable range of ordering. This structure appears above certain critical line as a function of interaction strength. The level clustering and level avoiding generic patterns reflect themselves in several intermittent regions between up-to three branches of spectral entropies. Linear scaling behavior of the widths of curvature probability distributions provides the conventionally adopted indication for the presence of quantum chaos. The mapping onto classical integrable Calogero-Moser gas provided useful insight into the complex level dynamics, including the soliton collisions representing the level avoidings and, in a range of model parameters, a novel view on the notion of quantum chaos formulated in terms of quantum numbers via the logistic equation. We found that apart from two limiting cases of E ⊗(b1 +b2) model (E ⊗e and Holstein model) the distribution of nearest neighbor spacings of this model is rather stable as to the change of parameters and different from Wigner one. This limiting distribution assumably shows scaling ∼ √ S at small S and resembles the semi-Poisson law P (S) = 4S exp(−2S) at S ≥ 1. The latter is believed to be universal and characteristic, e.g. at the transition between metal and insulator phases.

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Incipience of quantum chaos in the Jahn-Teller model

Cited by 18 publications

References 54 publications

Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Level-dynamic approach to the excited spectra of the Jahn-Teller model – kink-train lattice and ‘glassy’ quantum phase

Quantum chaos, localized states and clustering in excited spectra of Jahn–Teller models

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