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The long-range spectral density correlations (spectral rigidities$\bar{\Delta}_3(\bar n)$ and related spectral compressibilities) of the$E\otimes (b_1+b_2)$ Jahn-Teller model are found strongly nonuniversal withrespect to the Hamiltonian parameters and inhomogeneous with respect to thechoice of a partial energy segment. However, the spectral compressibilitiesfound for the partial spectral segments and averaged over a whole relevant partof the spectrum cumulate close to a well-defined limit pertaining to thesemi-Poisson statistics. This is in accordance with similar tendencies revealedin the short-range averaged statistical characteristics of this modelinvestigated in our previous paper [1]. We ascribe the nonuniversal andinhomogeneous nonintegrability behaviour to the changing degree of thebrokening of the rotation symmetry when changing parameters of our effectivelytwo-dimensional model. It results in a random distribution of the respectivelocalized wave functions at all scales up to the size of an available statespace. The multifractal behaviour of the wave functions is implied from theanalysis of their (averaged) fractal dimensions which range up to $1.5\pm 0.1$(for $\bar{D}_2$). This might imply the concept of the chaos-assistedtunnelling between the regions of reduced degree of stochasticity throughregions of high degree of stochasticity. It supports the analogy with thetwo-dimensional Anderson model with marginal-asymptotically far metal-insulatortransition. The features found allow us to classify the present model as amember of the class with a multifractal eigenfunction statistics characteristicfor the spectra with weakened level repulsion similar to the Anderson modelclose to the metal-insulator transition.Comment: 17 pages, 9 figures; published in J.Phys.A; sequel of Phys.Rev.E  v.73, 057202 (2006) [cond-mat/0510710

physical review. e, statistical, nonlinear and soft matter physics

Quantum chaotic patterns in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">E</mml:mi><mml:mo>⊗</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math>Jahn-Teller model

Quantum chaotic patterns in theE⊗(b1+b2)Jahn-Teller model