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arXiv:cond-mat/0610259 · Journal of Molecular Structure

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

Eva Majerníková, Serge Shpyrko

Published Jan 24, 2007• 1 citation
arXivHTMLPDF
DOI
10.1016/j.molstruc.2007.01.029

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We studied complex spectra of a two-level electron system coupled to two phonon (vibron) modes represented by the product of E and e Jahn-Teller model. For 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 a 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 level curvature probability distributions provides the conventionally adopted indication for the presence of quantum chaos. Level spacing probability distributions show peculiarities of the partial (for fixed quantum angular momentum) as well as of the cumulative (all angular momenta) case. The clustering of levels with two and three dominant spacings at fixed angular momenta causes notable deviations of the cumulative distributions from the Poissonian one.
The generalized multispin Jahn-Teller model on a finite lattice or formally equivalent Dicke model extended to two long-wavelength coherent bosons of different frequencies is shown to exhibit a crossover between the polaron-modified "quasi-normal" and the squeezed "radiation" domains. We investigate effects of two kinds of interfering fluctuations on the phase crossover and on statistical characteristics of boson complex spectra: (i) Fluctuations in the electron subsystem- finite-size quantum fluctuations- are responsible for the dephasing of the coherence in the radiation domain and for the moderate occupation of the excited states in the normal domain. In the quasiclassical limit, radiation phase implies existence of a coherent acoustic super-radiant phase. (ii) Level-spacing fluctuations in excited boson level subsystem with strong level repulsions. Related probability distributions are shown to be non-universally spread between the limiting universal Wigner-Dyson and Poisson distributions. We proved that the difference in boson frequencies is responsible for reaching the most stochastic limit of the Wigner-Dyson distribution. Instanton lattice as a sequence of tunneling events in the most chaotic radiation domain exhibits maximal number of level-avoidings (repulsions). The non-universality of the distributions is caused by boson correlations which compete the level repulsions.