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.

Besides the well-known Shannon entropy, there is a set of Shannon-like entropies which have applications in statistical and quantum physics. These entropies are functions of certain parameters and converge toward Shannon entropy when these parameters approach the value 1. We describe brie®y the most important Shannon-like entropies and present their graphical representations. Their graphs look almost identical, though by superimposing them it appears that they are distinct and characteristic of each Shannon-like entropy. We try to formulate the alternative entropic uncertainty relations by means of the Shannon-like entropies and show that all of them equally well express the uncertainty principle of quantum physics.

The selfconsistent ground state polaron potential of one-dimensional lattice of two-level molecules with spinless electrons and two dispersionless phonon modes with linear coupling and quantum phonon-assisted (nonadiabatic) transitions between the levels is found anharmonic in phonon displacements. As a function of these, the potential shows a crossover from two nonequivalent broad minima to a single narrow minimum which correspond to the positions of the levels in the ground state. Generalized variational approach respecting the mixing of levels (reflection) via a variational parameter implies prominent nonadiabatic effects: (i) In the limit of the symmetric E⊗e Jahn-Teller situation they cause transition between the regime of the predominantly one-level "heavy" polaron and a "light" polaron oscillating between the levels due to phonon assistance with almost vanishing polaron displacement. Vanishing polaron selflocalization implies enhancement of the electron transfer due to decrease of the "heavy" polaron mass (undressing) at the point of the transition. There can occur pairing of "light" polarons due to exchange of virtual phonons. Continuous transition to new energy ground state close to the transition from "heavy" polaron phase to "light" (bi)polaron phase occurs. In the "heavy" phase, we have found anomalous (anharmonic) enhancements of quantum fluctuations of the phonon coordinate, conjugated momentum and their product in the ground state as functions of the effective coupling which reach their maxima at E⊗e JT symmetry. They decrease rapidly to their harmonic values as soon as the "light" phase is stabilized. (ii) Nonadiabatic dependence of the polaron mass (Debye-Waller screening) on the optical phonon frequency appears. (iii) The contribution of Rabi oscillations to the transfer enhances significantly quantum shift of the insulator-metal transition line to higher values of the critical effective electron-phonon coupling supporting so the metallic phase. In the E⊗e JT case, insulator-metal transition can coincide with the transition between the "heavy" and the "light" (bi)polaron phase only at certain (strong) effective electron-phonon interaction.PACS number(s): 42.50.L, 31.30.Gs, 74.20.Mn

Interplay of nonlinear and quantum effects in the ground state of the E⊗(b 1 + b 2 ) Jahn-Teller model was investigated by the variational approach and exact numerical simulations. They result in the recognition of (i) importance of the admixture of the first excited state of the displaced harmonic oscillator of the symmetric phonon mode in the ground state of the system in the selftrapping-dominated regime; (ii) existence of the region of localized b 1 -undisplaced oscillator states in the tunneling-dominated regime. The effect (i) occurs owing to significant decrease of the ground state energy on account of the overlapping contribution of the symmetric phonon mode between the states of the same parity. This contribution considerably improves variational results especially in the selftrapping-dominated regime. Close to the E⊗e limit, the nonlinear effects of two-mode correlations turn to be effective due to the rotational symmetry of this case. In the tunneling-dominated regime the phonon wave functions behave like the strongly localized harmonic oscillator ground state and the effect (i) looses its significance. pacs[63.20.Kr,31.30.Gs,71.70.Ej ]

We study effects of Kac-Baker long-range dispersive interaction (LRI) between particles on kink properties in the discrete sine-Gordon model. We show that the kink width increases indefinitely as the range of LRI grows only in the case of strong interparticle coupling. On the contrary, the kink becomes intrinsically localized if the coupling is under some critical value. Correspondingly, the Peierls-Nabarro barrier vanishes as the range of LRI increases for supercritical values of the coupling but remains finite for subcritical values. We demonstrate that LRI essentially transforms the internal dynamics of the kinks, specifically creating their internal localized and quasilocalized modes.