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

We studied complex spectra of spin-two boson systems represented by E$\otimes$e and E$\otimes (b_1+b_2)$ Jahn-Teller models. For E$\otimes$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 $E\otimes(b_1+b_2)$ model ($E\otimes e$ 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 $\sim\sqrt{S}$ at small $S$ and resembles the semi-Poisson law $P(S)= 4S \exp (-2 S)$ at $S\geq 1$. The latter is believed to be universal and characteristic, e.g. at the transition between metal and insulator phases.Comment: Proceedings of the Jahn-Teller Conference, ICTP, Trieste, Aug.200

Nonlinear parametric instability in double-well lattices

A possibility of a nonlinear resonant instability of uniform oscillations in dynamical lattices with harmonic intersite coupling and onsite nonlinearity is predicted. Numerical simulations of a lattice with a double-well onsite anharmonic potential confirm the existence of the nonlinear instability with an anomalous value of the corresponding power index, 1.57, which is intermediate between the values 1 and 2 characterizing the linear and nonlinear (quadratic) instabilities. The anomalous power index may be a result of competition between the resonant quadratic instability and nonresonant linear instabilities. The observed instability triggers transition of the lattice into a chaotic dynamical state.Comment: A latex text file and three pdf files with figures. Physical Review E, in pres

Interplay of disorder and nonlinearity in Klein-Gordon models: Immobile kinks

We consider Klein-Gordon models with a $\delta$-correlated spatial disorder. We show that the properties of immobile kinks exhibit strong dependence on the assumptions as to their statistical distribution over the minima of the effective random potential. Namely, there exists a crossover from monotonically increasing (when a kink occupies the deepest potential well) to the non-monotonic (at equiprobable distribution of kinks over the potential minima) dependence of the average kink width as a function of the disorder intensity. We show also that the same crossover may take place with changing size of the system.Comment: 7 pages, 4 figure

Nonadiabatic effects in a generalized Jahn-Teller lattice model: heavy and light polarons, pairing and metal-insulator transition

The ground state polaron potential of 1D lattice of two-level molecules with spinless electrons and two Einstein phonon modes with quantum phonon-assisted transitions between the levels is found anharmonic in phonon displacements. The potential shows a crossover from two nonequivalent broad minima to a single narrow minimum corresponding to the level positions in the ground state. Generalized variational approach 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. It implies enhancement of the electron transfer due to decrease of the "heavy" polaron mass (undressing) at the point of the transition. Pairing of "light" polarons due to exchange of virtual phonons occurs. 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, there occurs anomalous (anharmonic) enhancements of quantum fluctuations of the phonon coordinate, momentum and their product as functions of the effective coupling. (ii) Dependence of the polaron mass on the optical phonon frequency appears.(iii) Rabi oscillations significantly enhance quantum shift of the insulator-metal transition line to higher values of the critical effective e-ph coupling supporting so the metallic phase. In the E-e JT case, insulator-metal transition coincide with the transition between the "heavy" and the "light" (bi)polaron phase at certain (strong) effective e-ph interaction.Comment: Paper in LaTex format (file jtseptx.tex) and 9 GIF-figures (ppic_1.gif,...ppic_9.gif

Kinks in the discrete sine-Gordon model with Kac-Baker long-range interactions

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. We also show that moving kinks radiate plane waves due to break of the Lorentz invariance by LRI.Comment: 11 pages (LaTeX) and 14 figures (Postscript); submitted to Phys. Rev.