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

The dynamics of excited phonon spectra of the Exe 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.Comment: 10 pages, 8 figures; published in European Physical Journal B; see also: cond-mat/050968

Entropic uncertainty measure for fluctuations in two-level electron-phonon models

Two-level electron-phonon systems with reflection symmetry linearly coupled to one or two phonon modes (exciton and E$\otimes(b_1+b_2)$ Jahn-Teller model) exhibit strong enhancement of quantum fluctuations of the phonon coordinates and momenta due to the complex interplay of quantum fluctuations and nonlinearities inherent to the models. We show that for the complex correlated quantum fluctuations of the anisotropic two-level systems the Shannon entropies of phonon coordinate and momentum and their sum yield their proper global description. On the other hand, the variance measures of the Heisenberg uncertainties suffer from several shortcomings to provide proper description of the fluctuations. Wave functions, related entropies and variances were determined by direct numerical simulations. Illustrative variational calculations were performed to demonstrate the effect on an analytically tractable exciton model.Comment: 14 pages, 10 figs, published in Eur.Phys.J 38 B (2004) 25-3

Stochastic storage models and noise-induced phase transitions

The most frequently used in physical application diffusive (based on the Fokker-Planck equation) model leans upon the assumption of small jumps of a macroscopic variable for each given realization of the stochastic process. This imposes restrictions on the description of the phase transition problem where the system is to overcome some finite potential barrier, or systems with finite size where the fluctuations are comparable with the size of a system. We suggest a complementary stochastic description of physical systems based on the mathematical stochastic storage model with basic notions of random input and output into a system. It reproduces statistical distributions typical for noise-induced phase transitions (e.g. Verhulst model) for the simplest (up to linear) forms of the escape function. We consider a generalization of the stochastic model based on the series development of the kinetic potential. On the contrast to Gaussian processes in which the development in series over a small parameter characterizing the jump value is assumed [Stratonovich R.L., Nonlinear Nonequilibrium Thermodynamics, Springer Series in Synergetics, vol.59, Springer Verlag, 1994], we propose a series expansion directly suitable for storage models and introduce the kinetic potential generalizing them.Comment: 10 pages, 1 figur

Ising instability of a Holstein phonon mode in graphene

We study the thermal distribution of phonons in a graphene sheet. Due to the two electronic bands there are two out-of-plane phonon modes with respect to the two sublattices. One of these modes undergoes an Ising transition by spontaneously breaking the sublattice symmetry. We calculate the critical point, the renormalization of the phonon frequency and the average lattice distortion. This transition might be observable in Raman scattering and in transport properties.Comment: 5 pages, 2 figure