245 research outputs found
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 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
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