Eur. Phys. J. B 66, 259-269 (2008)
https://doi.org/10.1140/epjb/e2008-00419-y

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

¹ Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta, 84511 Bratislava, Slovak Republic
² Department of Optics, Palacký University, Tř. 17. listopadu 50, 77207 Olomouc, Czech Republic
³ Institute for Nuclear Research, Ukrainian Academy of Sciences, pr. Nauki 47, Kiev, Ukraine

Corresponding author: ^a eva.majernikova@savba.sk

Received: 12 June 2008
Revised: 30 September 2008
Published online: 20 November 2008

Abstract

The dynamics of excited phonon spectra of the E⊗e 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.