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

TL;DR

This paper investigates the complex excited phonon spectra of the Jahn-Teller model, revealing a crossover to a glassy phase characterized by kink-train lattice structures and signs of quantum pre-chaos.

Contribution

It introduces a level-dynamic approach mapping the Jahn-Teller model onto a generalized Calogero-Moser gas, uncovering new intermediate phases and bifurcation signatures of pre-chaotic behavior.

Findings

Identification of a 'glassy' phase with maximum entropy in pseudoparticle accelerations.

Observation of bifurcations indicating pre-chaotic quantum behavior.

Coexistence of regular and chaotic spectral features across different regions.

Abstract

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.