Chaos and its quantization in dynamical Jahn-Teller systems.

@article{Yamasaki2003ChaosAI,
  title={Chaos and its quantization in dynamical Jahn-Teller systems.},
  author={Hisatsugu Yamasaki and Yuhei Natsume and Akira Terai and Katsuhiro Nakamura},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2003},
  volume={68 4 Pt 2},
  pages={
          046201
        }
}
We investigate the E(g) x in circle e(g) Jahn-Teller system for the purpose of revealing the nature of quantum chaos in crystals. This system simulates the interaction between the nuclear vibrational modes and the electronic motion in non-Kramers doublets for multiplets of transition-metal ions. Inclusion of the anharmonic potential due to the trigonal symmetry in crystals makes the system nonintegrable and chaotic. Besides the quantal analysis of the transition from Poisson to Wigner level… 
11 Citations

Figures and Topics from this paper

Chaos in Jahn-Teller Rattling
We unveil chaotic behavior hidden in the energy spectrum of a Jahn-Teller ion vibrating in a cubic anharmonic potential as a typical model for rattling in cage-structure materials. When we evaluate
Chaos-induced breaking of the Franck-Condon approximation
We investigate the vibrational structure of electronic spectra for the transition from the non-degenerate $A$ state to $E$ states in $E_g\otimes e_g$ Jahn-Teller systems with the trigonal field
Frustrated quantum-spin system on a triangle coupled with eg lattice vibrations: correspondence to Longuet-Higgins et al’s Jahn–Teller model
We investigate the frustrated quantum three-spin model (S1,S2,S3) of spin = 1/2 on a triangle, in which spins are coupled with lattice-vibrational modes through the antiferromagnetic exchange
Quantum chaos, localized states and clustering in excited spectra of Jahn–Teller models
Abstract We numerically studied complex excited spectra and their statistical characteristics of spin- two boson systems represented by the E ⊗ e and E ⊗ ( b 1  +  b 2 ) Jahn–Teller models. For the E
Level-dynamic approach to the excited spectra of the Jahn-Teller model – kink-train lattice and ‘glassy’ quantum phase
AbstractThe 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
Repulsively interacting fermions in a two-dimensional deformed trap with spin-orbit coupling
We investigate a two-dimensional system of fermions with two values of the internal (spin) degree of freedom. It is confined by a deformed harmonic trap and subject to a Zeeman field, Rashba or
Statistical properties of spectra in harmonically trapped spin–orbit coupled systems
We compute single-particle energy spectra for a one-body Hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin–orbit coupling and the Zeeman term. To
Quantum-"classical" correspondence in a nonadiabatic transition system.
  • H. Fujisaki
  • Physics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
TLDR
A nonadiabatic transition system which exhibits "quantum chaotic" behavior is investigated from quasiclassical aspects and numerically show that there is a sound correspondence between the quantum chaos and classical chaos for the system.
Entanglement induced by nonadiabatic chaos
We investigate entanglement between electronic and nuclear degrees of freedom for a model nonadiabatic system. We find that entanglement (measured by the von Neumann entropy of the subsystem for the
Entanglement and bifurcations in Jahn-Teller models
We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The $E\otimes\beta$ system models the coupling of a two-level electronic system, or qubit, to a single
...
1
2
...

References

SHOWING 1-8 OF 8 REFERENCES
Quantum signatures of chaos
The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2,
Quantum chaos : a new paradigm of nonlinear dynamics
Almost all the many past studies on chaos have been concerned with classical systems. This book, however, is one of the first to deal with quantum chaos, the natural progression from such classical
Chaos in atomic physics
Preface 1. Introduction 2. Chaos: tools and concepts 3. Chaos in classical mechanics 4. Chaos in quantum mechanics 5. The kicked rotor: paradigm of chaos 6. Microwave-driven surface state electrons
Introduction to Quantum Mechanics
I. THEORY. 1. The Wave Function. 2. The Time-Independent Schrodinger Equation. 3. Formalism. 4. Quantum Mechanics in Three Dimensions. 5. Identical Particles. II. APPLICATIONS. 6. Time-Independent
Quantum Chaos: An Introduction
Preface 1. Introduction 2. Billiard experiments 3. Random matrices 4. Floquet and tight-binding systems 5. Eigenvalue dynamics 6. Scattering systems 7. Semiclassical quantum mechanics 8. Applications
Mathematical Methods of Classical Mechanics
Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid