Related Experiment Video
Updated: Aug 6, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Incipience of quantum chaos in the Jahn-Teller model
1Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84 511 Bratislava, Slovak Republic. fyziemar@savba.sk
Abstract:
We studied complex spectra of a two-level electron system coupled to two phonon (vibron) modes represented by the product of E and e Jahn-Teller model. For particular rotation quantum numbers we found a coexistence of up to three regions of the spectra: (i) the dimerized region of long-range-ordered (extended) pairs of oscillating levels, (ii) the short-range-ordered (localized) "kink lattice" of avoiding levels, and (iii) the intermediate region of kink nucleation with variable range of ordering. This structure appears above a certain critical line as a function of interaction strength. The level clustering and level avoiding generic patterns reflect themselves in several intermittent regions between up to three branches of spectral entropies. Linear scaling behavior of the widths of level curvature probability distributions provides the conventionally adopted indication for the presence of quantum chaos. Level spacing probability distributions show peculiarities of the partial (for fixed quantum angular momentum) as well as of the cumulative (all angular momenta) case. The clustering of levels with two and three dominant spacings at fixed angular momenta causes notable deviations of the cumulative distributions from the Poissonian one.
Related Concept Videos
The Quantum-Mechanical Model of an Atom
The Uncertainty Principle
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
First Law: Particles in One-dimensional Equilibrium
The Entropy as a State Function
Entropy and the Second Law of Thermodynamics
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...