Serge Shpyrko

Uncertainty relations expressed by Shannon-like entropies

Besides the well-known Shannon entropy, there is a set of Shannon-like entropies which have applications in statistical and quantum physics. These entropies are functions of certain parameters and converge toward Shannon entropy when these parameters approach the value 1. We describe briefly the most important Shannon-like entropies and present their graphical representations. Their graphs look almost identical, though by superimposing them it appears that they are distinct and characteristic of each Shannon-like entropy. We try to formulate the alternative entropic uncertainty relations by means of the Shannon-like entropies and show that all of them equally well express the uncertainty principle of quantum physics.

Nonlinear effects in E ⊗ (b1 + b2) Jahn–Teller model: variational approach with excited phonon states and mode correlations

Interplay of nonlinear and quantum effects in the ground state of the E

Quantum chaotic patterns in the E (b1 + b2) Jahn-Teller model.

\otimes (b_1+b_2)

Kinks in the discrete sine-Gordon model with Kac-Baker long-range interactions

Jahn-Teller model was investigated by the {\it variational approach and exact numerical simulations}. They result in the recognition of (i) importance of the admixture of {\it the first excited state of the displaced harmonic oscillator} of the symmetric phonon mode in the ground state of the system in the selftrapping-dominated regime; (ii) existence of {\it the region of localized

Quantum chaos, localized states and clustering in excited spectra of Jahn–Teller models

b_1

Interplay of disorder and nonlinearity in Klein-Gordon models: Immobile kinks

-undisplaced oscillator states} in the tunneling-dominated regime. The effect (i) occurs owing to significant decrease of the ground state energy on account of the overlapping contribution of the symmetric phonon mode between the states of the same parity. This contribution considerably improves variational results especially in the selftrapping-dominated regime. Close to the E

Ground State of Quantum Jahn–Teller Model: Selftrapping vs. Correlated Phonon-assisted Tunneling

\otimes

Quantum phase crossover and chaos in a generalized Jahn–Teller lattice model

e limit, the nonlinear effects of {\it two-mode correlations} turn to be effective due to the rotational symmetry of this case. In the tunneling-dominated regime the phonon wave functions behave like the strongly localized harmonic oscillator ground state and the effect (i) looses its significance.

Incipience of quantum chaos in the Jahn-Teller model

We study statistical properties of excited levels of the E x (b_1+b_2) Jahn-Teller model. The multitude of avoided crossings of energy levels is generally claimed to be a testimony of quantum chaos. We found that apart from two limiting cases (E x e and Holstein model) the distribution of nearest-neighbor spacings is rather stable as to the change of parameters and different from the Wigner one. This limiting distribution assumably shows scaling ~

Nonadiabatic effects in a generalized Jahn-Teller lattice model: Heavy and light polarons, pairing, and the metal-insulator transition

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