Pavel Stránský

Quantum chaos in the nuclear collective model: Classical-quantum correspondence.

Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic classical features with energy and control parameters. Corresponding signatures are now verified also on the quantum level for different schemes of quantization and with a variable classicality constant.

Impact of quantum phase transitions on excited-level dynamics.

The influence of quantum phase transitions on the evolution of excited levels in the critical parameter region is discussed. The analysis is performed for one- and two-dimensional systems with first- and second-order ground-state transitions. Examples include the cusp and nuclear collective Hamiltonians. Applications in systems of higher dimensions are possible.

Classification of excited-state quantum phase transitions for arbitrary number of degrees of freedom

Abstract Classical stationary points of an analytic Hamiltonian induce singularities of the density of quantum energy levels and their flow with a control parameter in the systems infinite-size limit. We show that for a system with f degrees of freedom, a non-degenerate stationary point with index r causes a discontinuity (for r even) or divergence ( r odd) of the ( f − 1 )  th derivative of both density and flow of the spectrum. An increase of flatness for a degenerate stationary point shifts the singularity to lower derivatives. The findings are verified in an f = 3 toy model.

Scale invariance as a symmetry in physical and biological systems: listening to photons, bubbles and heartbeats

Many dynamical systems from different areas of knowledge can be studied within the theoretical framework of time series, where the system can be considered as a black box, that only needs to be “listened” to. In this framework, non‐correlated series (white noise) and strongly correlated series (brownian noise or periodic series) constitute two extremes. Certain dynamical systems auto‐organize in a critical state that is characterized by 1/f or flicker noise. The family of fβ noises (β≤0) is fractal because fragments of the series are statistically identical to the original time series. 1/f noise (β = −1) is critical because it maximizes important complexity‐related quantities as memory, information content, efficiency and fractality. 1/f noise has been observed in classical systems, but also in quantum systems, and could possibly offer a unifying bridge of understanding between the macroscopic and the quantum world. In the present article, we will discuss some examples from both worlds.

Quantum chaos in the nuclear collective model. II. Peres lattices

This is a continuation of our paper [Phys. Rev. E 79, 046202 (2009)] devoted to signatures of quantum chaos in the geometric collective model of atomic nuclei. We apply the method by Peres to study ordered and disordered patterns in quantum spectra drawn as lattices in the plane of energy vs average of a chosen observable. Good qualitative agreement with standard measures of chaos is manifested. The method provides an efficient tool for studying structural changes in eigenstates across quantum spectra of general systems.

Quantum phases and entanglement properties of an extended Dicke model

Abstract We study a simple model describing superradiance in a system of two-level atoms interacting with a single-mode bosonic field. The model permits a continuous crossover between integrable and partially chaotic regimes and shows a complex thermodynamic and quantum phase structure. Several types of excited-state quantum phase transitions separate quantum phases that are characterized by specific energy dependences of various observables and by different atom–field and atom–atom entanglement properties. We observe an approximate revival of some states from the weak atom–field coupling limit in the strong coupling regime.

Understanding chaos via nuclei

We use two models of nuclear collective dynamics-the geometric collective model and the interacting boson model-to illustrate principles of classical and quantum chaos. We propose these models as a suitable testing ground for further elaborations of the general theory of chaos in both classical and quantum domains.

Monodromy in Dicke superradiance

We study the focus-focus type of monodromy in an integrable version of the Dicke model. Classical orbits forming a pinched torus represent analogues of the dynamic superradiance under conditions of a closed system. Quantum signatures of monodromy appear in lattices of expectation values of various quantities in the Hamiltonian eigenstates and are related to an excited-state quantum phase transition. We demonstrate the breakdown of these structures with an increasing strength of non-integrable perturbation.

Excited-state quantum phase transitions in finite many-body systems

Quantum spectra of excited states of numerous collective many-body models show singularities related to stable and unstable stationary points of the corresponding classical dynamics. We show several examples of these singularities and discuss some of their consequences.

Chaotic dynamics in collective models of nuclei

We present results of an extensive analysis of classical and quantum signatures of chaos in the geometric collective model (GCM) and the interacting boson model (IBM) of nuclei. Apart from comparing the regular fraction of the classical phase space and the Brody parameter for the nearest neighbor spacing distribution in the quantum case, we also adopt (i) the Peres lattices allowing one to distinguish ordered and disordered parts of spectra and to reveal main ordering principles of quantum states, (ii) the geometrical method to determine the position where the transition from order to chaos occurs, and (iii) we look for the 1/fα power law in the power spectrum of energy level fluctuations. The Peres method demonstrates the adiabatic separation of collective rotations in the IBM.