We present a comprehensive analysis of the emerging order and chaos and enduring symmetries, accompanying a generic (high-barrier) first-order quantum phase transition (QPT). The interacting boson model Hamiltonian employed, describes a QPT between s
pherical and deformed shapes, associated with its U(5) and SU(3) dynamical symmetry limits. A classical analysis of the intrinsic dynamics reveals a rich but simply-divided phase space structure with a Henon-Heiles type of chaotic dynamics ascribed to the spherical minimum and a robustly regular dynamics ascribed to the deformed minimum. The simple pattern of mixed but well-separated dynamics persists in the coexistence region and traces the crossing of the two minima in the Landau potential. A quantum analysis discloses a number of regular low-energy U(5)-like multiplets in the spherical region, and regular SU(3)-like rotational bands extending to high energies and angular momenta, in the deformed region. These two kinds of regular subsets of states retain their identity amidst a complicated environment of other states and both occur in the coexistence region. A symmetry analysis of their wave functions shows that they are associated with partial U(5) dynamical symmetry (PDS) and SU(3) quasi-dynamical symmetry (QDS), respectively. The pattern of mixed but well-separated dynamics and the PDS or QDS characterization of the remaining regularity, appear to be robust throughout the QPT. Effects of kinetic collective rotational terms, which may disrupt this simple pattern, are considered.
We consider a low-dimensional model of convection in a horizontally magnetized layer of a viscous fluid heated from below. We analyze in detail the stability of hydromagnetic convection for a wide range of two control parameters. Namely, when changin
g the initially applied temperature difference or magnetic field strength, one can see transitions from regular to irregular long-term behavior of the system, switching between chaotic, periodic, and equilibrium asymptotic solutions. It is worth noting that owing to the induced magnetic field a transition to hyperchaotic dynamics is possible for some parameters of the model. We also reveal new features of the generalized Lorenz model, including both type I and III intermittency.
We study the competing order and chaos in a first-order quantum phase transition with a high barrier. The boson model Hamiltonian employed, interpolates between its U(5) (spherical) and SU(3) (deformed) limits. A classical analysis reveals regular (c
haotic) dynamics at low (higher) energy in the spherical region, coexisting with a robustly regular dynamics in the deformed region. A quantum analysis discloses, amidst a complicated environment, persisting regular multiplets of states associated with partial U(5) and quasi SU(3) dynamical symmetries.
We study the nature of the dynamics in a first-order quantum phase transition between spherical and prolate-deformed nuclear shapes. Classical and quantum analyses reveal a change in the system from a chaotic Henon-Heiles behavior on the spherical si
de into a pronounced regular dynamics on the deformed side. Both order and chaos persist in the coexistence region and their interplay reflects the Landau potential landscape and the impact of collective rotations.
We study the classical dynamics in a generic first-order quantum phase transition between the U(5) and SU(3) limits of the interacting boson model. The dynamics is chaotic, of Henon-Heiles type, in the spherical phase and is regular, yet sensitive to
local degeneracies, in the deformed phase. Both types of dynamics persist in the coexistence region resulting in a divided phase space.
We study the evolution of the dynamics across a generic first order quantum phase transition in an interacting boson model of nuclei. The dynamics inside the phase coexistence region exhibits a very simple pattern. A classical analysis reveals a robu
stly regular dynamics confined to the deformed region and well separated from a chaotic dynamics ascribed to the spherical region. A quantum analysis discloses regular bands of states in the deformed region, which persist to energies well above the phase-separating barrier, in the face of a complicated environment. The impact of kinetic collective rotational terms on this intricate interplay of order and chaos is investigated.
We present results of statistical analysis of solar wind turbulence using an approach based on the theory of Markov processes. It is shown that the Chapman-Kolmogorov equation is approximately satisfied for the turbulent cascade. We evaluate the firs
t two Kramers-Moyal coefficients from experimental data and show that the solution of the resulting Fokker-Planck equation agrees well with experimental probability distributions. Our results suggest the presence of a local transfer mechanism for magnetic field fluctuations in solar wind turbulence.
