Clustered chimera states in delay-coupled oscillator systems

We investigate chimera states in a ring of identical phase oscillators coupled in a time-delayed and spatially nonlocal fashion. We find novel clustered chimera states that have spatially distributed phase coherence separated by incoherence with adjacent coherent regions in antiphase. The existence of such time-delay induced phase clustering is further supported through solutions of a generalized functional self-consistency equation of the mean field. Our results highlight an additional mechanism for cluster formation that may find wider practical applications.     

Solvable model for chimera states of coupled oscillators

Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.     

The dynamics of chimera states in heterogeneous Kuramoto networks

We study a variety of mixed synchronous/incoherent (“chimera”) states in several heterogeneous networks of coupled phase oscillators. For each network, the recently-discovered Ott-Antonsen ansatz is used to reduce the number of variables in the partial differential equation (PDE) governing the evolution of the probability density function by one, resulting in a time-evolution PDE for a variable with as many spatial dimensions as the network. Bifurcation analysis is performed on the steady states of these PDEs. The results emphasise the commonality of the dynamics of the different networks, and provide stability information that was previously inferred.     

The emergence of chimera states in a network of nephrons

The kidney plays an essential role in our body, mainly by controlling secretion and reabsorption of water and salts. The kidneys consist of a large number of nephrons which are the functional units of the kidney. The interactions between these nephrons induce different behaviors which can be considered by a dynamical model. In this paper, a network of coupled nephron models and its dynamics is investigated. Numerical simulations of the network reveal various types of dynamical patterns depending on the coupling function and strength. One of the observed phenomenon is the emergence of chimera state. A chimera state is defined by the coexistence of coherent and incoherent groups in a network of identical oscillators. The occurrence of the chimera state can be related to the situation of disturbed synchronous oscillation of the TGF-mediated proximal pressure.     

Spectral and luminescent properties of some porphyrin compounds in different electronic states

The spectral and luminescent properties of some derivatives of tetraphenylporphyrin are studied at different concentrations of these compounds; the spectra of neutral and ionic forms are interpreted; and the quantum yields of ordinary and, in some cases, short-wavelength fluorescence from highly excited states are determined. The spectra of transient absorption from excited states, existing in the time range of tens of nanoseconds, are measured, and the quantum yields of formation of triplet molecules are estimated. Hypotheses regarding the mechanism of phototransformations of some porphyrins in chloroform are put forth.     

Spectral and thermodynamic properties of electrons in mobility gap states of covalent glasses

Spectral and thermodynamic properties of electrons (holes) in covalent semiconducting glasses are considered in which self-trapping of electron (hole) pairs is realized with negative effective correlation energy U^?. Unlike the Anderson model, electron (hole) pairing is restricted to a small part of the glass bonds. Ranges of the U^? values are found in which either pair effects (suppression of paramagnetism etc.) or single-particle effects predominate; the concentration of the pair states and of the occupied ones can roughly be estimated and can be fairly high. The problem of the coexistence of the Fermi level pinning and effective diamagnetism in glasses is discussed. Some related effects are briefly considered.     

Spectral functions and hole nuclear states

An explicit expression for the spectral function of hole nuclear states is given in the framework of the coherent fluctuation model. It is shown that the spectral function and single-particle width, centroid energy, quasiparticle effective mass, etc., are functionals of the ground-state nucleon density distribution. Calculation of the spectral functions for⁵⁸Ni,⁴⁰Ca,²⁸Si is carried out and the results are compared with the experimental data.     

Spectral singularities and zero energy bound states

Single particle scattering around zero energy is re-analysed in view of recent experiments with ultra-cold atoms, nano-structures and nuclei far from the stability valley. For non-zero orbital angular momentum the low energy scattering cross section exhibits dramatic changes depending on the occurrence of either a near resonance or a bound state or the situation in between, that is a bound state at zero energy. Such state is singular in that it has an infinite scattering length, behaves for the eigenvalues but not for the eigenfunctions as an exceptional point and has no pole in the scattering function. These results should be observable whenever the interaction or scattering length can be controlled.     

Synchronization patterns and chimera states in complex networks: Interplay of topology and dynamics

We review chimera patterns, which consist of coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics in networks of identical oscillators. We focus on chimera states involving amplitude as well as phase dynamics, complex topologies like small-world or hierarchical (fractal), noise, and delay. We show that a plethora of novel chimera patterns arise if one goes beyond the Kuramoto phase oscillator model. For the FitzHugh-Nagumo system, the Van der Pol oscillator, and the Stuart-Landau oscillator with symmetry-breaking coupling various multi-chimera patterns including amplitude chimeras and chimera death occur. To test the robustness of chimera patterns with respect to changes in the structure of the network, regular rings with coupling range R, small-world, and fractal topologies are studied. We also address the robustness of amplitude chimera states in the presence of noise. If delay is added, the lifetime of transient chimeras can be drastically increased.     

Spectral properties of superfluorescent pulses

We present a spectral analysis of the early stage of superfluorescent pulses. For systems with a Fresnel number near unity and a length long compared to the wavelength of the emitted radiation we find no perceptible frequency shifts or chips.     

Spectral states and state preference of galactic X-ray binaries

Using observations in the past four years with the All Sky Monitor (ASM) onboard the Rossi X-ray Timing Explorer (RXTE) and the Burst Alert Telescope (BAT) onboard the Swift, we demonstrate that the hard state and the soft state are the primary spectral states in galactic black hole and neutron star X-ray binaries. In addition, we show quantitatively the preference of the two spectral states for each of the 22 bright persistent sources.

     

Spectral properties of dye lasers

Starting from conventional rate equations describing the multimode operation of a laser with a broad homogeneous emission line, a system of approximately valid equations, suitable for both analytical and numerical studies of the spectral properties of laser radiation not too far from threshold, has been derived by introducing equations of motion for the spatial Fourier components of the inversion densityN(z, t), thus replacing the equation of motion forN(z, t) itself. Analytical solutions for steady-state operation were found and physically discussed in the following cases: (a) ring laser, (b) jet-stream laser with the active medium positioned either near one of the (Fabry-Perot) resonator mirrors or in the centre of the resonator, and (c) laser with a Fabry-Perot resonator completely filled with the active medium. The spectra thus calculated indicate that spatial hole burning is most efficient in providing mode co-existence in configuration (c), where it gives rise to a significant bandwidth. It is of minor importance, however, in case (b), where the spectrum differs only slightly from that of a ring laser, which is clearly free from hole-burning effects.     

Spectral properties of helical quantum wires

The spectrum of states of a helical quantum wire has been investigated theoretically. Eigenstates were found using an exact method based on alternating-direction implicit (ADI) evolution in imaginary time, for a wavefunction defined at discrete points in occupation number space and a nearest-neighbor interaction. A helical wire is a special case of a one-dimensional superlattice with an infinitesimal glide symmetry and associated glide-momentum quantum number. The continuous symmetry prevents the appearance of band gaps. Energy eigenstates have unquenched angular momentum--angular momentum increases with glide momentum. Band anharmonicity and angular momentum nonlinearity demonstrate effects of centrifugal acceleration.     

Nonclassical properties of coherent states

It is demonstrated that a weak measurement of the squared quadrature observable may yield negative values for coherent states. This result cannot be reproduced by a classical theory where quadratures are stochastic c-numbers. The nonclassicality of coherent states can be associated with negative values of the Terletsky–Margenau–Hill distribution.     

Statistical properties of polariton states

Summary The unitary transformation that relates free polarization and photon states to polariton states is constructed. The time evolution of an arbitrary initial state in terms of the polariton Hamiltonian is presented. The many-photon components of polariton states as well as the transition probabilities to polariton states and the intrinsec and time-dependent polariton squeezing are discussed.     

Stability properties of equilibrium states

The significance of stability of an equilibrium state under local perturbations of the dynamics (as defined in [1]) and the different degree of stability with respect to extended perturbations of states at phase transition points are discussed. The general conclusions are tested and illustrated in the example of the free Bose gas. A more transparent proof of the relation between local stability and the Kubo-Martin-Schwinger relation is given.