Quasi-stationary chaotic states in multi-dimensional Hamiltonian systems

We study numerically statistical distributions of sums of chaotic orbit coordinates, viewed as independent random variables, in weakly chaotic regimes of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam (FPU-β) oscillator chains with different boundary conditions and numbers of particles and a microplasma of identical ions confined in a Penning trap and repelled by mutual Coulomb interactions. For the FPU systems we show that, when chaos is limited within “small size” phase space regions, statistical distributions of sums of chaotic variables are well approximated for surprisingly long times (typically up to t≈10⁶) by a q-Gaussian (1<q<3) distribution and tend to a Gaussian (q=1) for longer times, as the orbits eventually enter into “large size” chaotic domains. However, in agreement with other studies, we find in certain cases that the q-Gaussian is not the only possible distribution that can fit the data, as our sums may be better approximated by a different so-called “crossover” function attributed to finite-size effects. In the case of the microplasma Hamiltonian, we make use of these q-Gaussian distributions to identify two energy regimes of “weak chaos”—one where the system melts and one where it transforms from liquid to a gas state-by observing where the q-index of the distribution increases significantly above the q=1 value of strong chaos.     

Angle-resolved photoemission spectroscopy of band tails and anomalous kinetics of underdoped cuprates

The electron-phonon interaction in cuprates with c-axis polarised optical phonons, which is roughly one order of magnitude stronger than superexchange, bounds holes into mobile bipolarons. Bipolarons pin the chemical potential within the charge-transfer gap of doped Mott insulators, accounting for unusual kinetics and thermodynamics of doped cuprates such as the Nernst and giant proximity effects, pseudo-gaps, and normal-state diamagnetism. We propose that “quasi-particle” peaks, “Fermi-arcs”, and high-energy “waterfalls” in the photoemission spectra of cuprates originate from the photo-ionization matrix elements of disorder-localised band-tails in the charge-transfer gap.     

Tsallis’ statistics in the variability of El Niño/Southern Oscillation during the Holocene epoch

Analysis of the Tsallis q-triplet for the variability of El Niño Southern Oscillation (ENSO) index during the Holocene epoch (last 11,000 years) is presented. Three periods are analyzed, 0-7000, 7000-9700, 9700-11,000 years before the present. During the first and the third periods, the q-index values have the expected usual relations between them (q_sens<1<q_stat<q_rel), and in the second one there is an inversion between q_stat and q_rel (q_stat>q_rel).     

Spin-charge gauge compositeness of electron in HTS: Hints from metal-insulator crossover and entropy behavior

We show that the coexistence of Fermi arcs and metal-insulator crossover of the in-plane resistivity can give a hint of a peculiar “gauge compositeness” of the electron in hole-doped high T_c cuprates and a similar hint also comes from the negative intercept at T=0 of the electronic entropy extrapolated from moderate temperatures in the “pseudogap phase”. An implementation of this “compositeness” within the spin-charge gauge approach is outlined and is employed to discuss the above phenomena.     

Energy-scale phenomenology and pairing via resonant spin-charge motion in FeAs, CuO, heavy-fermion and other exotic superconductors

Muon spin relaxation (μSR) studies of the “1111” and “122” FeAs systems have detected static magnetism with variably sized ordered moments in their parent compounds. The phase diagrams of FeAs, CuO, organic BEDT, A₃C₆₀ and heavy-fermion systems indicate competition between static magnetism and superconductivity, associated with first-order phase transitions at quantum phase boundaries. In both FeAs and CuO systems, the superfluid density n_s/m^* at T→0 exhibits a nearly linear scaling with T_c. Analogous to the roton-minimum energy scaling with the lambda transition temperature in superfluid ⁴He, clear scaling with T_c was also found for the energy of the magnetic resonance mode in cuprates, (Ba,K)Fe₂As₂, CeCoIn₅ and CeCu₂Si₂, as well as the energy of the superconducting coherence peak observed by angle resolved photo emission (ARPES) in the cuprates near (π,0). Both the superfluid density and the energy of these pair-non-breaking soft-mode excitations determine the superconducting T_c via phase fluctuations of condensed bosons. Combining these observations and common dispersion relations of spin and charge collective excitations in the cuprates, we propose a resonant spin-charge motion/coupling, “traffic-light resonance,” expected when the charge energy scale ε_F becomes comparable to the spin fluctuation energy scale ?ω_SF~J, as the process which leads to pair formation in these correlated electron superconductors.     

Transport of waves in disordered waveguides: A potential model

We study the statistical properties of wave transport in a disordered waveguide. We first derive the properties of a “building block” (BB) of length δL starting from a potential model consisting of thin potential slices. We then find a diffusion equation—in the space of transfer matrices that describe our system—which governs the evolution with the length L of the disordered waveguide of the transport properties of interest. The latter depend only on the mean free paths and on no other property of the slice distribution. The universality that arises demonstrates the existence of a generalized central-limit theorem. We have developed a numerical simulation in which the universal statistical properties of the BB found analytically are first implemented numerically, and then the various BBs are combined to construct the full waveguide. The reported results thus obtained are in good agreement with microscopic calculations, for both bulk and surface disorder.     

Nonlinear statistical coupling

By considering a nonlinear combination of the probabilities of a system, a physical interpretation of Tsallis statistics as representing the nonlinear coupling or decoupling of statistical states is proposed. The escort probability is interpreted as the coupled probability, with Q=1−q defined as the degree of nonlinear coupling between the statistical states. Positive values of Q have coupled statistical states, a larger entropy metric, and a maximum coupled-entropy distribution of compact-support coupled-Gaussians. Negative values of Q have decoupled statistical states and for −2<Q<0 a maximum coupled-entropy distribution of heavy-tail coupled-Gaussians. The conjugate transformation between the heavy-tail and compact-support domains is shown to be for coupled-Gaussian distributions. This conjugate relationship has been used to extend the generalized Fourier transform to the compact-support domain and to define a scale-invariant correlation structure with heavy-tail limit distribution. In the present paper, we show that the conjugate is a mapping between the source of nonlinearity in non-stationary stochastic processes and the nonlinear coupling which defines the coupled-Gaussian limit distribution. The effects of additive and multiplicative noise are shown to be separable into the coupled-variance and the coupling parameter Q, providing further evidence of the importance of the generalized moments.     

Effective action for strongly correlated electron systems

The su(2|1) coherent-state path-integral representation of the partition function of the t-J model of strongly correlated electrons is derived at finite doping. The emergent effective action is compared to the one proposed earlier on phenomenological grounds by Shankar to describe holes in an antiferromagnet [R. Shankar, Nucl. Phys. B 330 (1990) 433]. The t-J model effective action is found to have an important “extra” factor with no analogue in Shankar?s action. It represents the local constraint of no double electron occupancy and reflects the rearrangement of the underlying phase-space manifold due to the presence of strong electron correlation. This important ingredient is shown to be essential to describe the physics of strongly correlated electron systems.     

Variability of scaling parameters in non-conservative systems: Geophysical aspect

Newly obtained data on the critical dynamics of the drifting/fracturing sea ice in the Arctic Ocean were analyzed and compared with published data on the dynamic processes in the Earth’s crust. Substantial similarities were found in the scaling behavior of both geophysical systems; the most important of them is the b-value space/time variability including a pre-failure drop of this parameter. The b-value pattern of the ensemble of drifting ice floes is an analogue of the b-value distribution over areas and depths in tectonic structures. A common feature of the pre-failure state in the cryosphere and in the Earth’s crust is the increased degree of the energy conservation that manifests itself both in the sea ice consolidation prior to basin-wide ice pack fragmentations, and in involving harder geological formations in the fracture process before earthquakes, respectively. From the viewpoint of the conservative SOC concept, this relation between the system’s conservativity and the occurrence of large-scale fracture events means that the expected scale level of failure is determined by the system’s closeness to “true” SOC behavior.     

Properties of the Ising magnet confined in a corner geometry

The properties of Ising square lattices with nearest neighbor ferromagnetic exchange confined in a corner geometry, are studied by means of Monte Carlo simulations. Free boundary conditions at which boundary magnetic fields ±h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field −h acts. For temperatures T less than the critical temperature T_c of the bulk, this boundary condition leads to the formation of two domains with opposite orientation of the magnetization direction, separated by an interface which for T larger than the filling transition temperature T_f(h) runs from the upper left corner to the lower right corner, while for T<T_f(h) this interface is localized either close to the lower left corner or close to the upper right corner. It is shown that for T=T_f(h) the magnetization profile m(z) in the z-direction normal to the interface simply is linear and the interfacial width scales as w∝L, while for T>T_f(h) it scales as . The distribution P(?) of the interface position ? (measured along the z-direction from the corners) decays exponentially for T<T_f(h) from either corner, is essentially flat for T=T_f(h), and is a Gaussian centered at the middle of the diagonal for T>T_f(h). Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.     

Understanding the time dependence of atomic level populations in evolving plasmas

The time dependence of atomic level populations in evolving plasmas is studied using an eigenfunction expansion of the non-LTE rate equations. The work aims to develop understanding without the need for, and as an aid to, numerical solutions. The discussion is mostly limited to linear systems, especially those for optically thin plasmas, but the implicitly non-linear case of non-LTE radiative transfer is briefly discussed. Eigenvalue spectra for typical atomic systems are examined using results compiled by Hearon. Diagonal dominance and sign symmetry of rate matrices show that just one eigenvalue is zero (corresponding to the equilibrium state), that the remaining eigenvalues have negative real parts, and that oscillations, if any, are necessarily damped. Gershgorin's theorems are used to show that many eigenvalues are determined by the radiative lifetimes of certain levels, because of diagonal dominance. With other properties, this demonstrates the existence of both “slow” and “fast” time-scales, where the “slow” evolution is controlled by properties of meta-stable levels. It is shown that, when collisions are present, Rydberg states contribute only “fast” eigenvalues. This justifies use of the quasi-static approximation, in which atoms containing just meta-stable levels can suffice to determine the atomic evolution on time-scales long compared with typical radiative lifetimes. Analytic solutions for two- and three-level atoms are used to examine the basis of earlier intuitive ideas, such as the “ionizing plasma” approximation. The power and limitations of Gershgorin's theorems are examined through examples taken from the solar atmosphere. The methods should help in the planning and interpretation of both experimental and numerical experiments in which atomic evolution is important. While the examples are astrophysical, the methods and results are applicable to plasmas in general.     

Proving AGT conjecture as HS duality: Extension to five dimensions

We extend the proof from Mironov et al. (2011) [25], which interprets the AGT relation as the Hubbard-Stratonovich duality relation to the case of 5d gauge theories. This involves an additional q-deformation. Not surprisingly, the extension turns out to be straightforward: it is enough to substitute all relevant numbers by q-numbers in all the formulas, Dotsenko-Fateev integrals by the Jackson sums and the Jack polynomials by the MacDonald ones. The problem with extra poles in individual Nekrasov functions continues to exist, therefore, such a proof works only for β=1, i.e. for q=t in MacDonald?s notation. For β≠1 the conformal blocks are related in this way to a non-Nekrasov decomposition of the LMNS partition function into a double sum over Young diagrams.     

Information theoretic description of networks

We present a new information theoretic approach for network characterizations. It is developed to describe the general type of networks with n nodes and L directed and weighted links, i.e., it also works for the simpler undirected and unweighted networks. The new information theoretic measures for network characterizations are based on a transmitter-receiver analogy of effluxes and influxes. Based on these measures, we classify networks as either complex or non-complex and as either democracy or dictatorship networks. Directed networks, in particular, are furthermore classified as either information spreading and information collecting networks.The complexity classification is based on the information theoretic network complexity measure medium articulation (MA). It is proven that special networks with a medium number of links (L∼n^1.5) show the theoretical maximum complexity . A network is complex if its MA is larger than the average MA of appropriately randomized networks: MA>MA_r. A network is of the democracy type if its redundancy R<R_r, otherwise it is a dictatorship network. In democracy networks all nodes are, on average, of similar importance, whereas in dictatorship networks some nodes play distinguished roles in network functioning. In other words, democracy networks are characterized by cycling of information (or mass, or energy), while in dictatorship networks there is a straight through-flow from sources to sinks. The classification of directed networks into information spreading and information collecting networks is based on the conditional entropies of the considered networks (H(A/B)=uncertainty of sender node if receiver node is known, H(B/A)=uncertainty of receiver node if sender node is known): if H(A/B)>H(B/A), it is an information collecting network, otherwise an information spreading network.Finally, different real networks (directed and undirected, weighted and unweighted) are classified according to our general scheme.     

Structural modifications of diamond like carbon films induced by MeV nitrogen ion irradiation

Diamond-like carbon (DLC) films were deposited on Si(1 0 0) substrates using plasma deposition technique. The deposited films were irradiated using 2 MeV N⁺ ions at fluences of 1×10¹⁴, 1×10¹⁵ and 5×10¹⁵ ions/cm². Samples have been characterized by using Raman spectroscopy, X-ray photoelectron spectroscopy (XPS) and high-resolution transmission electron microscopy (HRTEM). Analysis of Raman spectra shows a gradual shift of both D and G band peaks towards higher frequencies along with an increase of the intensity ratio, I(D)/I(G), with increasing ion fluence in irradiation. These results are consistent with an increase of sp² bonding. XPS results also show a monotonic increase of sp²/sp³ hybridization ratio with increasing ion fluence. Plan view TEM images show the formation of clusters in the irradiated DLC films. HRTEM micrographs from the samples irradiated at a fluence of 5×10¹⁵ ions/cm² show the lattice image with an average interplanar spacing of 0.34 nm, revealing that the clusters are graphite clusters. The crystallographic planes in these clusters are somewhat distorted compared to the perfect graphite structure.     

Frequency-dependent linear and non-linear response properties of single carrier quantum dots: Role of effective mass and anharmonicity in the confinement potential

We explore the pattern of frequency-dependent linear and non-linear optical (NLO) response of one electron quantum dots harmonically confined in two dimensions. For some fixed values of transverse magnetic field strength (ω_c), and harmonic confinement potential (ω₀), the influence of effective mass (m^*) of the system and the symmetry breaking anharmonic interaction on the frequency-dependent linear (α), and the first (β), and second (γ) NLO responses of the dot is computed through linear variational route. The investigation reveals interesting roles played by the anharmonic interaction and effective mass in modulating the response properties.     

Tsallis, Rényi and nonextensive Gaussian entropy derived from the respective multinomial coefficients

We explore the generalization of the ordinary multinomial coefficient, based on the deformed q-multiplication and q-division. Aim of this study is to construct the appropriate multinomial coefficients, from which one can obtain the Tsallis, Rényi and nonextensive Gaussian entropy, respectively. We show that for all three above entropies there are two possible ways to define the generalized multinomial coefficient. Its consequence is discussed.     

Modeling cascading failures in congested complex networks

Cascading failures occur commonly in congested complex networks, where it may be expressed as the process of generation, diffusion and dissipation of congestion. Different from betweeness centrality, we introduce congestion effects to determine the load on the node. In terms of user equilibrium condition, congestion effects can be described by cost functions or link performance functions, which map link flows to travel times. By introducing conceptual “practical capacity” dynamics to cost functions, cascading failures are well discussed in terms of the degree of congestion in complex networks. Moreover, the efficiency dynamics of the network due to cascading failures is also investigated, and a transition phenomenon is uncovered independent of clustering effect.     

Variational treatment of Faraday waves in inhomogeneous Bose-Einstein condensates

Motivated by the recent experimental progress on the collective modes of a Bose-Einstein condensate whose atomic scattering length is tuned via Feshbach resonances, we analyze by variational means the dynamics of Faraday waves in trapped Bose-Einstein condensates. These waves can be excited by modulating periodically either the strength of the magnetic trap or the atomic scattering length. To study their dynamics, we develop a variational model that describes consistently both the bulk part of an inhomogeneous, low-density, cigar-shaped condensate and small-amplitude, small-wavelength Faraday waves. The main ansatz used in the variational treatment is tailored around a set of Gaussian envelopes and we show extensions for the high-density regime using a q-Gaussian function. Finally, we show explicitly that for drives of small amplitude, the two methods of obtaining Faraday waves are equivalent, and we discuss the existing experimental results.     

Neutrino mass and unification

I discuss the implications of the observed masses and mixings of neutrinos for unification beyond the standard model and point out the important role that ongoing searches for the remaining mixing angle θ₁₃, neutrinoless double beta decay as well as possible searches for a Z^′ at LHC can play in this discussion.