Itinerant memory dynamics and global bifurcations in chaotic neural networks

We have considered itinerant memory dynamics in a chaotic neural network composed of four chaotic neurons with synaptic connections determined by two orthogonal stored patterns as a simple example of a chaotic itinerant phenomenon in dynamical associative memory. We have analyzed a mechanism of generating the itinerant memory dynamics with respect to intersection of a pair of alpha branches of periodic points and collapse of a periodic in-phase attracting set. The intersection of invariant sets is numerically verified by a novel method proposed in this paper.     

Dynamic synchronization and chaos in an associative neural network with multiple active memories

Associative memory dynamics in neural networks are generally based on attractors. Retrieval based on fixed-point attractors works if only one memory pattern is retrieved at the time, but cannot enable the simultaneous retrieval of more than one pattern. Stable phase-locking of periodic oscillations or limit cycle attractors leads to incorrect feature bindings if the simultaneously retrieved patterns share some of their features. We investigate retrieval dynamics of multiple active patterns in a network of chaotic model neurons. Several memory patterns are kept simultaneously active and separated from each other by a dynamic itinerant synchronization between neurons. Neurons representing shared features alternate their synchronization between patterns, thus multiplexing their binding relationships. Our model includes a mechanism for self-organized readout or decoding of memory pattern coherence in terms of short-term potentiation and short-term depression of synaptic weights.     

Kink Structures of Spin-Polarized Electrons due to Electron-Magnon Scattering in Ferromagnetic State

We propose a model composed of spin-polarized itinerant electrons and bosonic spin-wave excitations, and study renormalization of the spin-polarized itinerant electron bands due to electron-magnon scattering. Spin-polarized kink structures are predicted in the normal state quasiparticle dynamics of ferromagnetic superconductor as UGe2. It is suggested that the angle-resolved photoemission experiment may be helpful in this respect.     

Chaotic itinerancy based on attractors of one-dimensional maps

A general methodology is described for constructing systems that have a slowly converging Lyapunov exponent near zero, based on one-dimensional maps with chaotic attractors. In certain parameter ranges, these relatively simple systems display the properties of intermittent dynamics known as chaotic itinerancy. We show that in addition to the local sensitivity characteristic of chaotic dynamics, these itinerant systems display a global sensitivity, in the sense that fine-scale additive noise may significantly change the natural measure on the large scale.     

Spin-fermion model near the quantum critical point: one-loop renormalization group results

We consider spin and electronic properties of itinerant electron systems, described by the spin-fermion model, near the antiferromagnetic critical point. We expand in the inverse number of hot spots in the Brillouin zone, N, and present the results beyond the previously studied N = infinity limit. We found two new effects: (i) Fermi surface becomes nested at hot spots, and (ii) vertex corrections give rise to anomalous spin dynamics and change the dynamical critical exponent from z = 2 to z>2. To first order in 1/N we found z = 2N/(N-2) which for a physical N = 8 yields z approximately 2.67.     

Dual nature of electron spin resonance in YbCo2Zn20 intermetallic compound

In single crystals of YbCo₂Zn₂₀ intermetallic compound, two coexisting types of electron spin resonance signals related to the localized magnetic moments of cobalt and to itinerant electrons have been observed in the 4.2–300 K temperature range. It is shown that the relative contribution of itinerant electrons to the total magnetization does not exceed 9%. We argue that the electron dynamics in YbCo₂Zn₂₀ and YbCuAl heavy fermion systems is determined by the effects produced by the magnetic subsystem of the localized 3d-electrons. We also discuss general aspects of the electron spin resonance spectroscopy in underdoped ytterbium-based intermetallics and the spectral manifestations of the interplay between the efficiency of the hybridization of f-electrons with the electrons filling outer atomic shells, crystal field effects, and the effects related to the proximity to the quantum critical point.     

Spin superstructure and noncoplanar ordering in metallic pyrochlore magnets with degenerate orbitals

We study double-exchange models with itinerant t(2g) electrons in spinel and pyrochlore crystals. In both cases the localized spins form a network of corner-sharing tetrahedra. We show that the strong directional dependence of t(2g) orbitals leads to unusual Fermi surfaces that induce spin superstructures and noncoplanar orderings for a weak coupling between itinerant electrons and localized spins. Implications of our results to ZnV(2)O(4) and Cd(2)Os(2)O(7) are also discussed.     

How effective delays shape oscillatory dynamics in neuronal networks

Synaptic, dendritic and single-cell kinetics generate significant time delays that shape the dynamics of large networks of spiking neurons. Previous work has shown that such effective delays can be taken into account with a rate model through the addition of an explicit, fixed delay (Roxin et al. (2005,2006) [29] and [30]). Here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions. Specifically, we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the asynchronous state. In this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity. We arrive at two general observations of physiological relevance that could not be explained in previous work. These are: 1 — fast oscillations are always supercritical for realistic transfer functions and 2 — traveling waves are preferred over standing waves given plausible patterns of local connectivity. We finally demonstrate that these results show good agreement with those obtained performing numerical simulations of a network of Hodgkin-Huxley neurons.     

Zero-THz spectroscopy of rotator phases

The molecular dynamical evolution from hertzian frequencies to the far infrared (THz) is reported for various kinds of rotator phase environment. The zero to THz frequency spectral profiles are analysed in terms of itinerant libration and developments on this theme. The systems analysed are (i) the plastic rotator phase of t-butyl chloride and solid solutions of this solute in tetramethylsilane; (ii) these results are compared with those from a spectral study in the range up to THz frequencies of t-butyl chloride in vitreous decalin solvent; (iii) single crystalline pentachloronitrobenzene and a pressed disc thereof. This solid is representative of a class of rotator phases where orientational disorder is gradually frozen in at low temperatures, unlike the plastic rotators; (iv) solid solutions of dipolar solute molecules in non-dipolar rotator phase benzene and tetramethylsilane. This is an attempt at evaluating the electrodynamics of dipole-dipole interaction.

The data over the complete range of frequency is rationalized in terms of the itinerant libration mean square torque and theoretical evaluations of the observable sub-THz Debye relaxation times. This is the first attempt at modelling the molecular dynamics of the various kinds of rotator phases over the complete range of frequency at which the kinematics and electrodynamics of the constituent molecules are observable, either as the complex dielectric permittivity or the optical power absorption coefficient. This methodology is named zero-THz spectroscopy. Used properly, it is one of the most incisive methods available for studies of molecular dynamics.     

Theory of valence mixing for rare-earth compounds

A theory for the mixed valence state of rare-earth compounds is presented. It includes the following features: (1) two types of electronic states-localized, highly correlated states and itinerant, non-correlated states; (2) a very strong Coulomb repulsion between localized states in the same site; (3) a Coulomb interaction between localized and itinerant states which drives the phase transition; and (4) hybridization between localized and itinerant states which produces the mixed valence state. It is shown that this model produces (a) at T = 0, a variation in the number of localized electrons which may vary in a smooth or in a discontinuous fashion as a function of pressure or alloying; (b) transitions at finite temperature which terminate in a classical critical point. Qualitative agreement with experiment is an encouraging feature of the model.     

Some applications of polarized inelastic neutron scattering in magnetism

A brief account of applications of polarized inelastic neutron scattering in condensed matter research is given. We show that full polarization analysis is the only tool allowing to discriminate unambiguously between different magnetic modes in various magnetic materials. We show by means of recent results in the Heisenberg ferromagnet EuS that the effects of dipolar interactions can be studied on a microscopic scale. Moreover, we have found for the first time indications for the divergence of the longitudinal fluctuations belowT _c. In the itinerant antiferromagnet chromium we demonstrate that the dynamics of the longitudinal and transverse excitations are very different, resolving a long standing puzzle concerning the slope of their dispersion. Finally, we show that a measurement of the polarization-dependent part of the cross section of non-centrosymmetric MnSi proves directly that the chirality of the magnetic fluctuations is left-handed.     

Superpositional Quantum Network Topologies

We introduce superposition-based quantum networks composed of (i) the classical perceptron model of multilayered, feedforward neural networks and (ii) the algebraic model of evolving reticular quantum structures as described in quantum gravity. The main feature of this model is moving from particular neural topologies to a quantum metastructure which embodies many differing topological patterns. Using quantum parallelism, training is possible on superpositions of different network topologies. As a result, not only classical transition functions, but also topology becomes a subject of training. The main feature of our model is that particular neural networks, with different topologies, are quantum states. We consider high-dimensionaldissipative quantum structures as candidates for implementation of the model.     

On the constructive role of noise in stabilizing itinerant trajectories in chaotic dynamical systems

This work aims at studying dynamical models of neural networks, which exhibit phase transitions between states of various complexities. We use the biologically motivated KIII model, which has demonstrated excellent performance as a robust dynamical memory device. KIII is a high-dimensional dynamical system with extremely fragmented boundaries between limit cycles, tori, fixed points, and chaotic attractors. We study the role of additive noise in the development of itinerant trajectories. Noise not only stabilizes aperiodic trajectories, but there is an optimum noise level with highly itinerant behavior. We speculate that the previously found optimum classification performance of KIII as a function of the noise level, also identified as chaotic resonance, is related to chaotic itinerant oscillations among various ordered states.     

A density matrix approach to the dynamical properties of a two-site Holstein model

The two-site Holstein model represents a first non-trivial paradigm for the interaction between an itinerant charge with a quantum oscillator, a very common topic in different ambits. Exact results can be achieved both analytically and numerically, nevertheless it can be useful to compare them with approximate, semi-classical techniques in order to highlight the role of quantum effects. In this paper we consider the adiabatic limit in which the oscillator is slower than the electron. A density matrix approach is introduced for studying the charge dynamics and the exact results are compared with two different approximations: a Born-Oppenheimer-based Static Approximation for the oscillator (SA) and a Quantum-classical (QC) dynamics.     

Chaotic itinerancy

Chaotic itinerancy is universal dynamics in high-dimensional dynamical systems, showing itinerant motion among varieties of low-dimensional ordered states through high-dimensional chaos. Discovery, basic features, characterization, examples, and significance of chaotic itinerancy are surveyed.     

Research on the origin of magneto-crystalline anisotropy in R2Fe14B compounds

A model for the calculation of the magneto-crystalline anisotropy in R₂Fe₁₄B (R is a rare earth) compounds is presented. According to the model, a combined effect on the R-ion, coming from both the crystal field of ligands and the electric field of itinerant electrons, results in the anisotropy of the compounds. An approach of calculating the interaction between the itinerant electrons and the central R-ion is given. Taking account of the combined effect, we calculated the temperature dependences of the anisotropy of all the five R₂Fe₁₄B-type (R = Pr, Nd, Tb, Dy and Ho) compounds with uniaxial anisotropy. The results are in good agreement with the experiments. The calculation has shown that the effect of the itinerant electrons plays an important role for the anisotropy of the compounds.     

Frustration-induced insulating chiral spin state in itinerant triangular-lattice magnets

We study the double-exchange model at half-filling with competing superexchange interactions on a triangular lattice, combining exact diagonalization and Monte?Carlo methods. We find that in between the expected itinerant ferromagnetic and 120° Yafet-Kittel phases a robust scalar-chiral, insulating spin state emerges. At finite temperatures the ferromagnet-scalar-chiral quantum critical point is characterized by anomalous bad-metal behavior in charge transport as observed in frustrated itinerant magnets R2Mo2O7.     

Non-gaussian velocity correlations in fluids

Several molecular dynamics experiments in monoatomic fluids indicate that the velocity v of a tagged particle has a clear non-Gaussian behaviour: here we present typical simulation data obtained for <v ²(0)v ²(t)>. We have previously found that at long times these non-Gaussian features can be explained in terms of a non-linear Langevin equation developed by Mori, Fujisaka and Shigematsu. Here we show that the latter approach can be the long-time version of the reduced model known as the non-linear itinerant oscillator. In principle, such a model can also reproduce the non-Gaussian behaviour at short times, as found in the simulations and confirmed by the proper sum rules. The reduced model is numerically solved in a particular one-dimensional overdamped case and the main features present in the computer experiment are found to be qualitatively reproduced.     

Quantum critical behavior of the cluster glass phase

In disordered itinerant magnets with arbitrary symmetry of the order parameter, the conventional quantum critical point between the ordered phase and the paramagnetic Fermi liquid (PMFL) is destroyed due to the formation of an intervening cluster glass (CG) phase. In this Letter, we discuss the quantum critical behavior at the CG-PMFL transition for systems with continuous symmetry. We show that fluctuations due to quantum Griffiths anomalies induce a first-order transition from the PMFL at T = 0, while at higher temperatures a conventional continuous transition is restored. This behavior is a generic consequence of enhanced non-Ohmic dissipation caused by a broad distribution of energy scales within any quantum Griffiths phase in itinerant systems.     

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.