Table of contents

We obtain the harmonic measure of diffusion-limited aggregate (DLA) clusters using a biased random-walk sampling technique which allows us to measure probabilities of random walkers hitting sections of clusters with unprecedented accuracy; our results include probabilities as small as 10^{- 80}. We find the multifractal D(q) spectrum including regions of small and negative q. Our algorithm allows us to obtain the harmonic measure for clusters more than an order of magnitude larger than those achieved using the method of iterative conformal maps, which is the previous best method. We find a phase transition in the singularity spectrum f(α) at α≈14 and also find a minimum q of D(q), q_min=0.9±0.05.

We consider a quantum quench in a system of free bosons, starting from a thermal initial state. As in the case where the system is initially in the ground state, any finite subsystem eventually reaches a stationary thermal state with a momentum-dependent effective temperature. We find that this can, in some cases, even be lower than the initial temperature. We also study lattice effects and discuss more general types of quenches.

We investigate the slow time scales that arise from aging of the paths during the process of path aggregation. This is studied using Monte Carlo simulations of a model aiming to describe the formation of fascicles of axons mediated by contact axon-axon interactions. The growing axons are represented as interacting directed random walks in two spatial dimensions. To mimic axonal turnover, random walkers are injected and whole paths of individual walkers are removed at specified rates. We identify several distinct time scales that emerge from the system dynamics and can exceed the average axonal lifetime by orders of magnitude. In the dynamical steady state, the position-dependent distribution of fascicle sizes obeys a scaling law. We discuss our findings in terms of an analytically tractable, effective model of fascicle dynamics.

The phenomenon of dynamical localization of matter wave solitons in optical lattices is first demonstrated and the conditions for its existence are discussed. In addition to the trapping linear periodic potential we use a periodic modulation of the nonlinearity in space to eliminate nonexistence regions of gap-solitons in reciprocal space. We show that when this condition is achieved, the observation of dynamical localization in true nonlinear regime becomes possible. The results apply to all systems described by the periodic nonlinear Schrödinger equation, including Bose-Einstein condensates of ultracold atoms trapped in optical lattices and arrays of waveguides or photonic crystals in nonlinear optics.

In this paper, we present the first experimental demonstration on continuous variable quantum key distribution using determinant Einstein-Podolsky-Rosen entangled states of optical field. By means of the instantaneous measurements of the quantum fluctuations of optical modes, respectively, distributed at sender and receiver, the random bits of secret key are obtained without the need for signal modulation. The post-selection boundaries for the presented entanglement-based scheme against both Gaussian collective and individual attacks are theoretically concluded. The final secret key rates of 84 kbits/s and 3 kbits/s are completed under the collective attack for the transmission efficiency of 80% and 40%, respectively.

Recently, several schemes for the experimental creation of Dicke states were described. In this paper, we show that all the n-qubit symmetric Dicke states with l (2⩽l⩽(n- 2)) excitations are inequivalent to the |GHZ⟩ state or the |W⟩ state under SLOCC, that the even n-qubit symmetric Dicke state with n/2 excitations is inequivalent to any even n-qubit symmetric Dicke state with l≠n/2 excitations under SLOCC, and that all the n-qubit symmetric Dicke states with l (2⩽l⩽(n- 2)) excitations satisfy Coffman, Kundu and Wootters' generalized monogamy inequality C₁₂²+...+C_1n²<C_1(2...n)²<1.

This work deals with a new family of models, which includes the sine-Gordon model and the double-sine-Gordon, triple-sine-Gordon and so on. The investigation is based on a deformation procedure, which is used to deform a well-known model, to get to the family of sine-Gordon models. Due to properties of the procedure, we get to the models and find the corresponding solutions explicitly, together with all the important features they engender.

We investigate the use of ground-based gravitational-wave interferometers for studies of the strong-field domain of QED. Interferometric measurements of phase velocity shifts induced by quantum fluctuations in magnetic fields can become a sensitive probe for nonlinear self-interactions among macroscopic electromagnetic fields. We identify pulsed magnets as a suitable strong-field source, since their pulse frequency can be matched perfectly with the domain of highest sensitivity of gravitational-wave interferometers. If these interferometers reach their future sensitivity goals, not only strong-field QED phenomena can be discovered but also further parameter space of hypothetical hidden-sector particles will be accessible.

We study ultracold atoms trapped in a one-dimensional optical lattice prepared in a Mott insulator state of finite extend and collectively coupled to a single cavity mode. Due to resonant dipole-dipole interactions among the atoms, electronic excitations get delocalized and form excitons. These excitons can be explicitly calculated and divided into two groups: antisymmetric modes which decouple from the cavity mode called dark excitons, and symmetric modes coupled to the cavity mode called bright excitons. In a typical geometry the most uniform exciton is coupled to the cavity photons much stronger than other symmetric bright states and dominates the optical response of the atoms (superradiant state). In the strong coupling regime this superradiant state mixes with a cavity photon to form a doublet of polariton states, and the other excitons play only a minor role in the dynamics. We analytically calculate the corresponding collective Rabi splitting including the nearest-neighbor dipole-dipole induced excitonic shifts, which strongly depend on the polarization of the cavity mode with respect to the lattice orientation.

Networks of elastic beams can deform either by stretching or bending of their members. The primary mode of deformation (bending or stretching) crucially depends on the specific details of the network architecture. In order to shed light on the relationship between microscopic geometry and macroscopic mechanics, we characterize the structural features of networks which deform uniformly, through the stretching of the beams only. We provide a convenient set of geometrical criteria to identify such networks, and derive the values of their effective elastic moduli. The analysis of these criteria elucidates the variability of mechanical response of elastic networks. In particular, our study rationalizes the difference in mechanical behavior of cellular and fiber networks.

We present an experimental study of the outflow of a hopper continuously vibrated by a piezoelectric device. Outpouring of grains can be achieved for apertures much below the usual jamming limit observed for non-vibrated hoppers. Granular flow persists down to the physical limit of one grain diameter, a limit reached for a finite vibration amplitude. For the smaller orifices, we observe an intermittent regime characterized by alternated periods of flow and blockage. Vibrations do not significantly modify the flow rates both in the continuous and the intermittent regime. The analysis of the statistical features of the flowing regime shows that the flow time significantly increases with the vibration amplitude. However, at low vibration amplitude and small orifice sizes, the jamming time distribution displays an anomalous statistics.

By using the technique of the attenuated total reflection, the complex second hyperpolarizability for the quadratic electro-optic effect of a linear conjugated polymer is determined at the wavelength of the absorption edge by employing the data measured from different guided wave resonance dips. The values and the signs of the real and imaginary parts of the second hyperpolarizability are simultaneously obtained without employing the Kramers-Kronig transformation.

Properties of cylindrical and spherical dust-ion-acoustic (DIA) shock waves in an unmagnetized dusty plasma are investigated. We use the hydrodynamic equations for inertial ions, a Boltzmann law for the electron density distribution, and the fluctuation of charges on immobile dust grains, to derive the modified Burgers equation. The latter, which contains a dissipative term arising from the dust charge fluctuation, governs the dynamics of cylindrical and spherical DIA shocks. Numerical solutions of the modified Burgers equation are presented. It is found that properties of the cylindrical and spherical DIA shock waves significantly differ from those of one-dimensional planar shock.

We study the vibrational modes of three-dimensional jammed packings of soft ellipsoids of revolution as a function of particle aspect ratio ε and packing fraction. At the jamming transition for ellipsoids, as distinct from the idealized case using spheres where ε=1, there are many unconstrained and nontrivial rotational degrees of freedom. These constitute a set of zero-frequency modes that are gradually mobilized into a new rotational band as |ε-1| increases. Quite surprisingly, as this new band is separated from zero frequency by a gap, and lies below the onset frequency for translational vibrations, ω^*, the presence of these new degrees of freedom leaves unaltered the basic scenario that the translational spectrum is determined only by the average contact number. Indeed, ω^* depends solely on coordination as it does for compressed packings of spheres. We also discuss the regime of large |ε-1|, where the two bands merge.

Energy dissipation via spin excitations is investigated for a hard ferromagnetic tip scanning a soft magnetic monolayer. We use the classical Heisenberg model with Landau-Lifshitz-Gilbert (LLG) dynamics including a stochastic field representing finite temperatures. The friction force depends linearly on the velocity (provided it is small enough) for all temperatures. For low temperatures, the corresponding friction coefficient is proportional to the phenomenological damping constant of the LLG equation. This dependence is lost at high temperatures, where the friction coefficient decreases exponentially. These findings can be explained by properties of the spin polarisation cloud dragged along with the tip.

We present studies of the transition between two types of filament evolution in the viscous catenary. In particular we examine the dependence of the observed behavior on the viscosity of the fluid, the initial radius of filament created, and the total length of the fluid. The kinematic viscosity is varied over two orders of magnitude, the filament radius by one order of magnitude, and the filament length by a factor of 3. We observe a clear transition as the so-called catenary number, dependent on the filament radius and length, increases past a certain value, but with no dependence on the viscosity of the fluid. This is a confirmation of theoretical predictions over a significantly greater range of viscosities than previous experiments.

Three-dimensional imaging of silicon nanoclusters array in silicon-rich silicon oxide layers was evidenced and studied. The atom probe tomography technique allows to give the composition of the nanoclusters and the composition of the interface with the silica matrix. These results give new insights for the understanding of the properties of Si-based photonic devices.

Local structure of ReOFeAs (Re=La, Pr, Nd, Sm) system has been studied as a function of chemical pressure varied due to different rare-earth size. Fe K-edge extended X-ray absorption fine structure (EXAFS) measurements in the fluorescence mode has permitted to compare systematically the inter-atomic distances and their mean square relative displacements (MSRD). We find that the Fe-As bond length and the corresponding MSRD hardly show any change, suggesting the strongly covalent nature of this bond, while the Fe-Fe and Fe-Re bond lengths decrease with decreasing rare-earth size. The results provide important information on the atomic correlations that could have direct implication on the superconductivity and magnetism of ReOFeAs system, with the chemical pressure being a key ingredient.

Elastic properties of the alloys Ti₃AlC and T i₃AlN are derived from the first-principles total energy calculations based on the full-potential linear muffin-tin Orbital (FP-LMTO) method. From the computed elastic constants, theoretical values of Young's modulus, shear modulus, Poisson's ratio, sound velocities and Debye temperature are evaluated. By analysing the ratio between the bulk and shear moduli, it is found that Ti₃AlN is ductile in nature, whose ductility is expected to be greater than that of Ti₃Al, whereas T i₃AlC is found to be brittle. The site-projected density of states and the charge density plots have been used to analyse the chemical bonding between the Ti₆N and T i₆C cluster and the surrounding metallic lattice of Al atoms. This further reveals that the strong covalent nature of Ti-C bonds in Ti₃AlC, together with the high Young, shear and bulk moduli, make the compound more brittle than Ti₃AlN.

We report a study on the structural modifications induced in amorphous silicon dioxide (a-SiO₂) by electron irradiation in the dose range from 1.2·10³ to 5·10⁶ kGy. This study has been performed by investigating the properties of the ²⁹Si hyperfine structure of the E '_γ center by electron paramagnetic resonance (EPR) spectroscopy. Our data suggest that the structural modifications induced by irradiation take place through the nucleation of confined high-defective and densified regions statistically dispersed into the whole volume of the material. In addition, we have estimated that in the high dose limit (D⩾10⁵ kGy) the degree of densification associated to the local (within the defective regions) polyamorphic transition follows a characteristic power law dependence on the dose given by bD^ν, where b=(2.0±0.3)·10^-3, ν=0.160±0.004 and D is the irradiation dose measured in kGy.

We reexamine the nature of the metallic phase of the one-dimensional half-filled Holstein model of spinless fermions. To this end, we determine the Tomonaga-Luttinger–liquid correlation parameter K_ρ by large-scale density matrix renormalisation group (DMRG) calculations, exploiting i) the leading-order scaling relations between the ground-state energy and the single-particle excitation gap and ii) the static charge structure factor in the long-wavelength limit. While both approaches give almost identical results for intermediate-to-large phonon frequencies, we find contrasting behaviour in the adiabatic regime: i) K_ρ>1 (attractive) vs. ii) K_ρ< 1 (repulsive). The latter result for the correlation exponent is corroborated by data obtained for the momentum distribution function n(k), which puts the existence of an attractive metallic state in the spinless fermion Holstein model into question. We conclude that the scaling relation must be modified in the presence of electron-phonon interactions with noticeable retardation.

A theoretical model is presented which explains the dominant decoherence process in a microcavity polariton condensate. The mechanism which is invoked is the effect of self-phase modulation, whereby interactions transform polariton number fluctuations into random energy variations. The model shows that the phase coherence decay, g⁽¹⁾(τ), has a Kubo form, which can be Gaussian or exponential, depending on whether the number fluctuations are slow or fast. This fluctuation rate also determines the decay time of the intensity correlation function, g⁽²⁾(τ), so it can be directly determined experimentally. The model explains recent experimental measurements of a relatively fast Gaussian decay for g⁽¹⁾(τ), but also predicts a regime, further above threshold, where the decay is much slower.

We present a large-N variational approach to describe the magnetism of insulating doped semiconductors based on a disorder-generalization of the resonating-valence-bond theory for quantum antiferromagnets. This method captures all the qualitative and even quantitative predictions of the strong-disorder renormalization group approach over the entire experimentally relevant temperature range. Finally, by mapping the problem on a hard-sphere fluid, we could provide an essentially exact analytic solution without any adjustable parameters.

In a non-polar geometry for non-cubic ferromagnetic materials, it is shown that the X-ray absorption dichroism spectrum is composed of a non-magnetic contribution (natural dichroism) emanating from the reduced crystal symmetry and a magnetic contribution from spin-orbit coupling and spin polarization. Their computation at the L_{2, 3} edges of the half-metal CrO₂ chromium site, illustrate the good agreement with experiment. This is found only when both dichroic contributions are taken into account. Moreover, X-ray magnetic dichroism sum rules can be applied directly to extract the spin and orbital magnetic moments only after removing the natural dichroism from the full spectrum.

The electromagnetic response of graphene and the spectrum of collective plasmon excitations are studied as a function of wave vector and frequency. Our calculation is based on the tight-binding band structure, including both valleys. As a result, near the Dirac points we find plasmons whose dispersion is similar to that obtained in the single-valley approximation by Dirac fermions with some anisotropy though. In contrast to the calculation for a single Dirac cone, we find a stronger damping of the plasmon modes due to interband absorption. Our calculation also reveals effects due to deviations from the linear Dirac spectrum as we increase the Fermi energy, indicating an anisotropic behavior with respect to the wave vector of the external electromagnetic field.

In recent years it has become clear that complex oxides provide an exceptional platform for the discovery of new physics as well as a considerable challenge to our understanding of correlated electrons. The tendency of these materials to display nanoscale electronic and magnetic inhomogeneity is a good example. Here, we have applied a variety of experimental techniques to investigate this magneto-electronic phase separation in a model system —the doped cobaltite La_1−xSr_xCoO₃. Comparing experimental data over a wide range of doping with statistical simulations, we conclude that the magneto-electronic inhomogeneity is driven solely by inevitable local compositional fluctuations at nanoscopic length scales. The phase separation is thus doping fluctuation-driven rather than electronically driven, meaning that more complex electronic phase separation models are not required to understand the observed phenomena in this material.

Using Monte Carlo simulations we verify that the rare-earth compound LiHoF₄ is a very good realization of a dipolar Ising model. With only one free parameter our calculations for the magnetization, specific heat and inverse susceptibility match experimental data at a quantitative level in the 0.5–3 kelvin range, including the ferromagnetic transition at 1.53  K. Using parallel tempering methods and reaching system sizes up to 32000 dipoles with periodic boundary conditions, we are able to give evidence of the logarithmic corrections predicted in renormalization group theory. Due to the long range and angular dependence of the dipolar model, sample shape and domains play a crucial role in the ordered state. We consider surface corrections to Griffiths's theorem, which arise in finite macroscopic samples and lead to a theory of magnetic domains. We find a domain wall energy of 0.059 erg/cm² and predict that the ground-state domain structure for cylinders with a demagnetization factor N>0 consists of thin parallel sheets of opposite magnetization, with a width depending on the demagnetization factor.

We study the electronic transport in a graphene-based ferromagnet/insulator/d-wave superconductor (F/I/S) junction by use of the Dirac-Bogoliubov-de Gennes equation. The effects of spin polarization in the F region, barrier strength in the I region, and Fermi wave vector mismatch between the F and S regions are taken into account. It is found that the differential conductance and shot noise are strongly modulated by these parameters and display different features compared with other junctions. One interesting finding is that, at zero bias voltage and the maximum orientation angle of the superconductive gap α=π/4, the conductance, shot noise and Fano factor are only controlled by one parameter, i.e. the spin polarization, irrespective of all the other parameters. This universal feature could be applied to measure the magnitude of the spin polarization induced in graphene.

In scope of this paper, DSC, small-angle X-ray scattering (SAXS), electro-optic and dielectric studies have been done on BaTiO₃ nanoparticles dispersed in a ferroelectric liquid-crystalline (FLC) matrix. Electro-optic studies showed slightly lower spontaneous polarization, faster response time and relatively higher coercive voltage for the nanocomposite as compared to the pure FLC mixture. Dielectric measurements revealed a lower relative dielectric permittivity for the nanocomposite. This paper addresses all the issues starting from the kind of nanoparticles and FLC materials used for the preparation of nanocomposites, the various measurements done and a detailed discussion on the observed results.

We study the correlations of two-dimensional dipolar bosons with excitons in semiconductor bilayers as a specific case, in the whole temperature-concentration region. We show that at low concentrations, the Bose degeneracy is accompanied by strong multi-particle correlations and the system behaves as a Bose liquid. At high concentrations the repulsion suppresses quantum coherence and the system behaves as a classical liquid down to a temperature lower than typical for a Bose gas. The interaction energy of the particles is a sensitive tool for a measurement of the correlations. This theory can apply to other systems of bosons with extended interaction.

We report experiments in nanometer-scaled superconductor/normal metal hybrid devices which show that in a small window of contact resistances, crossed Andreev reflection (CAR) can dominate the nonlocal transport for all energies below the superconducting gap. Besides crossed Andreev reflection, elastic cotunneling (EC) and nonlocal charge imbalance can be identified as competing subgap transport mechanisms in temperature-dependent four-terminal nonlocal measurements. We demonstrate a systematic change of the nonlocal resistance vs. bias characteristics with increasing contact resistances, which can be varied in the fabrication process. For samples with higher contact resistances, CAR is weakened relative to EC in the midgap regime, possibly due to dynamical Coulomb blockade. Gaining control of crossed Andreev reflection is an important step towards the realization of a solid-state entangler.

We report the ⁷⁵As-NMR study on a single crystal of the hole-doped iron-pnictide superconductor Ba_0.72K_0.28Fe₂As₂ (T_c=31.5 K). We find that the Fe antiferromagnetic spin fluctuations are anisotropic and are weaker compared to underdoped copper-oxides or cobalt-oxide superconductors. The spin lattice relaxation rate 1/T₁ decreases below T_c with no coherence peak and shows a stepwise variation at low temperatures, which is indicative of multiple superconducting gaps, as in the electron-doped Pr(La)FeAsO_{1- x}F_x. Furthermore, no evidence was obtained for a microscopic coexistence of a long-range magnetic order and superconductivity.

The magnetic and electronic properties of the transition metal (TM) (V, Cr, Mn, Fe, Co, Ni, Cu) doped In₂O₃ have been theoretically studied by using the density functional theory. When two TM ions are placed close to each other (TM-TM distance of about 3.4 Å), the ferromagnetic ordering is found to be the lowest-energy configuration. The only exception is Fe, which possesses a half-filled 3d band. However, for further separation distance of about 7.2 Å, only Co, Ni and Cu ions (having more than half-filled 3d band) still prefer the ferromagnetic orientation, while V, Cr, or Mn ions (having less than half-filled 3d band) prefer antiferromagnetic ordering. The energies of the 3d band for TM ions show a decrease with increasing TM atomic number. For V, Cr and Mn, the 3d bands are merged with the conduction band, and show less hybridization with the host valence band; while for Co, Ni and Cu, the 3d bands show strong hybridization with the host valence band mainly formed by the oxygen 2p state. In this situation, polarized holes are formed on the oxygen sites close to the TM ions. Moreover, V-doped In₂O₃ is found to meet the requirements for a strong donor-mediated ferromagnetism.

Magnetic impurities bridging nanocontacts and break junctions of nearly magnetic metals may lead to permanent moments, analogous to the giant moments well known in the bulk case. A numerical renormalization group (NRG) study shows that, contrary to mean-field–based expectations, a permanent moment never arises within an Anderson model, which invariably leads to strong Kondo screening. In the presence of an additional ferromagnetic intersite exchange coupling between leads and impurity, realistic for nearly ferromagnetic leads, the NRG may instead stabilize a permanent moment. The resulting state is a rotationally invariant spin, which differs profoundly from mean field and whose physical properties are those of a ferromagnetic Kondo model as opposed to the more conventional antiferromagnetic one, where the localized moment gets eventually screened by the conduction electrons. A sign inversion of the zero-bias anomaly and other spectroscopic signatures of the switch from regular to ferromagnetic Kondo are outlined.

We present a non-neutral stochastic model for the dynamics taking place in a meta-community ecosystems in the presence of migration. The model provides a framework for describing the emergence of multiple ecological scenarios and behaves in two extreme limits either as the unified neutral theory of biodiversity or as the Bak-Sneppen model. Interestingly, the model shows a condensation phase transition where one species becomes the dominant one, the diversity in the ecosystems is strongly reduced and the ecosystem is non-stationary. This phase transition extends the principle of competitive exclusion to open ecosystems and might be relevant for the study of the impact of invasive species in native ecologies.

Intracellular transport by molecular motors proceeds in two steps: long-range transport along microtubules and local delivery via actin filaments. A recent in vitro experiment has revealed that the actin-based motor myosin V can diffuse along microtubules and can enhance the processivity of cargos pulled by the microtubule-based motor kinesin-1 (Ali M. Y. et al., Proc. Natl. Acad. Sci. U.S.A., 105 (2008) 4691). Here we present a stochastic model for cargo transport by a directional motor (kinesin) and a diffusing motor (myosin). By using a subset of the experimental data of Ali et al. to adjust our model parameters, we are able to describe all experimental results. In our model, the myosins do not influence kinesin's motion and only act as tethers which allow the kinesin to rebind. Furthermore we find that the run length of the cargo increases exponentially with the number of myosins.

In 2005, Nagler and Claussen (Phys. Rev. E, 71 (2005) 067103) investigated the time series of the elementary cellular automata (ECA) for possible (multi)fractal behavior. They eliminated the polynomial background at^b through the direct fitting of the polynomial coefficients a and b. We here reconsider their work eliminating the polynomial trend by means of the multifractal-based detrended fluctuation analysis (MF-DFA) in which the wavelet multiresolution property is employed to filter out the trend in a more speedy way than the direct polynomial fitting and also with respect to the wavelet transform modulus maxima (WTMM) procedure. In the algorithm, the discrete fast wavelet transform is used to calculate the trend as a local feature that enters the so-called details signal. We illustrate our result for three representative ECA rules: 90, 105, and 150. We confirm their multifractal behavior and provide our results for the scaling parameters.

We consider a current-biased dc SQUID in the presence of an applied time-dependent bias current or magnetic flux. The phase dynamics of such a Josephson device is equivalent to that of a quantum particle trapped in a 1D anharmonic potential, subject to external time-dependent control fields, i.e. a driven multilevel quantum system. The problem of finding the required time-dependent control field that will steer the system from a given initial state to a desired final state at a specified final time is formulated in the framework of optimal-control theory. Using the spectral filter technique, we show that the selected optimal field which induces a coherent population transfer between quantum states is represented by a carrier signal having a constant frequency but which is time-varied both in amplitude and phase. The sensitivity of the optimal solution to parameter perturbations is also addressed.