Table of contents

Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this behavior of the variance occurs when the complementary cumulative distribution function of waiting times is asymptotically described by a slowly varying function. In this case, we derive a general representation of the laws of superslow diffusion for both biased and unbiased versions of the model and, to illustrate the obtained results, consider two particular classes of waiting-time distributions.

Important developments in fault-tolerant quantum computation using the braiding of anyons have placed the theory of braid groups at the very foundation of topological quantum computing. Furthermore, the realization by Kauffman and Lomonaco that a specific braiding operator from the solution of the Yang-Baxter equation, namely the Bell matrix, is universal implies that in principle all quantum gates can be constructed from braiding operators together with single qubit gates. In this paper we present a new class of braiding operators from the Temperley-Lieb algebra that generalizes the Bell matrix to multi-qubit systems, thus unifying the Hadamard and Bell matrices within the same framework. Unlike previous braiding operators, these new operators generate directly, from separable basis states, important entangled states such as the generalized Greenberger-Horne-Zeilinger states, cluster-like states, and other states with varying degrees of entanglement.

We derive a Kubo-type formula that describes proper non-equilibrium stationary states for finite-size systems. We first argue that the usual Kubo formula considers only equilibrium states of the perturbed system, which are inappropriate to describe transport properties. Moreover, we show that the standard Kubo formula for the dc conductance is only appropriate in the thermodynamic limit. We demonstrate that taking into consideration explicitly the coupling to the leads/baths solves both problems. This approach results in well-behaved response functions, without the singular contributions from degenerate states encountered when Kubo formulae for infinite-size systems are inappropriately used for finite-size systems. We also derive a second, more efficient formulation which is valid only for a set of special physical quantities, which includes the charge current density operator.

A mechanism for the cooperative directed transport in two-dimensional ratchet potentials is proposed. With the aid of mutual couplings among particles, coordinated unidirectional motion along the ratchet direction can be achieved by transforming the energy from the transversal rocking force (periodic or stochastic) to the work in the longitude direction. Analytical predictions on the relation between the current and other parameters for the ac-driven cases are given, which are in good agreement with numerical simulations. Stochastic driving forces can give rise to the resonant directional transport. The effect of the free length, which has been explored in experiments on the motility of bipedal molecular motors, is investigated for both the single- and double-channel cases. The mechanism and results proposed in this letter may both shed light on the collective locomotion of molecular motors and open ways on studies in two-dimensional collaborative ratchet dynamics.

A simple kinematic model for the trajectories of Listeria monocytogenes is generalized to a dynamical system rich enough to exhibit the resonant Hopf bifurcation structure of excitable media and simple enough to be studied geometrically. It is shown how L. monocytogenes trajectories and meandering spiral waves are organized by the same type of attracting set.

We propose a geometric phase gate in a decoherence-free subspace with trapped ions. The quantum information is encoded in the Zeeman sublevels of the ground state and two physical qubits to make up one logical qubit with ultra-long coherence time. Single- and two-qubit operations together with the transport and splitting of linear ion crystals allow for a robust and decoherence-free scalable quantum processor. For the ease of the phase gate realization we employ one Raman laser field on four ions simultaneously, i.e. no tight focus for addressing. The decoherence-free subspace is left neither during gate operations nor during the transport of quantum information.

We present an alternative quantization procedure for the one-dimensional non-relativistic quantum mechanics. We show that, for the case of a free particle and a particle in a box, the complete classical and quantum correspondence can be obtained using this formulation. The resulting wave packets do not disperse and strongly peak on the classical paths. Moreover, for the case of the free particle, they satisfy minimum uncertainty relation.

We present a mathematical analysis of records drawn from independent random variables with a drifting mean. To leading order the change in the record rate is proportional to the ratio of the drift velocity to the standard deviation of the underlying distribution. We apply the theory to time series of daily temperatures for given calendar days, obtained from historical climate recordings of European and American weather stations as well as re-analysis data. We conclude that the change in the mean temperature has increased the rate of record-breaking events in a moderate but significant way: for the European station data covering the time period 1976–2005, we find that about 5 of the 17 high temperature records observed on average in 2005 can be attributed to the warming climate.

The production of charmed and beauty baryons in proton-proton collisions at high energies is analyzed within the modified quark-gluon string model. We present some predictions for the experiments on the forward beauty baryon production in pp collisions at LHC energies. This analysis allows us to find useful information on the Regge trajectories of the heavy (b) mesons and the fragmentation functions of quarks to the bottom baryons.

Cold atoms in atom wires may be transported, along large distances and with selectable direction, by modifying only the shape of the physical wire and the time dependence of its electric current in a basic atom wire trap. The design of this "magnetic micropump" is based on the ratchet concept. Its transport of cold atoms is shown by symmetry analysis and by direct numerical simulation. The numerical simulation should be considered as proof of principle; more physically realistic designs may be required to achieve transport in experiment. The micropump design could also be used to transport magnetised beads in microfluidic applications.

A Generalized Langevin Equation with exponential memory is proposed for the dynamics of a massive intruder in a dense granular fluid. The model reproduces numerical correlation and response functions, violating the Equilibrium Fluctuation-Dissipation Relations. The source of memory is identified in the coupling of the tracer velocity V with a spontaneous local velocity field U in the surrounding fluid: fluctuations of this field introduce a new time scale with its associated length scale. Such identification allows us to measure the intruder's fluctuating entropy production as a function of V and U, obtaining a neat verification of the fluctuation relation.

We experimentally probe the vicinity of the jamming point J, located at a density ϕ corresponding to random close packing (ϕ_rcp=0.842), in two dimensional, bidisperse packings of foam bubbles. We vary the density of the foam layer and extract geometrical measures by image analysis. We confirm the predicted scaling of the average contact number Z with ϕ and compare the distribution of local contact numbers to a simple model. We further establish that the distribution of areas p(A) strongly depends on ϕ. Finally, we find that the distribution of contact forces p(f) systematically varies with density.

Coarse-grained simulations are used to demonstrate that knotted filaments in shear flow at zero Reynolds number exhibit remarkably rich dynamic behaviour. For stiff filaments that are weakly deformed by the shear forces, the knotted filaments rotate like rigid objects in the flow. But away from this regime the interplay between shear forces and the flexibility of the filament leads to intricate regular and chaotic modes of motion that can be divided into distinct families. The set of accessible mode families depends to first order on a dimensionless number that relates the filament length, the elastic modulus, the friction per unit length and the shear rate.

The mass transfer between immiscible two liquid phases can be greatly accelerated by bubbling gas through a reactor (Bird R. B., Stewart W. E. and Lightfoot E. N., Transport Phenomena, 2nd edition (John Wiley and Sons) 2002). Therefore, the physical phenomenon occurring during the passage of a rising bubble through an immiscible two-liquid interface is of particular interest. The passage of the bubble through the oil (upper phase)/water (lower phase) interface starts with an upward lifting of the interface, and the bubble attracts a column of the water phase upwards keeping a film of the water phase around itself. In the present study, a particular remark is given to the influence of different interface tensions retracting the water film, after the water film ruptured, which lays on the interface between air and silicone oil. Unlike the previous studies on the rupture of a single liquid film in a gas which is pulled due to the identical surface tension, this system can form concentric ripples on the outer interface of the water film (oil/water interface) around the bubble due to the weak interface tension. Then, numerous micro water droplets break out from the fully grown ripples.

We have cooled a macroscopic LC electrical resonator using feedback-cooling combined with an ultrasensitive dc Superconducting Quantum Interference Device (SQUID) current amplifier. The resonator, with resonance frequency of 11.5 kHz and bath temperature of 135 mK, is operated in the high coupling limit so that the SQUID back-action noise overcomes the intrinsic resonator thermal noise. The effect of correlations between the amplifier noise sources clearly show up in the experimental data, as well as the interplay of the amplifier noise with the resonator thermal noise. The lowest temperature achieved by feedback is 14 μK, corresponding to 26 resonator photons, and approaches the limit imposed by the noise energy of the SQUID amplifier.

The emergence of a sequence of alternating intense and elongated eastward-westward bands i.e. zonal jets in the atmosphere of the giant planets and in Earth's oceans have been widely investigated. Nevertheless jets formation and role as material barriers remain still unclear. Jets are generated in a quasi-2D turbulent flow due to the latitudinal variation of the Coriolis parameter (the so-called β-effect) which modifies the inverse cascade process channeling energy towards zonal modes. In previous experiments we have investigated the impact of the variation of the rotation rate, of the domain geometry and of the initial spectra on jets organization in a decaying regime. In this work we investigate the formation of jets in a continuously forced flow, we characterize the observed regime and also we attempt to verify the existence of an universal regime corresponding to the so-called zonostrophic turbulence. The experimental set-up consists of a rotating tank where turbulence is generated by electromagnetically forcing a shallow layer of an electrolyte solution, and the variation of the Coriolis parameter has been simulated by the parabolic profile assumed by the free surface of the fluid under rotation. Flow measurements have been performed using image analysis.

The free decay of MHD turbulence at large Reynolds numbers is studied numerically using a shell model. We study the statistical properties based on a representative sample of realisations (128 realisations for each type of initial conditions) over a period of 10⁵ large-scale turnover times. The performed simulations show that the free-decaying nonhelical MHD turbulence can demonstrate two different scenarios of evolution in spite of similar initial conditions. Within the first scenario, the cross-helicity accumulation is so fast that the energy cascade vanishes before significant magnetic energy dissipates. Then the system approaches the state of maximal cross-helicity. Within the second scenario, the cascade process continues to remain active until time 10⁴ in units of large-scale turnover time. Then the magnetic field becomes vastly helical due to magnetic helicity conservation. Thus the magnetic energy does not dissipate with kinetic energy.

This paper provides the first demonstration that an hydrogenated annealed crystalline silicon may be used as a source of protons in laser-driven acceleration experiments. We analyze and compare the proton production from two silicon targets excited by a sub-nanosecond laser. One target (treated) was hydrogenated and annealed, while the other (untreated) did not undergo these procedures. The experimental results show that for the treated target, the number of generated protons is ∼1.4×10¹⁵ sr⁻¹ while for the other it is ∼3.6×10¹³ sr⁻¹. Their maximum energy is about 2 MeV with a laser intensity three order of magnitude lower than in previous experiments. We obtain an increase of 80% in the proton kinetic energy and of 200% in the proton current as well as a large amount of Si^q+ ions (1⩽q⩽14) with respect to the untreated target. A deconvolution procedure based on a Boltzmann-like distribution is applied for the analysis of time-of-flight (TOF) spectra of proton and silicon ion beams.

The performance of a low-pass screen designed to block electromagnetic waves in a stop band is shown to have an upper bound defined by the static electric and magnetic polarizability per unit area of the screen. The bound is easy to calculate for all angles of incidence and polarizations, and applies regardless of how complicated the screen's microstructure is. For a homogeneous dielectric sheet the bound for TM polarization is more restrictive than the bound for TE, but this is not generally true for a screen with microstructure. The results are verified by measurements and simulations of oblique transmission through an array of split ring resonators, printed on a dielectric substrate.

The dynamics of turbulence and plasma flows has been studied experimentally by means of Doppler reflectometry during the transition from low to high confinement mode in the stellarator TJ-II. Close to the transition threshold, gradual transitions are achieved showing an intermediate, oscillatory transient phase that facilitates the study of the mechanisms involved in the transition. A coupling between sheared flows and turbulence level is measured which reveals a characteristic predator-prey behavior consistent with the L-H transition models based on turbulence-driven flows.

The present paper is devoted to the relativistic statistical theory, introduced in Phys. Rev. E, 66 (2002) 056125 and Phys. Rev. E, 72 (2005) 036108, predicting the particle distribution function p(E)=exp_κ(−β[E−μ]) with and κ²<1. This, experimentally observed, relativistic distribution, at low energies behaves as the exponential, Maxwell-Boltzmann classical distribution, while at high energies presents power-law tails. Here, we obtain the evolution equation, conducting asymptotically to the above distribution, by using a new deductive procedure, starting from the relativistic BBGKY hierarchy and by employing the relativistic molecular chaos hypothesis.

Monte Carlo simulations of a two-dimensional, random-field Ising model with an ac driving field are used to study the relaxation-to-creep transition of domain-wall motion at low temperatures. The resultant complex susceptibility χ=χ'−iχ'' exhibits features in agreement with the experiments of ultrathin ferromagnetic and ferroelectric films: the semicircle and straight line in the χ'-χ'' plot are Cole-Cole signatures of relaxation and creep states, respectively. The exponent β describing the creep motion is measured, and an intermediate state between the relaxation and creep states is identified.

Martensitic materials quenched from the austenite phase can show hugely different conversion kinetics: explosively rapid ("athermal"), or slowly incubated ("isothermal"). This traditional sharp distinction was queried by experiments finding conversion-incubation delay tails even in athermal martensites, at temperatures where only austenite should exist. To understand martensitic kinetics, we perform systematic Monte Carlo temperature-quench simulations of a protoypical martensitic model of S=0, ±1 strain pseudospins, with compatibility-induced, power law anisotropic interactions, and no extrinsic disorder. We find both athermal or isothermal behaviour in the same model, depending on parameters. In the athermal regime, the puzzling experimental temperature-time behaviour for conversions is reproduced: explosive conversions (below a spinodal), do indeed coexist with rising incubation-delay tails. A Vogel-Fulcher divergence at transition is predicted, in a region of tweed-like precursors. Incubations are explained as searches for rare, finite-scale transitional states, that are explicitly identified. Although complex textural changes occur during incubation, the energies are quite flat, in a signature of entropy barriers. The model suggests systematic quench experiments in martensites.

We demonstrate that the quantum dynamics of a many-body Fermi-Bose system can be simulated using a Gaussian phase-space representation method. In particular, we consider the application of the mixed fermion-boson model to ultracold quantum gases and simulate the dynamics of dissociation of a Bose-Einstein condensate of bosonic dimers into pairs of fermionic atoms. We quantify deviations of atom-atom pair correlations from Wick's factorization scheme, and show that atom-molecule and molecule-molecule correlations grow with time, in clear departures from pairing mean-field theories. As a first-principles approach, the method provides benchmarking of approximate approaches and can be used to validate dynamical probes for characterizing strongly correlated phases of fermionic systems.

Roughness of random walks in the presence of a Laplacian field is studied in two dimensions for various strengths of the field parametrized by η. We find an η_c∼4.5±0.3 at which a transition occurs from a tortuous fractal structure to a one-dimensional profile of the walk. At η_c, the walks are self-affine with a roughness exponent ζ=0.80±0.05. For increasing η-values, the roughness exponent increases.

The ability to generate a change of the lattice parameter in a near-surface layer of a controllable thickness by ion implantation of strontium titanate is reported here using low-energy He⁺ ions. The induced strain follows a distribution within a typical near-surface layer of 200 nm as obtained from structural analysis. Due to the clamping effect from the underlying layer, only perpendicular expansion is observed. Maximum distortions up to 5–7% are obtained with no evidence of amorphisation at fluences of 10¹⁶ He⁺ ions/cm² and ion energies in the range 10–30 keV.

Competing ferro- and antiferromagnetic exchange interactions may lead to the formation of bound magnon pairs in the high-field phase of a frustrated quantum magnet. With decreasing field, magnon pairs undergo a Bose-condensation prior to the onset of a conventional one-magnon instability. We develop an analytical approach to study the zero-temperature properties of the magnon-pair condensate, which is a bosonic analog of the BCS superconductors. The representation of the condensate wave function in terms of the coherent bosonic states reveals the spin-nematic symmetry of the ground state and allows one to calculate various static properties. Sharp quasiparticle excitations are found in the nematic state with a small finite gap. We also predict the existence of a long-range–ordered spin-nematic phase in the frustrated chain material LiCuVO₄ at high fields.

Precise absolute far–infra-red magneto-transmission experiments have been performed under magnetic fields up to 28 T on a series of single Ga_0.24In_0.76As quantum wells n-type modulation doped at different levels. The transmission spectra have been simulated with a multilayer dielectric model. This allows us to extract the imaginary part of the optical response function which reveals new singular features related to electron-phonon interactions. In addition to the expected polaronic effects due to the longitudinal (LO) phonons, one observes other interactions with the transverse optical (TO) phonons and a new kind of carrier concentration-dependent interaction with interface phonons. This system provides a unique opportunity to study multiple types of electron-phonon interactions in a single type of compound.

We show that graphene in a strong magnetic field with partially filled Landau levels sustains charged collective excitations —bound states of a neutral magnetoplasmon and free particles. In the limit of low density of excess charges, these are bound three-particle complexes. Some of these states are optically bright and may be detected in spectroscopy experiments, providing a direct probe of electron-electron interactions in graphene. The charged excitations can be classified using the geometrical symmetries —non-commutative magnetic translations and generalized rotations— in addition to the dynamical SU₄ symmetry in graphene. From the SU₄ symmetry point of view, such excitations are analogous to bound states of two quarks and one antiquark with four flavors. We establish a flavor optical selection rule to identify the bright states for experimental studies.

We study adiabatic quantum quenches across a quantum multicritical point (MCP) using a quenching scheme that enables the system to hit the MCP along different paths. We show that the power-law scaling of the defect density with the rate of driving depends non-trivially on the path, i.e., the exponent varies continuously with the parameter α that defines the path, up to a critical value α=α_c; on the other hand for α⩾α_c, the scaling exponent saturates to a constant value. We show that dynamically generated and path(α)-dependent effective critical exponents associated with the quasicritical points lying close to the MCP (on the ferromagnetic side), where the energy-gap is minimum, lead to this continuously varying exponent. The scaling relations are established using the integrable transverse XY spin chain and generalized to a MCP associated with a d-dimensional quantum many-body systems (not reducible to two-level systems) using adiabatic perturbation theory. We also calculate the effective path-dependent dimensional shift d₀(α) (or the shift in center of the impulse region) that appears in the scaling relation for special paths lying entirely in the paramagnetic phase. The numerically obtained results are in good agreement with analytical predictions.

We investigated the valence band structure of graphite oxide by photoelectron spectroscopy at the Pohang Accelerator Laboratory, Korea. The typical sp² hybridization states found in graphite were also seen in graphite oxide. However, the π state disappeared near the Fermi level because of bonding between the π and oxygen-related states originating from graphite oxide, indicating electron transfer from graphite to oxygen and resulting in a downward shift of the highest occupied molecular orbital (HOMO) state to higher binding energies. The band gap opening increased to about 1.8 eV, and additional oxygen-related peaks were observed at 8.5 and 27 eV. The electronic states of graphite were also found in graphite oxide. Thus, graphite oxide has an electronic structure similar to that of pristine graphite except for the states near the Fermi level and oxygen-related states.

We investigate the existence of end points in the dispersion of Holstein polarons in various dimensions, using the Momentum Average (MA) approximation which has proved to be very accurate for this model. An end point separates momenta for which the lowest-energy state is a discrete level, i.e., an infinitely-lived polaron, from those where the lowest-energy feature is a continuum in which the "polaron" is signalled by a resonance with a finite lifetime. While such end points are known to not appear in 1D, we show here that they are generic in 3D if the particle-boson coupling is not too strong. The 2D case is "critical": a pure 2D Holstein model has no end points, like the 1D case. However, any amount of interlayer hopping leads to 3D-like behavior. As a result, such end points are expected to appear in the spectra of layered, quasi-2D systems described by Holstein models. Generalizations to other models are also briefly discussed.

The ultrafast response of the prototype Mott-Hubbard system (V_1−xCr_x)₂O₃ was systematically studied with fs pump-probe reflectivity, allowing us to clearly identify the effects of the metal-insulator transition on the transient response. The isostructural nature of the phase transition in this material made it possible to follow across the phase diagram the behaviour of the detected coherent acoustic wave, whose average value and lifetime depend on the thermodynamic phase and on the correlated electron density of states. It is also shown how coherent lattice oscillations can play an important role in some changes affecting the ultrafast electronic peak relaxation at the phase transition, changes which should not be mistakenly attributed to genuine electronic effects. These results clearly show that a thorough understanding of the ultrafast response of the material over several tenths of ps is necessary to correctly interpret its sub-ps excitation and relaxation regime, and appear to be of general interest also for other strongly correlated materials.

We discuss the problem of full counting statistics for periodic pumping. The probability generating function is usually defined on a circle of the "physical" values of the counting parameter, with its periodicity corresponding to charge quantization. The extensive part of the generating function can either be an analytic function on this circle or have singularities. These two cases may be interpreted as different thermodynamic phases in time domain. We discuss several examples of phase transitions between these phases for classical and quantum systems. Finally, we prove a criterion for the "analytic" phase in the problem of a quantum pump for non-interacting fermions.

For a class of transition metal materials residual resistivity is observed to decrease when the materials are deformed and short-range order is removed. We investigate this counter-intuitive behavior with an ab initio theoretical study of the residual resistivity of several late transition metal-rich disordered alloys. The calculations are performed using the Korringa-Kohn-Rostoker (KKR) method applied to the Kubo-Greenwood formalism. The electronic effects arising from short-range ordering and clustering within the disorder are described using the non-local coherent-potential approximation (NL-CPA). We find a simple, general explanation of this K-state–like effect in terms of changes to the amplitude for d-electron hopping between majority late transition metal nearest-neighbor atoms at the Fermi energy.

We study the phase dynamics in coupled Josephson junctions described by a system of nonlinear differential equations. Results of detailed numerical simulations of charge creation in the superconducting layers and the longitudinal plasma wave (LPW) nucleation are presented. We demonstrate the different time stages in the development of the LPW and present the results of FFT analysis at different values of bias current. The correspondence between the breakpoint position on the outermost branch of current voltage characteristics (CVC) and the growing region in time dependence of the electric charge in the superconducting layer is established. The effects of noise in the bias current and the external microwave radiation on the charge dynamics of the coupled Josephson junctions are found. These effects introduce a way to regulate the process of LPW nucleation in the stack of IJJ.

Applying pressure driving to a single layer of aqueous foam bubbles induces a void propagation that is a surprisingly close analog of dynamic crack propagation. Depending on the rate of applied stress, both a ductile and a brittle mode of propagation are observed, the latter at much higher propagation speeds. A pronounced velocity gap is found, with a well-defined upper limit to the ductile crack speed and a well-defined lower limit to the brittle propagation speed. Both limits can be quantitatively explained by analyzing processes on the scale of single bubbles and single films, respectively, confirming the importance of the microscopic (single-bubble) scale for the overall description of these fracture phenomena. We find that the brittle crack velocity is limited by the speed of wave propagation in the foam, so that the brittle mode can be understood as a supersonic crack.

The adsorption of a single polymer to a flat surface in shear is investigated using Brownian hydrodynamics simulations and scaling arguments. Competing effects are disentangled: in the absence of hydrodynamic interactions, shear drag flattens the chain and thus enhances adsorption. Hydrodynamic lift on the other hand gives rise to long-ranged repulsion from the surface which preempts the surface-adsorbed state via a discontinuous desorption transition, in agreement with theoretical arguments. Chain flattening is dominated by hydrodynamic lift, so overall, shear flow weakens the adsorption of flexible polymers. Surface friction due to small-wavelength surface potential corrugations is argued to weaken the surface attraction as well.

The promise of punishment and reward in promoting public cooperation is debatable. While punishment is traditionally considered more successful than reward, the fact that the cost of punishment frequently fails to offset gains from enhanced cooperation has lead some to reconsider reward as the main catalyst behind collaborative efforts. Here we elaborate on the "stick vs. carrot" dilemma by studying the evolution of cooperation in the spatial public goods game, where besides the traditional cooperators and defectors, rewarding cooperators supplement the array of possible strategies. The latter are willing to reward cooperative actions at a personal cost, thus effectively downgrading pure cooperators to second-order free-riders due to their unwillingness to bear these additional costs. Consequently, we find that defection remains viable, especially if the rewarding is costly. Rewards, however, can promote cooperation, especially if the synergetic effects of cooperation are low. Surprisingly, moderate rewards may promote cooperation better than high rewards, which is due to the spontaneous emergence of cyclic dominance between the three strategies.

We study the evolution of inhomogeneous spherical perturbations in the universe in a way that generalizes the spherical top-hat collapse in a straightforward manner. For that purpose we will derive a dynamical equation for the density contrast in the context of a Lemaître-Tolman-Bondi metric and construct solutions with and without a cosmological constant for the evolution of a spherical perturbation with a given initial radial profile.