Table of contents

We study a random walk model in which the jumping probability to a site is dependent on the number of previous visits to the site, as a model of the mobility with memory. To this end we introduce two parameters called the memory parameter α and the impulse parameter p. From extensive numerical simulations, we found that various limited mobility patterns such as sub-diffusion, trapping, and logarithmic diffusion could be observed. Through memory, a long-ranged directional anticorrelation kinetically induces sub-diffusive and trapping behaviors, and transition between them. With random jumps by the impulse parameter, a trapped walker can escape from the trap very slowly, resulting in an ultraslow logarithmic diffusive behavior. Our results suggest that the memory of walker's has-beens can be one mechanism explaining many of the empirical characteristics of the mobility of animated objects.

A symmetric and conserved energy-momentum tensor for a scalar field in a moving medium is derived using the Gordon metric. When applied to an electromagnetic field, the method gives a similar result. This approach thus points a way out of the old Abraham-Minkowski controversy about the correct energy-momentum tensors for the electromagnetic field in a material medium. The new tensor describes the properties of the field alone while the Abraham tensor contains information about the field coupled to the medium.

We study quantum transport of matter waves in anisotropic three-dimensional disorder. First, we show that structured correlations can induce rich effects, such as anisotropic suppression of the white-noise limit and inversion of the transport anisotropy. Second, we show that the localization threshold (mobility edge) is strongly affected by a disorder-induced shift of the energy states, which we calculate. Our work is directly relevant to ultracold-matter waves in optical disorder, and implications on recent experiments are discussed. It also offers scope for further studies of anisotropy effects in other systems with controlled disorder, where counterparts of the discussed effects can be expected.

A vortex in a topological superconductor induces two Majorana fermions (MFs), one in the core and the other at the sample edge. Here we demonstrate that edge MFs can be transported and braided by turning gate voltages on and off at the point-like constriction junctions between samples. The controllable high mobility of edge MFs is due to the topological property, namely an edge MF appears when the sample perimeter includes odd vorticity, and disappears for even vorticity. As shown explicitly by solving the time-dependent Bogoliubov-de Gennes equation, disturbance to the quantum coherence of MFs during braiding is negligibly small in this scheme due to the point-like application of the gate voltage. The present work bridges for the first time the fundamental topological features of edge MFs and their adiabatic dynamics which is important for performing topological quantum computation.

We show that the operation and the output power of a quantum heat engine that converts incoherent thermal energy into coherent cavity photons can be optimized by manipulating quantum coherences. The gain or loss in the efficiency at maximum power depends on the details of the output power optimization. Quantum effects tend to enhance the output power and the efficiency as the photon occupation in the cavity is decreased.

A recent measurement of the neutrino velocity by the OPERA experiment and the prediction of energy loss of superluminal neutrinos via the pair creation process ν → νe⁺e⁻ stimulated a search of isolated e⁺e⁻ pairs in detectors with good tracking capability traversed by a large flux of high-energy neutrinos like NOMAD. NOMAD has already searched for similar topologies. These results can be reinterpreted to provide stringent limits on special-relativity-violating parameters separately for each ν species.

We propose detecting the magnetic field gradient produced by the magnetic dipole moment of a single atom by using ions in an entangled state trapped a few μm from the dipole. This requires measuring magnetic field gradients of order 10⁻¹³ tesla/μm. We discuss applications in determining magnetic moments of a wide variety of ion species, for investigating the magnetic substructure of ions with level structures that are not suitable for laser cooling and detection, and for studying exotic or rare ions, and molecular ions. The scheme may also be used for measuring spin imbalances of neutral atoms or atomic ensembles trapped by optical dipole forces. As the proposed method relies on techniques that are well established in ion trap quantum information processing, it is within reach of current technology.

We study trapping of a cold atom by a single vortex line in an extreme type-II superconducting chip, allowing for pinning and friction. We evaluate the atom's spin flip rate and its dephasing due to the vortex fluctuations in equilibrium and find that they decay rapidly when the distance to the vortex exceeds the magnetic penetration length. We find that there are special spin orientations, depending on the spin location relative to the vortex, at which spin dephasing is considerably reduced while perpendicular directions have a reduced spin flip rate.

Dynamics of symmetric and antisymmetric 2-solitons and 3-solitons is studied in the model of the nonlinear dual-core coupler and its $\mathcal{PT}$-symmetric version. Regions of the convergence of the injected perturbed symmetric and antisymmetric N-solitons into symmetric and asymmetric quasi-solitons are found. In the $\mathcal{PT}$-symmetric system, with the balanced gain and loss acting in the two cores, borders of the stability against the blowup are identified. Notably, in all the cases the stability regions are larger for antisymmetric 2-soliton inputs than for their symmetric counterparts, on the contrary to previously known results for fundamental solitons (N = 1). Dynamical regimes (switching) are also studied for the 2-soliton injected into a single core of the coupler. In particular, a region of splitting of the input into a pair of symmetric solitons is found, which is explained as a manifestation of the resonance between the vibrations of the 2-soliton and oscillations of energy between the two cores in the coupler.

The doorway state phenomenon has been recently analysed in many different systems, both quantum and classical. The systems range from nuclei to sedimentary valleys, therefore covering a range in size of 19 orders of magnitude. It also applies to systems with chaotic spectra as well as to integrable systems. In all these works, the doorway state has been discussed only in the energy or frequency domains. In this letter we present numerical and experimental results for a quasi–one-dimensional elastic system which presents a doorway state and, for the first time, the temporal evolution of the phenomenon is measured directly.

Two-dimensional plasma crystals are characterized by a strong up-and-down asymmetry not only due to gravity but also due to the presence of plasma flow at the location of particles. We study for the first time the interaction of a single-layer plasma crystal with charged extra particles located above it (upstream of the flow of ions). Upstream extra particles tend to move between the rows of particles in the crystal, accelerate to supersonic speeds, and excite attraction-dominated Mach cones and wakes in the crystal.

Based on the Hamiltonian equation of motion of the ϕ⁴ theory with quenched random fields, we study the depinning phase transition of the domain-wall motion in two-dimensional magnets. With the short-time dynamic approach, we numerically determine the transition field and critical exponents. The results show that the fundamental Hamiltonian equation of motion belongs to a universality class very different from those effective equations of motion.

Amplitude modulation atomic force microscopy allows quantifying energy dissipation in the nanoscale with great accuracy with the use of analytical expressions that account for the fundamental frequency and higher harmonics. Here, we focus on the effects of sub-harmonic excitation on energy dissipation and its quantification. While there might be several mechanisms inducing sub-harmonics, a general analytical expression to quantify energy dissipation whenever sub-harmonics are excited is provided. The expression is a generalization of previous findings. We validate the expression via numerical integration by considering capillary forces and provide experimental evidence of sub-harmonic excitation for a range of operational parameters.

We present a finite-element model to analyze the buckling behaviours of two-dimensional nanowire (NW) networks. When the classical beam model is applied to model the building block NW it is found that the simple plate theory can be approximately used to describe this network. However, it is known that surface effects become dominant when the thickness of the NW reduces to nanoscale. Therefore, the buckling behaviours of the networks can be significantly affected by surface effects. Then the classical beam theory together with the Young-Laplace equation is applied to give a modified beam model to capture the surface effects. The results from this modified model demonstrate that the surface effects have significant influence not only on the critical force but also on the buckling modes, which suggests that the above simple plate theory fails to describe the networks when the surface effects are considered.

A critical Ising strip with confining boundaries characterized by arbitrary and different surface magnetic field variables is considered by the exact variational formulation of Mikheev and Fisher. As one of the most important scaling densities in films we study the universal functions of the energy density profiles which exhibit strong nonmonotonous behavior near the confining boundaries. We also examine their short-distance expansion that reveals novel universal amplitudes associated with the distant-wall corrections. They manifest nontrivial crossover behaviors from positive to negative values as the fields variables are freely varied. As an indispensable part of our new formulation of the generalized distant-wall correction de Gennes-Fisher universal amplitude we derive in a self-contained manner within the present approach the Casimir amplitudes that may change their nature twice under the strong influence of surface fields: from repulsive to attractive and vice versa along certain trajectories. Our findings strongly suggest a surprising role of the stress-tensor within one of the distant-wall corrections, given that similar discovery for standard extraordinary and ordinary surface universality classes was based on the conformal invariance symmetry which is broken under the present boundary conditions. We also show that a constituent part of the de Gennes-Fisher amplitude, defined in a generalized sense, is not hyperuniversal in two dimensions, contrary to earlier results for standard boundary conditions in this dimension.

We present a new method for exact enumeration of self-avoiding walks on critical percolation clusters. It can handle very long walks by exploiting the clusters' low connectivity and self-similarity. We have implemented the method in 2D and used it to enumerate walks of more than 1000 steps with over 10¹⁷⁰ conformations. The exponents ν and γ, governing the scaling behavior of the end-to-end distance and the number of configurations, as well as the connectivity constant μ could thus be determined with unprecedented accuracy. The method will help answering long-standing questions regarding this particular problem and can be used to check and gauge other methods, analytical and numerical. It can be adapted to higher dimensions and might also be extended to similar systems.

We report the geometrical effect of graded buckled multiwalled carbon nanotube arrays on the electrical transport properties in the diffusive regime, via successive breakdown caused by the Joule heating. This breakdown occurs in the straighter region. Empirical relations involving the current-carrying ability, resistance, breakdown power, threshold voltage, diameter and length of carbon nanotube arrays are discussed on the basis of an extensive set of experimental data along with justification. The experimental results are corroborated by the density functional tight-binding calculations of electronic band structure. The band gap decreases as buckleness increases leading to the enhancement in the current-carrying ability and elucidating the role of buckleness in carbon nanotubes.

Small-size effect and surface effect are two of the most specific intrinsic properties of nanostructures, both of which are of great significance to the related applications. In this letter, the nonlocal Euler-Bernoulli beam model, together with surface elasticity and surface tension are implemented to investigate the buckling behavior of axially compressed carbon nanotubes. Explicit expression of solutions to the critical buckling loads corresponding to typical boundary conditions is presented. Through contrast to molecular dynamics results, it is vitally important to note that both small-size effect and surface effect have a profound consequence and should be taken into account thoroughly.

Using a sum rule approach we investigate the dipole oscillation of a spin-orbit coupled Bose-Einstein condensate confined in a harmonic trap. The crucial role played by the spin polarizability of the gas is pointed out. We show that the lowest dipole frequency exhibits a characteristic jump at the transition between the stripe and spin-polarized phase. Near the second-order transition between the spin-polarized and the single minimum phase the lowest frequency is vanishingly small for large condensates, reflecting the divergent behavior of the spin polarizability. We compare our results with recent experimental measurements as well as with the predictions of effective mass approximation.

Although the physics for breakdown initiation in gases in generally well understood, the process of breakdown initiation in liquids is much less clear. A large number of experimental data on the breakdown in water revealed that the breakdown voltage in water is of the same magnitude as in the case of gases. This means that the breakdown in liquids can occur not at the extremely high electric fields required by the Paschen curve, but at those that only slightly exceed the breakdown electric fields in atmospheric-pressure molecular gases. This letter contains the results of experimental study on electrical breakdown characteristics in water vapor in microgaps between two parallel electrodes. Measurements were performed for the pressures of 24.15 torr, 20.85 torr and 14.55 torr with the gap size ranging from 40 μm to 900 μm. Considering that the atmospheric pressure sources operate in ambient air which unavoidably contains water vapor it is of great importance to investigate the basic processes and properties of discharges in water vapor.

Recently huge interest has been focussed on Ge-intercalated graphene. In order to address the effect of Ge on the electronic structure, we study Ge-intercalated free-standing C₆ and C₈ bilayer graphene, bulk C₆Ge and C₈Ge, as well as Ge-intercalated graphene on a SiC(0001) substrate, by density functional theory. In the presence of SiC(0001), there are three ways to obtain n-type graphene: i) intercalation between C layers; ii) intercalation at the interface to the substrate in combination with Ge deposition on the surface; and iii) cluster intercalation. All other configurations under study result in p-type states irrespective of the Ge coverage. We explain the origin of the different doping states and establish the conditions under which a transition occurs.

On the example of the prototypical multiferroic bismuth ferrite the microscopic origin of the spin flexoelectricity responsible for the spin cycloid ordering is analyzed. It is shown how the three basic structural distortions corresponding to the frozen-phonon modes of an ideal perovskite lattice result in the coexistence of the spin canting and the spin cycloidal ordering. On the basis of a simple formula for the antisymmetric Dzyaloshinskii-Moriya superexchange the inhomogenous magnetoelectric contribution to the theromodynamic potential is derived and the values of the microscopic parameters corresponding to the spin canting and the spin cycloid are determined.

Designing and optimizing cost functions and energy landscapes is a problem encountered in many fields of science and engineering. These landscapes and cost functions can be embedded and annealed in experimentally controllable spin Hamiltonians. Using an approach based on group theory and symmetries, we examine the embedding of Boolean logic gates into the ground-state subspace of such spin systems. We describe parameterized families of diagonal Hamiltonians and symmetry operations which preserve the ground-state subspace encoding the truth tables of Boolean formulas. The ground-state embeddings of adder circuits are used to illustrate how gates are combined and simplified using symmetry. Our work is relevant for experimental demonstrations of ground-state embeddings found in both classical optimization as well as adiabatic quantum optimization.

We have measured the pressure and temperature dependences of the resistivity and the thermoelectric power of anatase, TiO₂. The resistivity varies with T³ at high temperatures, and its absolute value is in the 1 Ωcm range. Below 60 K, the resistivity is activated. Most surprisingly, the activation energy shows non-monotonic pressure dependence. The thermoelectric power has a very high value and its temperature dependence resembles that of polaronic materials. We suggest a large polaronic model to describe the temperature and pressure dependence of the two transport coefficients.

The pairing symmetry is one of the major issues in the study of iron-based superconductors. We adopt a ten-orbital model by using the maximally localized Wannier functions based on the first-principles band structure calculations combined with the J₁-J₂ model for KFe₂As₂, the phase diagram of pairing symmetries is constructed. We find that the pairing symmetry for KFe₂As₂ is a nodal (s_x²y² + s_x²+y²)-wave in the folded Brillouin zone with two iron atoms per unit cell. This pairing symmetry can explain the experiments observed nodes, and it also can be tested by future experiments.

The "rainbow", where the light waves with different frequencies separate spatially, is confined in a self-similar waveguide with a hollow core coated by a coaxial dielectric/liquid-crystal multilayer. Due to the intrinsic self-similar furcation of the system, multiple transmission bands emerge in the photonic band structure, a "rainbow" is trapped as cladding modes in the waveguide. Both photonic bands and transmission modes can be tuned by changing temperature, hence the "rainbow" changes the colors in the waveguide. This effect can be applied in designing temperature-dependent integrated photonic devices, such as tunable on-chip spectroscopy, on-chip color-sorters, and photon sorters for spectral imaging.

Magnetoelectric (ME) effect at Co₂MnSi/BaTiO₃ (001) interfaces is demonstrated by using the first-principle calculations. Within paraelectric state, the calculated phase diagram reveals that the modified MnMn/TiO₂ (MM/TO) interface could be stabilized under Mn-rich and Co-rich condition. Compared with previous Fe/BaTiO₃ (Duan C. G. et al., Phys. Rev. Lett., 97 (2006) 047201) and Fe₃O₄/BaTiO₃ (Niranjan M. K. et al., Phys. Rev. B, 78 (2008) 104405) interfaces, more net change in interface magnetization can be achieved at MM/TO interface when electric polarization reverses. The results suggest a sizable interface ME effect may be attained at Mn-rich Co₂MnSi/BaTiO₃ (001) interface, hence potential application in the area of electrically controlled magnetism.

The isovalent substitution effect of Ru in CeFe_1−xRu_xAsO (0 ⩽ x ⩽ 1) has been systematically studied by powder X-ray diffraction, electrical resistivity, magnetization, and specific heat measurements. The antiferromagnetic (AFM) ordering of both d and 4f electrons are suppressed upon Ru doping, followed by Pauli paramagnetism (d electrons) and local moment paramagnetism (4f electrons) with strong ferromagnetic fluctuation, respectively. Neither superconductivity above 2 K nor pronounced Kondo screening are observed in the substitution phase diagram. Combined with published results of the cerium-based quaternary compounds CeMXO(M = Fe, Ru; X = P, As), our data suggest that the end member CeRuAsO is on the verge of becoming an FM Kondo lattice. Meanwhile, the ground state of 4f electrons in the quaternary CeMXO system should be determined by both the interlayer d-f Kondo coupling (J_Kondo) and the intralayer Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction (J_RKKY), which are both very sensitive to the change in crystal structure.

We perform a theoretical prediction of the structure of amorphous YCrO₃. We obtained equivalent amorphous structures by means of two independent first principles density functional theory based methods: molecular dynamics and stochastic quenching. In our structural analysis we include radial and angle distribution functions as well as calculations of bond lengths and average coordination numbers. We find Cr⁺³ atoms situated in slightly distorted oxygen octahedra throughout the amorphous structures and that the distribution of these octahedra is disordered. The presence of the same Cr⁺³ local environments that give rise to ferroelectricity in the orthorhombic perovskite structure suggests that the amorphous phase of YCrO₃ may also exhibit ferroelectric properties.

In this work we investigate the collective behavior of self-propelled particles that deform due to local pairwise interactions. We demonstrate that this deformation alone can induce alignment of the velocity vectors. The onset of collective motion is analyzed. Applying a Gaussian-core repulsion between the particles, we find a transition to disordered non-collective motion under compression. We here explain that this reflects the reentrant fluid behavior of the general Gaussian-core model now applied to a self-propelled system. Truncating the Gaussian potential can lead to cluster crystallization or more disordered cluster states. For intermediate values of the Gaussian-core potential we observe for the first time laning for deformable self-propelled particles. Finally, without the core potential, but including orientational noise, we connect our description to the Vicsek approach for self-propelled particles with nematic alignment interactions.

While contagion (information, infection, etc.) spreading has been extensively studied recently, the role of active local agents has not been fully considered. Here, we propose and study a model of spreading which takes into account the strength or quality of contagions as well as the local probabilistic dynamics occurring at various nodes. Transmission occurs only after the quality-based fitness of the contagion has been evaluated by the local agent. We study such spreading dynamics on Erdös-Rényi as well as scale free networks. The model exhibits quality-dependent exponential time scales at early times leading to a slowly evolving quasi-stationary state. Low prevalence is seen for a wide range of contagion quality for arbitrary large networks. We also investigate the activity of nodes and find a power-law distribution with a robust exponent independent of network topology. These properties, while absent in standard theoretical models, are observed in recent empirical observations.

We study the relationship between microscopic structure and viscosity in non-Brownian suspensions. We argue that the formation and opening of contacts between particles in flow effectively leads to a negative selection of the contacts carrying weak forces. We show that an analytically tractable model capturing this negative selection correctly reproduces scaling properties of flows near the jamming transition. In particular, we predict that i) the viscosity η diverges with the coordination number z as η ∼ (z_c − z)^{−(3+θ)/(1+θ)}, ii) the operator which governs flow displays a low-frequency mode that controls the divergence of viscosity, at a frequency ω_min ∼ (z_c − z)^{(3+θ)/(2+2θ)}, and iii) the distribution of forces displays a scale f* that vanishes near jamming as f*/〈f〉 ∼ (z_c − z)^1/(1+θ) where θ characterizes the distribution of contact forces P(f) ∼ f^θ at jamming, and where z_c is the Maxwell threshold for rigidity.

We analyse the thermal motion of a holographically trapped non-spherical force probe, capable of interrogating arbitrary samples with nanometer resolution. High speed video stereo-microscopy is used to track the translational and rotational coordinates of the micro-tool in three dimensions, and the complete 6 × 6 stiffness matrix for the system is determined using equipartition theorem. The Brownian motion of the extended structure is described in terms of a continuous distribution of thermal ellipsoids. A centre of optical stress, at which rotational and translational motion is uncoupled, is observed and controlled. Once calibrated, the micro-tool is deployed in two modes of operation: as a force sensor with <150 femto-Newton sensitivity, and in a novel form of photonic force microscopy.

The correspondence between long-delayed systems and one-dimensional spatially extended media enables a direct interpretation of purely temporal phenomena in terms of spatio-temporal patterns. On the basis of this result, we provide the evidence of a characteristic spatio-temporal dynamics —coarsening— in a long-delayed bistable system. Nucleation, propagation and annihilation of fronts, leading eventually to a single phase, are observed in an experiment based on a laser with opto-electronic feedback. A numerical and analytical study of a general phenomenological model is also performed and compared with the experimental findings.

Boolean networks serve as discrete models of regulation and signaling in biological cells. Identifying the key controllers of such processes is important for their understanding and planning further analysis. We quantify the dynamical impact of a node as the probability of damage spreading after switching the node's state. The leading eigenvector of the adjacency matrix is a good predictor of dynamical impact in case of long-term spreading. Quality of prediction is further improved when eigenvector centrality is based on the weighted matrix of activities rather than the unweighted adjacency matrix. Simulations are performed with random Boolean networks and a model of signaling in fibroblasts. The findings are supported by analytic arguments from a linear approximation of damage spreading.

The order parameter fluctuations of seismicity are investigated upon considering a natural time window of fixed length sliding through the consecutive earthquakes that occurred in California. We previously found that when this length corresponds to a time period of the order of a few months, the fluctuations exhibit a global minimum before the strongest mainshock. Here, we show that in California, during the twenty five year period 1979–2003, minima of the fluctuations are identified 1 to 5 months before four out of five mainshocks with magnitude M = 7.0 or larger as well as before the M = 6.9 Northridge earthquake. These minima are accompanied by minima of the exponent α of the Detrended Fluctuation Analysis (DFA) of the earthquake magnitude time series, which since α < 0.5 indicate anticorrelated behavior. These results of DFA alone cannot serve for prediction purposes, but do so when combined with the aforementioned minima in the fluctuations of the order parameter of seismicity identified in natural time analysis.