Table of contents

We present a method that enables the implementation of full three-dimensional (3D) transformation media with minimized anisotropy. It is based on a special kind of shape-preserving mapping and a subsequent optimization process. For sufficiently smooth transformations, the resulting anisotropy can be neglected, paving the way for practically realizable 3D devices. The method is independent of the considered wave phenomenon and can thus be applied to any field for which a transformational technique exists, such as acoustics or thermodynamics. Full 3D isotropy has an additional important implication for optical transformation media, as it eliminates the need for magnetic materials in many situations. To illustrate the potential of the method, we design 3D counterparts of transformation-based electromagnetic squeezers and bends.

The electron band around the M point in the $({\text{Ba}_{1-x}}{{\text{K}}_{x}}){\text{Fe}_{2}}{\text{As}_{2}}$ compound, which is completely lifted up above the Fermi level for $x>0.7$ and hence its Fermi surface (FS) disappears, can still play the role of the main pairing resource by exchanging inter-band repulsive interaction with the main hole band (h1) around the $\Gamma$ point. This hidden electron band, which develops the superconducting order parameter (OP) ${{\Delta }_{e}}$ but has no FS, displays a shadow gap feature which is easily detected by various experimental probes such as angle-resolved photoemission spectroscopy (ARPES) and tunneling measurements. We also show that the formation of the nodal gap ${{\Delta }_{\text{nodal}}}$ with ${{A}_{1g}}$ symmetry on another hole pocket (h2) around the $\Gamma$ point with a larger FS is stabilized due to the balance of the inter-band repulsive interactions from the main hole band (h1) with the OP ${{\Delta }_{h1}}={{\Delta }_{+}}$, and the hidden electron band with the OP ${{\Delta }_{e}}={{\Delta }_{-}}$.

Can quantum theory be seen as a special case of a more general probabilistic theory, as classical theory is a special case of the quantum one? We study here the class of generalized probabilistic theories defined by the order of interference they exhibit as proposed by Sorkin. A simple operational argument shows that the theories require higher-order tensors as a representation of physical states. For the third-order interference we derive an explicit theory of 'density cubes' and show that quantum theory, i.e. theory of density matrices, is naturally embedded in it. We derive the genuine non-quantum class of states and non-trivial dynamics for the case of a three-level system and show how one can construct the states of higher dimensions. Additionally to genuine third-order interference, the density cubes are shown to violate the Leggett–Garg inequality beyond the quantum Tsirelson bound for temporal correlations.

We present a theory in Maxwellian form for gravitational waves in a flat background. This requires us to identify the gravitational analogues of the electric and magnetic fields for light. An important novelty, however, is that our analogues are not vector fields but rather rank-two tensor fields; in place of a three-component vector at each point in space, as in electromagnetism, our fields are three by three symmetric matrices at each point. The resulting Maxwell-like equations lead directly to a Poynting theorem for the local energy density associated with a gravitational wave and to associated local properties including densities of momentum and angular momentum.

The stabilization of Cooper pairs of bound electrons in the background of a Fermi sea is the origin of superconductivity and the paradigmatic example of the striking influence of many-body physics on few-body properties. In the quantum-mechanical three-body problem the famous Efimov effect yields unexpected scaling relations among a tower of universal states. These seemingly unrelated problems can now be studied in the same setup thanks to the success of ultracold atomic gas experiments. In light of the tremendous effect of a background Fermi sea on two-body properties, a natural question is whether a background can modify or even destroy the Efimov effect. Here we demonstrate how the generic problem of three interacting particles changes when one particle is embedded in a background Fermi sea, and show that Efimov scaling persists. It is found in a scaling that relates the three-body physics to the background density of fermionic particles.

A numerical exploration of a gain–loss nonlinear Schrödinger equation was carried out utilizing over 180 000 core hours to conduct more than 10 000 unique simulations in an effort to characterize the model's six dimensional parameter space. The study treated the problem in full generality, spanning a minimum of eight orders of magnitude for each of three linear and nonlinear gain terms and five orders of magnitude for higher order nonlinearities. The gain–loss nonlinear Schrödinger equation is of interest as a model for spin wave envelopes in magnetic thin film active feedback rings and analogous driven damped nonlinear physical systems. Bright soliton trains were spontaneously driven out of equilibrium and behaviors stable for tens of thousands of round trip times were numerically identified. Nine distinct complex dynamical behaviors with lifetimes on the order of ms were isolated as part of six identified solution classes. Numerically located dynamical behaviors include: (i) low dimensional chaotic modulations of bright soliton trains; (ii) spatially symmetric/asymmetric interactions of solitary wave peaks; (iii) dynamical pattern formation and recurrence; (iv) steady state solutions; and (v) intermittency. Simulations exhibiting chaotically modulating bright soliton trains were found to qualitatively match previous experimental observations. Ten new dynamical behaviors, eight demonstrating long lifetimes, are predicted to be observable in future experiments.

For reliable and consistent quantum information processing carried out on a quantum network, the network structure must be fully known and a desired initial state must be accurately prepared on it. In this paper, for a class of spin networks with only its single node accessible, we provide two continuous-measurement-based methods to achieve the above requirements; the first identifies the unknown network structure with a high probability, based on a continuous-time Bayesian update of the graph structure and the second is, with the use of an adaptive measurement technique, able to deterministically drive any mixed state to a spin coherent state for network initialization.

We consider the effect of contact interaction in a prototypical quantum spin Hall system of pseudo-spin-1/2 particles. A strong effective magnetic field with opposite directions for the two spin states restricts two-dimensional particle motion to the lowest Landau level. While interaction between same-spin particles leads to incompressible correlated states at fractional filling factors as known from the fractional quantum Hall effect, these states are destabilized by interactions between opposite spin particles. Exact results for two particles with opposite spin reveal a quasi-continuous spectrum of extended states with a large density of states at low energy. This has implications for the prospects of realizing the fractional quantum spin Hall effect in electronic or ultra-cold atom systems. Numerical diagonalization is used to extend the two-particle results to many bosonic particles and trapped systems. The interplay between an external trapping potential and spin-dependent interactions is shown to open up new possibilities for engineering exotic correlated many-particle states with ultra-cold atoms.

Oxide heterostructures have been shown to exhibit unusual physics and hold the promise of novel electronic applications. We present a set of criteria to select and design interfaces, particularly those that can sustain a high-density two-dimensional electron gas (2DEG). We describe how first-principles calculations can contribute to a qualitative and quantitative understanding, illustrated with the key issue of band alignment. Band offsets determine on which side of the interface the 2DEG will reside, as well as the degree of confinement. We use hybrid density functional calculations to determine the band alignments of a number of complex oxides, considering materials with different types of conduction-band character, polar or nonpolar character and band insulators as well as Mott insulators. We suggest promising materials combinations that could lead to a 2DEG with optimized properties, such as high 2DEG densities and high electron mobilities.

Chiral Majorana-fermion modes are shown to emerge as edge excitations in a superconductor–topological-insulator hybrid structure that is subject to a magnetic field. The velocity of this mode is tunable by changing the magnetic-field magnitude and/or the superconductor's chemical potential. We discuss how quantum-transport measurements can yield experimental signatures of these modes. A normal lead coupled to the Majorana-fermion edge state through electron tunneling induces resonant Andreev reflections from the lead to the grounded superconductor, resulting in a distinctive pattern of differential-conductance peaks.

We investigate experimentally the emergence of collective motion in the bulk of an active suspension of Escherichia coli bacteria. When increasing the concentration from a dilute to a semi-dilute regime, we observe a continuous crossover from a dynamical cluster regime to a regime of 'bio-turbulence' convection patterns. We measure a length scale characterizing the collective motion as a function of the bacteria concentration. For bacteria fully supplied with oxygen, the increase of the correlation length is almost linear with concentration and at the largest concentrations tested, the correlation length could be as large as 24 bacterial body sizes (or 7–8 when including the flagella bundle). In contrast, under conditions of oxygen shortage the correlation length saturates at a value of around 7 body lengths.

Using particle-in-cell simulations, we study the interaction of few-mJ–few-cycle laser pulses with an underdense plasma at resonant density. In this previously unexplored regime, it is found that group velocity dispersion is a key ingredient of the interaction. The concomitant effects of dispersion and plasma nonlinearities cause a deceleration of the wakefield phase velocity, which becomes sub-relativistic. Electron injection in this sub-relativistic wakefield is enhanced and leads to the production of a femtosecond electron bunch with a picocoulomb of charge in the 5–10 MeV energy range. Such an electron bunch is of great interest for application to ultrafast electron diffraction. In addition, in this dispersion dominated regime, it is shown that positively chirped laser pulses can be used as a tuning knob for compensating for plasma dispersion, increasing the laser amplitude during self-focusing and optimizing the trapped charge.

With the combination of a single crystal diamond anvil cell and a polycapillary half-lens, the local structural evolution around germanium in tetrahedrally networked quartz-like α-GeO₂ has been investigated using extended x-ray absorption fine structure spectroscopy of up to 14 GPa by multiple-scattering analysis method. While the first shell Ge–O bond distances show a slight contraction with increasing pressure, the third shell Ge–O bond distances are found to decrease dramatically. The sluggish lengthening of the first shell Ge–O bond distances, initiated by coordination increase from fourfold to sixfold, occurs in the 7–14 GPa range just when the third shell Ge–O bond distances fall in the region of the second shell Ge–Ge bond distances. Moreover, these features are accompanied by the closing of intertetrahedral Ge–O–Ge angles and the opening of two intratetrahedral O–Ge–O angles, whose topological configuration surprisingly exhibits a helical chirality along the c axis that is opposite to the double helices of the corner-linked GeO₄ tetrahedra. These results suggest that the high-pressure phase transitions in quartz and quartz-like materials could be associated with a structural instability that is driven by the drastic collapse of the next-nearest-neighbour anion shell, which is consistent with the emergence of high-symmetry anion sublattice. Our findings provide crucial insights into the densification mechanisms of quartz-like oxides, which would have broad implications for our understanding of the metastability of various post-quartz crystalline phases and pressure-induced amorphization.

We demonstrate a quantum key distribution (QKD) testbed for room temperature single photon sources based on defect centres in diamond. A BB84 protocol over a short free-space transmission line is implemented. The performance of nitrogen-vacancy (NV) as well as silicon-vacancy defect (SiV) centres is evaluated. An extrapolation for the future applicability of such sources in quantum information processing is discussed.

We discuss in some detail the implications of the suggestion made by P D Burrow and G A Gallup on the physics of anion formation and of resonant electron attachment in gas-phase anthracene molecules.

The shape resonances computed in the title paper are shown to be approximately 1.8 eV too high.

The effect of chemotaxis on migration of adhesive and proliferative cells on a substrate is analyzed by employing two approaches: by solving a stochastic discrete lattice model for cell dynamics and by deriving and solving a continuum macroscopic equation for cell density. The phenomenon of front propagation is investigated in the framework of the two approaches both for positive and negative chemotaxis. A good agreement between the results of the lattice model and of the continuum model is observed both for front velocities and front profiles. The theoretical model is also able to match recent experimental observations on glioma cell migration.

We present an accurate ab initio description of the magnetic exchange force microscopy (MExFM). As a prototypical system, the antiferromagnetic NiO(001) surface probed with a Fe tip is investigated. The tip–surface interaction is described on two levels. Short-range chemical and exchange forces between the tip apex and the surface atoms are described in the framework of spin-polarized density functional theory while long-range van der Waals forces are considered within a mesoscopic tip model. For the Ni atoms in the NiO surface as well as the Fe atoms of the tip apex, an on-site repulsion U in the transition-metal 3d shells is included. In order to understand the tip–surface interaction, we investigate the changes in the electronic structure of tip and surface versus distance. The resulting frequency shifts and MExFM images are in good qualitative agreement with experimental data.

Establishing the hybrid entanglement among a growing amount of matter and photonic quantum bits is necessary for scalable quantum computation and long-distance quantum communication. Here we demonstrate that charged excitonic complexes forming in strongly correlated quantum dot molecules are able to generate tripartite hybrid entanglement under proper carrier quantization. The mixed orbitals of the molecule construct multi-level ground states with sub-meV hole tunneling energy and relatively large electron hybridization energy. We show that appropriate size and interdot spacing keeps the electron particle weakly localized, opening extra recombination channels by correlating ground-state excitons. This allows for creation of higher order entangled states. Nontrivial hole tunneling energy, renormalized by multi-particle interactions, facilitates the realization of the energy coincidence among only certain components of the molecule optical spectrum. This translates to the emergence of favorable spectral components in a multi-body excitonic complex which sustain principal oscillator strengths throughout the electric field-induced hole tunneling process. We particularly analyze whether the level broadening of favorable spin configurations could be manipulated to eliminate the distinguishability of photons.

We demonstrate the direct formation of vibronic ground state RbCs molecules by photoassociation of ultracold atoms followed by radiative stabilization. The photoassociation proceeds through deeply bound levels of the (2)³Π_0⁺ state. From analysis of the relevant free-to-bound and bound-to-bound Franck–Condon factors, we have predicted and experimentally verified a set of photoassociation resonances that lead to efficient creation of molecules in the v = 0 vibrational level of the X¹Σ⁺ electronic ground state. We also compare the observed and calculated laser intensity required to saturate the photoassociation rate. We discuss the prospects for using short-range photoassociation to create and accumulate samples of ultracold polar molecules in their rovibronic ground state.

Populations of biological cells that communicate with each other can organize themselves to generate large-scale patterns. Examples can be found in diverse systems, ranging from developing embryos, cardiac tissues, chemotaxing ameba and swirling bacteria. The similarity, often shared by the patterns, suggests the existence of some general governing principle. On the other hand, rich diversity and system-specific properties are exhibited, depending on the type of involved cells and the nature of their interactions. The study on the similarity and the diversity constitutes a rapidly growing field of research. Here, we introduce a new class of self-organized patterns of cell populations that we term as 'cellular trail networks'. They were observed with populations of rat microglia, the immune cells of the brain and the experimental evidence suggested that haptotaxis is the key element responsible for them. The essential features of the observed patterns are well captured by the mathematical model cells that actively crawl and interact with each other through a decomposing but non-diffusing chemical attractant laid down by the cells. Our finding suggests an unusual mechanism of socially cooperative long-range signaling for the crawling immune cells.

I propose a model of mutually interacting particles on an M-dimensional unit sphere. I derive the dynamics of the particles by extending the dynamics of the Kuramoto–Sakaguchi model. The dynamics include a natural-frequency matrix, which determines the motion of a particle with no external force, and an external force vector. The position (state variable) of a particle at a given time is obtained by the projection transformation of the initial position of the particle. The same projection transformation gives the position of the particles with the same natural-frequency matrix. I show that the motion of the center of mass of an infinite number of heterogeneous particles whose natural-frequency matrices are obtained from a class of multivariate Lorentz distribution is given by an M-dimensional ordinary differential equation in closed form. This result is an extension of the Ott–Antonsen theory.

A joint theoretical–experimental study focusing on the description of the ferromagnetic resonance response of thin films in the presence of periodic perturbations introduced on the upper film surface is presented. From the viewpoint of theory, these perturbations may exist in the form of any kind of one- or two-dimensional rectangular defect arrays patterned onto one surface of the magnetic film. Indeed, the defects may be pits or bumps, or ion-implanted regions with a lower saturation magnetization. The complete set of response functions, given by the components of the frequency and wave-vector dependent dynamic magnetic susceptibility tensor of the film exposed to microwave excitation, are provided and are used to explain the experimental data. This allows us to obtain the response of the system due to microwave absorption, from which the zero wave-vector spin-wave modes in the field-frequency spectra, including their intensity, are calculated. Explicit calculations for periodic defects featuring the shape of stripes, dots and rectangles are given in detail, as well as experimental results for stripe-like defects prepared either by topographical depressions or by ion implantation of thin magnetic films. The excellent agreement of the theoretical and experimental results manifests the validity of the presented model.

The fractional quantized Hall state at the filling factor ν = 5/2 is of special interest due to its possible application for quantum computing. Here we report on the optimization of growth parameters that allowed us to produce two-dimensional electron gases (2DEGs) with a 5/2 gap energy up to 135 mK. We concentrated on optimizing the molecular beam epitaxy (MBE) growth to provide high 5/2 gap energies in 'as-grown' samples, without the need to enhance the 2DEGs properties by illumination or gating techniques. Our findings allow us to analyse the impact of doping in narrow quantum wells with respect to conventional DX-doping in Al_xGa_1−xAs. The impact of the setback distance between doping layer and 2DEG was investigated as well. Additionally, we found a considerable increase in gap energy by reducing the amount of background impurities. To this end growth techniques like temperature reductions for substrate and effusion cells and the reduction of the Al mole fraction in the 2DEG region were applied.

Self-assembly due to capillary forces is a common method for generating two-dimensional mesoscale structures from identical floating particles at the liquid–air interface. Designing building blocks to obtain a desired mesoscopic structure is a scientific challenge. We show herein that it is possible to shape the particles with a low cost three-dimensional printer, for composing specific mesoscopic structures. Our method is based on the creation of capillary multipoles inducing either attractive or repulsive forces. Since capillary interactions can be downscaled, our method opens new paths toward low cost microfabrication.

In contrast to the broad knowledge about aqueous polyelectrolyte solutions, less is known about the properties in aprotic and apolar solvents. We therefore investigate the behavior of sulfonated polyelectrolytes in sodium form in the presence of different solvents via all-atom molecular dynamics simulations. The results clearly reveal strong variations in ion condensation constants and polyelectrolyte conformations for different solvents like water, dimethyl sulfoxide (DMSO) and chloroform. The binding free energies of the solvent contacts with the polyelectrolyte groups validate the influence of different solvent qualities. With regard to the ion condensation behavior, the numerical findings show that the explicit values for the condensation constants depend on the preferential binding coefficient as derived by the evaluation of Kirkwood–Buff integrals. Surprisingly, the smallest ion condensation constant is observed for DMSO compared to water, whereas in the presence of chloroform, virtually no free ions are present, which is in good agreement to the donor number concept. In contrast to the results for the low condensation constants, the sodium conductivity in DMSO is smaller compared to water. We are able to relate this result to the observed smaller diffusion coefficient for the sodium ions in DMSO.

In the framework of dielectric theory, the static non-local self-energy of an electron near an ultra-thin polarizable layer has been calculated and applied to study binding energies of image-potential states near free-standing graphene. The corresponding series of eigenvalues and eigenfunctions have been obtained by numerically solving the one-dimensional Schrödinger equation. The image-potential state wave functions accumulate most of their probability outside the slab. We find that the random phase approximation (RPA) for the non-local dielectric function yields a superior description for the potential inside the slab, but a simple Fermi–Thomas theory can be used to get a reasonable quasi-analytical approximation to the full RPA result that can be computed very economically. Binding energies of the image-potential states follow a pattern close to the Rydberg series for a perfect metal with the addition of intermediate states due to the added symmetry of the potential. The formalism only requires a minimal set of free parameters: the slab width and the electronic density. The theoretical calculations are compared with experimental results for the work function and image-potential states obtained by two-photon photoemission.

Here we study the alkali metal induced effects on an ordered and aligned sexiphenyl monolayer on Cu(110) with angle-resolved UV spectroscopy (ARUPS). The caesium (Cs) induced gap states could clearly be identified by orbital tomography, a method based on ARUPS, which allows both the orbital character of these states and the molecular orientation to be determined. We show that with increasing alkali metal dose, doping proceeds in three distinct steps. Initially, Cs decouples the molecular monolayer from the substrate, with emptying of the lowest unoccupied molecular orbital (LUMO) that had been filled on hybridization with the substrate. Further Cs exposure refills the LUMO. Finally a filling of the LUMO + 1 by charge transfer from the alkali metal occurs. Remarkably, although long range order is not preserved and the molecular planes tilt away from the surface, the molecules remain aligned parallel to the $[1 \bar 1 0]$ azimuth during the whole doping process.

The influence of micromagnetic objects on the dynamic magnetic excitation in magnetic thin films is studied by imprinting periodic domain wall patterns through selective ion irradiation in exchange biased Ni₈₁Fe₁₉/IrMn structures. For high domain wall densities an increased precessional frequency is achieved. The zero field resonance of the domain wall state hereby depends directly on the stripe period, showing a pronounced increase with decrease of domain wall spacing. With the abrupt annihilation of magnetic domain walls with an applied bias field a jump-like decrease in precessional frequency takes place. The experimental data and micromagnetic simulations prove that the characteristic collective dynamic mode for the domain wall configurations is attributed to strongly coupled tilted magnetization structure. This is evidenced by an overlapping Néel wall structure for the narrowly spaced imprinted antiparallel unidirectional anisotropy state. The controlled introduction of high density frozen-in micromagnetic objects is a novel way to control the dynamic magnetic properties of continuous magnetic thin films.

We explore the effect of all-optical feedback on the steady state dynamics of optomechanical arrays arising from various topologies. First we consider an array comprised of a pair of independent optomechanical cavities coupled reversibly via their optical modes. Next we consider an optomechanical network formed from coupling two optical modes with interactions mediated via a common mechanical mode. Finally we extend the analysis to a large network of N-coupled optomechanical systems. Our results show implementing an-all optical feedback loop in each arrangement can enhance the degree of steady state entanglement between inter cavity optical and mechanical modes.

We report on the experimental observation of transverse modulations in proton beams accelerated from micrometer thick targets which were irradiated with ultra-short (30 fs) laser pulses of a peak intensity of 5 × 10²⁰ W cm⁻². The net-like proton beam modulations were recorded using radiochromic film and the data suggest a dependence on laser energy and target thickness for their onset and strength. Numerical simulations suggest that intensity-dependent instabilities in the laser-produced plasma at the target front side lead to electron beam break-up or filamentation, then serving as the source of the observed proton beam modulations.

We present a comprehensive study of the spectral and transport properties in the Anderson–Holstein model both in and out of equilibrium using the functional renormalization group (fRG). We show how the previously established machinery of Matsubara and Keldysh fRG can be extended to include the local phonon mode. Based on the analysis of spectral properties in equilibrium we identify different regimes depending on the strength of the electron–phonon interaction and the frequency of the phonon mode. We supplement these considerations with analytical results from the Kondo model. We also calculate the nonlinear differential conductance through the Anderson–Holstein quantum dot and find clear signatures of the presence of the phonon mode.

Regions of quantum states generalize the classical notion of error bars. High posterior density (HPD) credible regions are the most powerful of region estimators. However, they are intractably hard to construct in general. This paper reports on a numerical approximation to HPD regions for the purpose of testing a much more computationally and conceptually convenient class of regions: posterior covariance ellipsoids (PCEs). The PCEs are defined via the covariance matrix of the posterior probability distribution of states. Here it is shown that PCEs are near optimal for the example of Pauli measurements on multiple qubits. Moreover, the algorithm is capable of producing accurate PCE regions even when there is uncertainty in the model.

We determine the minimal number of qubits that it is necessary to have access to in order to transform Dicke states into other Dicke states. In general, the number of qubits in Dicke states cannot be increased via transformation gates by accessing only a single qubit, in direct contrast to other multipartite entangled states such as GHZ, W and cluster states. We construct a universal optimal gate which adds spin-up qubits or spin-down qubits to any Dicke state by minimal access. We also show the existence of a universal gate which transforms any size of Dicke state as long as it has access to at least the required number of qubits. Our results have important consequences for the generation of Dicke states in physical systems such as ion traps, all-optical setups and cavity-quantum electrodynamic settings where they can be used for a variety of quantum information processing tasks.

The single-particle spectral function for an incompressible fractional quantum Hall state in the presence of a scalar short-ranged attractive impurity potential is calculated via exact diagonalization within the spherical geometry. In contrast to the noninteracting case, where only a single bound state below the lowest Landau level forms, electron–electron interactions strongly renormalize the impurity potential, effectively giving it a finite range, which can support many quasi-bound states (long-lived resonances). Averaging the spectral weights of the quasi-bound states and extrapolating to the thermodynamic limit, for filling factor ν = 1/3 we find evidence consistent with localized fractionally charged e/3 quasi-particles. For ν = 2/5, the results are slightly more ambiguous, due to finite size effects and possible bunching of Laughlin-quasi-particles.

Quasi-particle interference (QPI) measurements have provided a powerful tool for determining the momentum dependence of the gap of unconventional superconductors. Here we examine the possibility of using such measurements to probe the frequency and momentum dependence of the electron self-energy. For illustration, we calculate the QPI response function for a cuprate-like Fermi surface with an electron self-energy from a random phase approximation. Then we try to re-extract the self-energy from the dispersion of the peaks in the QPI response function using different approaches. We show that in principle it is possible to extract the self-energy from the QPI response for certain nested momentum directions. We discuss some of the limitations that one faces.

Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the long-time behaviour appears untreatable with direct numerical methods. We develop novel analytic methods based on the theory of random unitary operations which help us to determine explicitly the asymptotic dynamics of quantum walks on two-dimensional finite integer lattices with percolation. Based on this theory, we find new unexpected features of percolated walks like asymptotic position inhomogeneity or special directional symmetry breaking.

We present a two-fluid description for iron-based superconductors, which contains an itinerant electron Fermi-liquid and a local moment spin-liquid, coupled together via an effective Hund's rule interaction. We examine the low-energy collective behavior of such a system. We find that an electron–spinon composite mode emerges in the intermediate coupling regime, which may account for the hump-dip behavior observed in the recent scanning tunneling spectroscopy experiments. The superconductivity and spin-density-wave phases are consistently described within the same framework. Possible experimental tests are also proposed.