Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects, we devise an analytically solvable model of susceptible-infected spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of the lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times, the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late-time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to a fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.

Magnetite, ${\mathrm{Fe}}_3{\mathrm{O}}_4$, is the first magnetic material discovered and utilized by mankind in Ancient Greece, yet it still attracts attention due to its puzzling properties. This is largely due to the quest for a full and coherent understanding of the Verwey transition that occurs at $T_V=124\mathrm{K}$ and is associated with a drop of electric conductivity and a complex structural phase transition. A recent detailed analysis of the structure, based on single crystal diffraction, suggests that the electron localization pattern contains linear three-Fe-site units, the so-called trimerons. Here, we show that whatever the electron localization pattern is, it partially survives up to room temperature as short-range correlations in the high-temperature cubic phase, easily discernible by diffuse scattering. Additionally, ab initio electronic structure calculations reveal that characteristic features in these diffuse scattering patterns can be correlated with the Fermi surface topology.

The topologically protected conducting state is expected to exist on the entire surface of three-dimensional topological insulators (TIs). Using concurrent measurements of the local and nonlocal conduction, we provide experimental evidence for the topological robustness of the surface-conducting states of bulk-insulating ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$ crystalline flakes. The detailed investigation of local and nonlocal charge conductance on the top surfaces, combining with the comprehensive numerical simulation, reveals that the charge current is widely distributed over the entire surface of a TI. Our findings show evidence of the presence of the topologically protected conducting state at the side wall with irregularly stacked edges between the top and bottom surfaces. This study provides a reliable means of accurately characterizing the topological surface states with inherent nonlocal surface-dominant conducting channels in a TI.

We present shape-preserving spatially accelerating electromagnetic wave packets in curved space: wave packets propagating along nongeodesic trajectories while periodically recovering their structure. These wave packets are solutions to the paraxial and nonparaxial wave equations in curved space. We analyze the dynamics of such beams propagating on surfaces of revolution, and find solutions that propagate along a variety of nongeodesic trajectories, with their intensity profile becoming narrower (or broader) in a scaled self-similar fashion. Such wave packets reflect the interplay between the curvature of space and interference effects. Finally, we extend this concept to nonlinear accelerating beams in curved space supported by the Kerr nonlinearity. Our study concentrates on optical settings, but the underlying concepts directly relate to general relativity.

We report results of the magnetization and ac susceptibility measurements down to very low fields on a single crystal of the perovskite manganite, $\mathrm{La}{}_{0.82}\mathrm{Ca}{}_{0.18}\mathrm{MnO}{}_3$. This composition falls in the intriguing ferromagnetic insulator region of the manganite phase diagram. In contrast to earlier beliefs, our investigations reveal that magnetically (and in every other sense), this is a single-phase system with a ferromagnetic ordering temperature of around 170 K. However, this ferromagnetic state is magnetically frustrated, and the system exhibits pronounced glassy dynamics below 90 K. Based on measured dynamical properties, we propose that this quasi-long-ranged ferromagnetic phase, and the associated superspin glass behavior, is the true magnetic state of the system, rather than being a macroscopic mixture of ferromagnetic and antiferromagnetic phases, as often suggested. Our results provide an understanding of the quantum phase transition from an antiferromagnetic insulator to a ferromagnetic metal via this ferromagnetic insulating state as a function of $x$ in $\mathrm{La}{}_{1-x}\mathrm{Ca}{}_x\mathrm{MnO}{}_3$, in terms of the possible formation of magnetic polarons.

Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green’s observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional $p+ip$ superconductor both support so-called Ising non-Abelian anyons. Here, we establish a similar correspondence between the ${\mathbb{Z}}_3$ Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-$2e$ Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that—unlike Ising anyons—allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane’s construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a twofold ground-state degeneracy on a torus. In contrast to a $p+ip$ superconductor, vortices do not yield additional particle types, yet depending on nonuniversal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.

On the basis of first-principles calculations, we show that the M-type hexaferrite ${\mathrm{BaFe}}_{12}{\mathrm{O}}_{19}$ exhibits frustrated antiferroelectricity associated with its trigonal bipyramidal ${\mathrm{Fe}}^{3+}$ sites. The ferroelectric state of ${\mathrm{BaFe}}_{12}{\mathrm{O}}_{19}$, reachable by applying an external electric field to the antiferroelectric state, can be made stable at room temperature by appropriate element substitution or strain engineering. Thus, M-type hexaferrite, as a new type of multiferoic with coexistence of antiferroelectricity and ferrimagnetism, provides a basis for studying the phenomenon of frustrated antiferroelectricity and realizing multiple-state memory devices.

We derive an effective Hamiltonian that describes the dynamics of electrons in the conduction band of monolayer transition metal dichalcogenides (TMDC) in the presence of perpendicular electric and magnetic fields. We discuss in detail both the intrinsic and the Bychkov-Rashba spin-orbit coupling induced by an external electric field. We point out interesting differences in the spin-split conduction band between different TMDC compounds. An important consequence of the strong intrinsic spin-orbit coupling is an effective out-of-plane $g$ factor for the electrons that differs from the free-electron $g$ factor $g\simeq 2$. We identify a new term in the Hamiltonian of the Bychkov-Rashba spin-orbit coupling that does not exist in III-V semiconductors. Using first-principles calculations, we give estimates of the various parameters appearing in the theory. Finally, we consider quantum dots formed in TMDC materials and derive an effective Hamiltonian that allows us to calculate the magnetic field dependence of the bound states in the quantum dots. We find that all states are both valley and spin split, which suggests that these quantum dots could be used as valley-spin filters. We explore the possibility of using spin and valley states in TMDCs as quantum bits, and conclude that, due to the relatively strong intrinsic spin-orbit splitting in the conduction band, the most realistic option appears to be a combined spin-valley (Kramers) qubit at low magnetic fields.

We present a combined experimental and theoretical study of the proximity effect in an atomic-scale controlled junction between two different superconductors. Elaborated on a Si(111) surface, the junction comprises a Pb nanocrystal with an energy gap ${\mathrm{\Delta }}_1=1.2\mathrm{meV}$, connected to a crystalline atomic monolayer of lead with ${\mathrm{\Delta }}_2=0.23\mathrm{meV}$. Using in situ scanning tunneling spectroscopy, we probe the local density of states of this hybrid system both in space and in energy, at temperatures below and above the critical temperature of the superconducting monolayer. Direct and inverse proximity effects are revealed with high resolution. Our observations are precisely explained with the help of a self-consistent solution of the Usadel equations. In particular, our results demonstrate that in the vicinity of the Pb islands, the Pb monolayer locally develops a finite proximity-induced superconducting order parameter, well above its own bulk critical temperature. This leads to a giant proximity effect where the superconducting correlations penetrate inside the monolayer a distance much larger than in a nonsuperconducting metal.

The application of postselection to a weak quantum measurement leads to the phenomenon of weak values. Expressed in units of the measurement strength, the displacement of a quantum coherent measuring device is ordinarily bounded by the eigenspectrum of the measured observable. Postselection can enable an interference effect that moves the average displacement far outside this range, bringing practical benefits in certain situations. Employing the Fisher-information metric, we argue that the amplified displacement offers no fundamental metrological advantage, due to the necessarily reduced probability of success. Our understanding of metrological advantage is the possibility of a lower uncertainty in the estimate of an unknown parameter with a large number of trials. We analyze a situation in which the detector is pixelated with a finite resolution and in which the detector is afflicted by random displacements: imperfections that degrade the fundamental limits of parameter estimation. Surprisingly, weak-value amplification is no more robust to them than a technique making no use of the amplification effect brought about by a final, postselected measurement.

The technical merits of weak-value-amplification techniques are analyzed. We consider models of several different types of technical noise in an optical context and show that weak-value-amplification techniques (which only use a small fraction of the photons) compare favorably with standard techniques (which use all of them). Using the Fisher-information metric, we demonstrate that weak-value techniques can put all of the Fisher information about the detected parameter into a small portion of the events and show how this fact alone gives technical advantages. We go on to consider a time-correlated noise model and find that a Fisher-information analysis indicates that the standard method can have much larger information about the detected parameter than the postselected technique. However, the estimator needed to gather the information is technically difficult to implement, showing that the inefficient (but practical) signal-to-noise estimation of the parameter is usually superior. We also describe other technical advantages unique to imaginary weak-value-amplification techniques, focusing on beam-deflection measurements. In this case, we discuss combined noise types (such as detector transverse jitter, angular beam jitter before the interferometer, and turbulence) for which the interferometric weak-value technique gives higher Fisher information over conventional methods. We go on to calculate the Fisher information of the recently proposed photon-recycling scheme for beam-deflection measurements and show it further boosts the Fisher information by the inverse postselection probability relative to the standard measurement case.

Although ${\mathrm{CO}}_2$ and ${\mathrm{SiO}}_2$ both belong to group-IV oxides, they exhibit remarkably different bonding characteristics and phase behavior at ambient conditions. At room temperature, ${\mathrm{CO}}_2$ is a gas, whereas ${\mathrm{SiO}}_2$ is a covalent solid with rich polymorphs. A recent successful synthesis of the silicon-carbonate solid from the reaction between ${\mathrm{CO}}_2$ and ${\mathrm{SiO}}_2$ under high pressure [M. Santoro et al., Proc. Natl. Acad. Sci. U.S.A. 108, 7689 (2011)] has resolved a long-standing puzzle regarding whether a ${\mathrm{Si}}_x{\mathrm{C}}_{1-x}{\mathrm{O}}_2$ compound between ${\mathrm{CO}}_2$ and ${\mathrm{SiO}}_2$ exists in nature. Nevertheless, the detailed atomic structure of the ${\mathrm{Si}}_x{\mathrm{C}}_{1-x}{\mathrm{O}}_2$ crystal is still unknown. Here, we report an extensive search for the high-pressure crystalline structures of the ${\text{Si}}_x{\text{C}}_{1-x}{\text{O}}_2$ compound with various stoichiometric ratios (${\mathrm{SiO}}_2:{\mathrm{CO}}_2$) using an evolutionary algorithm. Based on the low-enthalpy structures obtained for each given stoichiometric ratio, several generic structural features and bonding characteristics of Si and C in the high-pressure phases are identified. The computed formation enthalpies show that the ${\mathrm{SiC}}_2{\mathrm{O}}_6$ compound with a multislab three-dimensional (3D) structure is energetically the most favorable at 20 GPa. Hence, a stable crystalline structure of the elusive ${\mathrm{Si}}_x{\mathrm{C}}_{1-x}{\mathrm{O}}_2$ compound under high pressure is predicted and awaiting future experimental confirmation. The ${\mathrm{SiC}}_2{\mathrm{O}}_6$ crystal is an insulator with elastic constants comparable to typical hard solids, and it possesses nearly isotropic tensile strength as well as extremely low shear strength in the 2D plane, suggesting that the multislab 3D crystal is a promising solid lubricant. These valuable mechanical and electronic properties endow the ${\mathrm{SiC}}_2{\mathrm{O}}_6$ crystal for potential applications in tribology and nanoelectronic devices, or as a stable solid-state form for ${\mathrm{CO}}_2$ sequestration.

In this article, we analyze the Casimir-Polder interaction of atoms with a solid grating and the repulsive interaction between the atoms and the grating in the presence of an external laser source. The Casimir-Polder potential is evaluated exactly in terms of Rayleigh reflection coefficients and via an approximate Hamaker approach. The laser-tuned repulsive interaction is given in terms of Rayleigh transmission coefficients. The combined potential landscape above the solid grating is probed locally by diffraction of Bose-Einstein condensates. Measured diffraction efficiencies reveal information about the shape of the potential landscape in agreement with the theory based on Rayleigh decompositions.

We discuss a renewal process in which successive events are separated by scale-free waiting time periods. Among other ubiquitous long-time properties, this process exhibits aging: events counted initially in a time interval $[0,t]$ statistically strongly differ from those observed at later times $[t_a,t_a+t]$. The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. In complex, disordered media, processes with scale-free waiting times play a particularly prominent role. We set up a unified analytical foundation for such anomalous dynamics by discussing in detail the distribution of the aging renewal process. We analyze its half-discrete, half-continuous nature and study its aging time evolution. These results are readily used to discuss a scale-free anomalous diffusion process, the continuous-time random walk. By this, we not only shed light on the profound origins of its characteristic features, such as weak ergodicity breaking, along the way, we also add an extended discussion on aging effects. In particular, we find that the aging behavior of time and ensemble averages is conceptually very distinct, but their time scaling is identical at high ages. Finally, we show how more complex motion models are readily constructed on the basis of aging renewal dynamics.

We demonstrate that femtosecond filaments can set up an extended and robust thermal waveguide structure in air with a lifetime of several milliseconds, making possible the very-long-range guiding and distant projection of high-energy laser pulses and high-average power beams. As a proof of principle, we demonstrate guiding of 110-mJ, 7-ns, 532-nm pulses with 90% throughput over $\sim 15$ Rayleigh lengths in a 70-cm-long air waveguide generated by the long time-scale thermal relaxation of an array of femtosecond filaments. The guided pulse was limited only by our available laser energy. In general, these waveguides should be robust against the effects of thermal blooming of extremely high-average-power laser beams.

Secure encryption is an essential feature of modern communications, but rapid progress in illicit decryption brings a continuing need for new schemes that are harder and harder to break. Inspired by the time-varying nature of the cardiorespiratory interaction, here we introduce a new class of secure communications that is highly resistant to conventional attacks. Unlike all earlier encryption procedures, this cipher makes use of the coupling functions between interacting dynamical systems. It results in an unbounded number of encryption key possibilities, allows the transmission or reception of more than one signal simultaneously, and is robust against external noise. Thus, the information signals are encrypted as the time variations of linearly independent coupling functions. Using predetermined forms of coupling function, we apply Bayesian inference on the receiver side to detect and separate the information signals while simultaneously eliminating the effect of external noise. The scheme is highly modular and is readily extendable to support different communications applications within the same general framework.

We propose a new class of tensor-network states, which we name projected entangled simplex states (PESS), for studying the ground-state properties of quantum lattice models. These states extend the pair-correlation basis of projected entangled pair states to a simplex. PESS are exact representations of the simplex solid states, and they provide an efficient trial wave function that satisfies the area law of entanglement entropy. We introduce a simple update method for evaluating the PESS wave function based on imaginary-time evolution and the higher-order singular-value decomposition of tensors. By applying this method to the spin-$1/2$ antiferromagnetic Heisenberg model on the kagome lattice, we obtain accurate and systematic results for the ground-state energy, which approach the lowest upper bounds yet estimated for this quantity.

Packings of hard polyhedra have been studied for centuries due to their mathematical aesthetic and more recently for their applications in fields such as nanoscience, granular and colloidal matter, and biology. In all these fields, particle shape is important for structure and properties, especially upon crowding. Here, we explore packing as a function of shape. By combining simulations and analytic calculations, we study three two-parameter families of hard polyhedra and report an extensive and systematic analysis of the densest known packings of more than 55 000 convex shapes. The three families have the symmetries of triangle groups (icosahedral, octahedral, tetrahedral) and interpolate between various symmetric solids (Platonic, Archimedean, Catalan). We find optimal (maximum) packing-density surfaces that reveal unexpected richness and complexity, containing as many as 132 different structures within a single family. Our results demonstrate the importance of thinking about shape not as a static property of an object, in the context of packings, but rather as but one point in a higher-dimensional shape space whose neighbors in that space may have identical or markedly different packings. Finally, we present and interpret our packing results in a consistent and generally applicable way by proposing a method to distinguish regions of packings and classify types of transitions between them.

Quantum fluctuations become particularly relevant in highly frustrated quantum magnets and can lead to new states of matter. We provide a simple and robust scenario for inducing magnetic vortex crystals in frustrated Mott insulators. By considering a quantum paramagnet that has a gapped spectrum with six-fold degenerate low-energy modes, we study the magnetic-field-induced condensation of these modes. We use a dilute gas approximation to demonstrate that a plethora of multi-$\mathbf{Q}$ condensates are stabilized for different combinations of exchange interactions. This rich quantum phase diagram includes magnetic vortex crystals, which are further stabilized by symmetric exchange anisotropies. Because skyrmion and domain-wall crystals have already been predicted and experimentally observed, this novel vortex phase completes the picture of emergent crystals of topologically nontrivial spin configurations.

The Green-Kubo formula relates the spatial diffusion coefficient to the stationary velocity autocorrelation function. We derive a generalization of the Green-Kubo formula that is valid for systems with long-range or nonstationary correlations for which the standard approach is no longer valid. For the systems under consideration, the velocity autocorrelation function $⟨v(t+\tau )v(t)⟩$ asymptotically exhibits a certain scaling behavior and the diffusion is anomalous, $⟨x^2(t)⟩\simeq 2D_{\nu }{t}^{\nu }$. We show how both the anomalous diffusion coefficient $D_{\nu }$ and the exponent $\nu$ can be extracted from this scaling form. Our scaling Green-Kubo relation thus extends an important relation between transport properties and correlation functions to generic systems with scale-invariant dynamics. This includes stationary systems with slowly decaying power-law correlations, as well as aging systems, systems whose properties depend on the age of the system. Even for systems that are stationary in the long-time limit, we find that the long-time diffusive behavior can strongly depend on the initial preparation of the system. In these cases, the diffusivity $D_{\nu }$ is not unique, and we determine its values, respectively, for a stationary or nonstationary initial state. We discuss three applications of the scaling Green-Kubo relation: free diffusion with nonlinear friction corresponding to cold atoms diffusing in optical lattices, the fractional Langevin equation with external noise recently suggested to model active transport in cells, and the Lévy walk with numerous applications, in particular, blinking quantum dots. These examples underline the wide applicability of our approach, which is able to treat very different mechanisms of anomalous diffusion.