Entanglement properties of bipartite unitary operators are studied via their local invariants, namely the entangling power $e_p$ and a complementary quantity, the gate typicality $g_t$. We characterize the boundaries of the set $K_2$ representing all two-qubit gates projected onto the plane $(e_p,g_t)$ showing that the fractional powers of the swap operator form a parabolic boundary of $K_2$, while the other bounds are formed by two straight lines. In this way, a family of gates with extreme properties is identified and analyzed. We also show that the parabolic curve representing powers of swap persists in the set $K_N$ for gates of higher dimensions ($N>2$). Furthermore, we study entanglement of bipartite quantum gates applied sequentially $n$ times, and we analyze the influence of interlacing local unitary operations, which model generic Hamiltonian dynamics. An explicit formula for the entangling power of a gate applied $n$ times averaged over random local unitary dynamics is derived for an arbitrary dimension of each subsystem. This quantity shows an exponential saturation to the value predicted by the random matrix theory, indicating “thermalization” in the entanglement properties of sequentially applied quantum gates that can have arbitrarily small, but nonzero, entanglement to begin with. The thermalization is further characterized by the spectral properties of the reshuffled and partially transposed unitary matrices.

Bistable microelectrodes with an S-shaped current-voltage characteristic have recently been shown to oscillate under current control, when connected in parallel. In other systems with equivalently coupled bistable components, such oscillatory instabilities have not been reported. In this paper, we derive a general criterion for when an ensemble of coupled bistable components may become oscillatorily unstable. Using a general model, we perform a stability analysis of the ensemble equilibria, in which the components always group in three or fewer clusters. Based thereon, we give a necessary condition for the occurrence of collective oscillations. Moreover, we demonstrate that stable oscillations may persist for an arbitrarily large number of components, even though, as we show, any equilibrium with two or more components on the middle, autocatalytic branch is unstable.

While linear response theory, manifested by the fluctuation dissipation theorem, can be applied at any level of coarse-graining, nonlinear response theory is fundamentally of a microscopic nature. For perturbations of equilibrium systems, we develop an exact theoretical framework for analyzing the nonlinear (second-order) response of coarse-grained observables to time-dependent perturbations, using a path-integral formalism. The resulting expressions involve correlations of the observable with coarse-grained path weights. The time-symmetric part of these weights depends on the paths and perturbation protocol in a complex manner; in addition, the absence of Markovianity prevents slicing of the coarse-grained path integral. We show that these difficulties can be overcome and the response function can be expressed in terms of path weights corresponding to a single-step perturbation. This formalism thus leads to an extrapolation scheme where measuring linear responses of coarse-grained variables suffices to determine their second-order response. We illustrate the validity of the formalism with an exactly solvable four-state model and the near-critical Ising model.

Symmetric informationally complete measurements (SICs) are elegant, celebrated, and broadly useful discrete structures in Hilbert space. We introduce a more sophisticated discrete structure compounded by several SICs. A SIC compound is defined to be a collection of $d^3$ vectors in $d$-dimensional Hilbert space that can be partitioned in two different ways: into $d$ SICs and into $d^2$ orthonormal bases. While a priori their existence may appear unlikely when $d>2$, we surprisingly find an explicit construction for $d=4$. Remarkably this SIC compound admits a close relation to mutually unbiased bases, as is revealed through quantum state discrimination. Going beyond fundamental considerations, we leverage these exotic properties to construct a protocol for quantum key distribution and analyze its security under general eavesdropping attacks. We show that SIC compounds enable secure key generation in the presence of errors that are large enough to prevent the success of the generalization of the six-state protocol.

The spin excitations of the $S=1/2$ anisotropic triangular antiferromagnet ${\mathrm{Ca}}_3\mathrm{Re}{\mathrm{O}}_5{\mathrm{Cl}}_2$ were investigated by inelastic neutron-scattering experiments. The spin excitation spectrum exhibits sharp dispersive modes in addition to a spinonlike continuum. The sharp modes exhibit large and small dispersions along the intrachain ($K$) and interchain directions ($L$), respectively, reflecting a one-dimensional character modified by interchain interactions. The dispersion intensity along the interchain direction is enhanced at the wave vectors around ($K, L)=(0.25,\pm 1.0)$ and (0.75, 0.0) (in reciprocal lattice units, r.l.u.). This enhancement is well explained by the formation of bound spinon pairs. These features are reminiscent of the spin excitations observed in the prototypical compound ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Cl}}_4$ [Coldea, et al., Phys. Rev. Lett. 86, 1335 (2001); Phys. Rev. B 68, 134424 (2003)]. The consistency with the simulated spectrum based on the random-phase approximation is better for ${\mathrm{Ca}}_3\mathrm{Re}{\mathrm{O}}_5{\mathrm{Cl}}_2$ than for ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Cl}}_4$, indicating that the spin system in the former remains closer to a Tomonaga-Luttinger liquidlike disordered state. In addition, the low-energy modes exhibit a wave-vector shift along the $\pm K$ direction, suggesting that uniform intrachain Dzyaloshinskii-Moriya interactions are more relevant in ${\mathrm{Ca}}_3\mathrm{Re}{\mathrm{O}}_5{\mathrm{Cl}}_2$.

Social hierarchy is central to decision-making in the coordinated movement of many swarming species. Here we propose a hierarchical swarm model in the spirit of the Vicsek model of self-propelled particles. We show that, as the hierarchy becomes important, the swarming transition changes from the weak first-order transition observed for egalitarian populations, to a stronger first-order transition for intermediately strong hierarchies, and finally the discontinuity reduces until vanish, where the order-disorder transition appears to be absent in the extremely despotic societies. Associated to this we observe that the spatial structure of the swarm, as measured by the correlation between the density and velocity fields, is strongly mediated by the hierarchy. A two-group model and vectorial noise are also studied for verification. Our results point out the particular relevance of the hierarchical structures to swarming transitions when doing specific case studies.

A IV-VI compound SnTe is proposed to be a topological crystalline insulator (TCI), and the band structures have been studied by using angle-resolved photoemission spectroscopy (ARPES). However, the topological surface states (TSSs) that hallmark the nontrivial topology disperse mostly in the unoccupied side where access via ARPES is limited. Here we investigate the (111) face of a SnTe film by using pump-probe ARPES. We find distinct energy sections in the unoccupied side that behave differently in terms of the excitation and recovery dynamics. From these different behaviors, the boundaries of these sections are attributed to the edges of the conduction and valence bands. High statistics data reveal that the TSSs are traversing the band gap, which evidences that SnTe belongs to a TCI. We also find that the bulk bands near the gap show splitting, which is attributed to the Rashba effect occurring in the dipolar surface region.

We study the relaxation of linear polymer molecules following fast uniaxial extension. Polystyrene melts of $M_w=80$ kg/mol are elongated at a Rouse-Weissenberg number ${\text{Wi}}_R=1.5$ to Hencky strain $\varepsilon =3$, where steady state is approached using a filament stretch rheometer. Samples were quenched for different duration of stress relaxation at constant Hencky strain to preserve molecular conformation by rapid cooling below the glass transition temperature. Expansion of ex situ small-angle neutron-scattering data in spherical harmonics shows experimental evidence for the decoupling of local and global relaxation phenomena from highly stretched states. This work demonstrates both that the decoupling can be seen in the spherical harmonics expansion and that it can be seen even for short chains provided the initial state is highly oriented.

We propose a method to generate multimode N00N states with arrays of ultracold atoms. Our protocol requires a strong relative offset among the wells and a drive of the interparticle interaction at a frequency resonant with the offsets. The proposal is demonstrated by a numerical and a Floquet analysis of the quantum dynamics of a ring-shaped atomtronics circuit made of $M$ weakly coupled optical traps. We generate a hierarchy of energy scales down to very few low-energy states where N00N dynamics takes place, making multimode N00N states appear at nearly regular time intervals. The production of multimode N00N states can be probed by time-of-flight imaging. Such states may be used to build a multiple beam splitter.

The flourishing of fake news is supported by recommendation algorithms of online social networks, which, based on previous user activity, provide content adapted to their preferences and so create filter bubbles. We introduce an analytically tractable voter model with personalized information, in which an external field tends to align the agent's opinion with the one she held more frequently in the past. Our model shows a surprisingly rich dynamics despite its simplicity. An analytical mean-field approach, confirmed by numerical simulations, allows us to build a phase diagram and to predict if and how consensus is reached. Remarkably, polarization can be avoided only for weak interaction with personalized information and if the number of agents is below a threshold. We compute analytically this critical size, which depends on the interaction probability in a strongly nonlinear way.

Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four distinct degree distributions, we show that the spectral density of the adjacency matrices of dense random networks is determined by the strength of the degree fluctuations. In particular, the eigenvalue distribution of dense networks with an exponential degree distribution is governed by a simple equation, from which we uncover a logarithmic singularity in the spectral density. We also derive a relation between the fourth moment of the eigenvalue distribution and the variance of the degree distribution, which leads to a sufficient condition for the breakdown of the Wigner semicircle law for dense random networks. Based on the same relation, we propose a classification scheme of the distinct universal behaviors of the spectral density in the dense limit. Our theoretical findings should lead to important insights on the mean-field behavior of models defined on graphs.

In this paper, we investigate and develop scaling laws as a function of external nondimensional control parameters for heat and momentum transport for nonrotating, slowly rotating, and rapidly rotating turbulent convection systems, with the end goal of forging connections and bridging the various gaps between these regimes. Two perspectives are considered, one where turbulent convection is viewed from the standpoint of an applied temperature drop across the domain and the other with a viewpoint in terms of an applied heat flux. While a straightforward transformation exists between the two perspectives, indicating equivalence, it is found the former provides a clear set of connections that bridge between the three regimes. Our generic convection scalings, based upon an inertial-Archimedean balance, produce the classic diffusion-free scalings for the nonrotating limit and the slowly rotating limit. This is characterized by a free-falling fluid parcel on the global scale possessing a thermal anomaly on par with the temperature drop across the domain. In the rapidly rotating limit, the generic convection scalings are based on a Coriolis-inertial-Archimedean (CIA) balance, along with a local fluctuating-mean advective temperature balance. This produces a scenario in which anisotropic fluid parcels attain a thermal wind velocity and where the thermal anomalies are greatly attenuated compared to the total temperature drop. We find that turbulent scalings may be deduced simply by consideration of the generic nondimensional transport parameters—local Reynolds ${\text{Re}}_{\ell }=U\ell /\nu$; local Péclet ${\text{Pe}}_{\ell }=U\ell /\kappa$; and Nusselt number $\text{Nu}=U\vartheta /(\kappa \mathrm{\Delta }T/H)$—through the selection of physically relevant estimates for length $\ell$, velocity $U$, and temperature scales $\vartheta$ in each regime. Emergent from the scaling analyses is a unified continuum based on a single external control parameter, the convective Rossby number, ${\text{Ro}}_C=\sqrt{g\alpha \mathrm{\Delta }T/4{\mathrm{\Omega }}^{2}H}$, that strikingly appears in each regime by consideration of the local, convection-scale Rossby number ${\text{Ro}}_{\ell }=U/\left(2\mathrm{\Omega }\ell \right)$. Thus we show that ${\text{Ro}}_C$ scales with the local Rossby number ${\text{Ro}}_{\ell }$ in both the slowly rotating and the rapidly rotating regimes, explaining the ubiquity of ${\text{Ro}}_C$ in rotating convection studies. We show in non-, slowly, and rapidly rotating systems that the convective heat transport, parametrized via ${\text{Pe}}_{\ell }$, scales with the total heat transport parameterized via the Nusselt number Nu. Within the rapidly rotating limit, momentum transport arguments generate a scaling for the system-scale Rossby number, ${\text{Ro}}_H$, that, recast in terms of the total heat flux through the system, is shown to be synonymous with the classical flux-based CIA scaling, ${\text{Ro}}_{\text{CIA}}$. These, in turn, are then shown to asymptote to ${\text{Ro}}_H\sim {\text{Ro}}_{\text{CIA}}\sim {\text{Ro}}_C^2$, demonstrating that these momentum transport scalings are identical in the limit of rapidly rotating turbulent heat transfer.

Knowledge of the ground state of a homogeneous quantum many-body system can be used to find the exact ground state of a dual inhomogeneous system with a confining potential. We first identify the complete family of one-dimensional parent Hamiltonians with a ground state of Bijl-Jastrow form in free space. For each instance in this family, the dual trapped system is shown to include a one-body harmonic potential and two-body long-range interactions. The extension to anharmonic potentials and quantum solids with Nosanov-Jastrow ground-state wave functions is also presented. We apply this exact mapping to construct eigenstates of trapped systems from free-space solutions for different choices of the pair correlation functions entering the Bijl-Jastrow form. This construction is user friendly and allows one to readily rederive known instances of quasisolvable and integrable models, as well as to introduce unexplored examples. Among the latter, we describe a Lieb-Liniger-Coulomb model whose exact ground state is a McGuire soliton solution embedded in a harmonic trap.

Link prediction is a paradigmatic problem in network science with a variety of applications. In latent space network models this problem boils down to ranking pairs of nodes in the order of increasing latent distances between them. The network model with hyperbolic latent spaces has a number of attractive properties suggesting it must be a powerful tool to predict links, but the past work in this direction reported mixed results. Here we perform a systematic investigation of the utility of latent hyperbolic geometry for link prediction in networks. We first show that some measures of link prediction accuracy are extremely sensitive with respect to inaccuracies in the inference of latent hyperbolic coordinates of nodes. This observation leads us to the development of a hyperbolic network embedding method, the hyperlink embedder, which we show maximizes the accuracy of such inference, compared to existing hyperbolic embedding methods. Applying this method to synthetic and real networks, we then find that when it comes to predicting obvious missing links hyperbolic link prediction—for short, hyperlink—is rarely the best but often competitive, compared to a multitude of other methods. However, hyperlink appears to be at its best, maximizing its competitive power, when the task is to predict less obvious missing links that are really hard to predict. These links include missing links in incomplete networks with large fractions of missing links, missing links between nodes that do not have any common neighbors, and missing links between dissimilar nodes at large latent distances. Overall these results suggest that the harder a specific link prediction task the more seriously one should consider using hyperbolic geometry.

We study what kind of topological crystalline insulator phase emerges from nodal line semimetal phases in the face centered cubic system, which is not indicated by topological indices when spin-orbit coupling (SOC) is introduced. We construct an effective model, which hosts two different nodal lines phases, and calculated mirror Chern numbers in it by introducing SOC. As a result, we find that the two nodal line phases with different nodal line configurations are mapped to different topological crystalline insulator phases. This result shows that turning off SOC and checking the nodal line configuration can distinguish the two topological crystalline insulator phases, which have not been distinguished by previous methods.

A novel rheoscopic fluid displaying coloration due to flow-induced birefringence is investigated through laboratory experiments to ascertain if it satisfies the stress-optic law in fluids in direct stress field measurements of Newtonian fluids. To validate this experimentally, two types of spin-up experiments ensuring two-dimensional flows were performed: color visualization using the rheoscopic fluid and velocity field measurement by particle image velocimetry. Using a wave-number analysis, the orientation angle of the birefringence was determined from a single color snapshot in axisymmetric and unidirectional flows. Direct comparisons between color and shear stress values made it possible to establish a unique relation between the two, verifying that the stress-optic law can be applied in the fluid. The results of the present study suggest a promising avenue toward enabling temporally and spatially resolved stress field measurements in Newtonian fluids.

We apply a microscopic theory of polarization and magnetization to crystalline insulators at zero temperature and consider the orbital electronic contribution of the linear response to spatially varying, time-dependent electromagnetic fields. The charge and current density expectation values generally depend on both the microscopic polarization and magnetization fields, and on the microscopic free charge and current densities. But contributions from the latter vanish in linear response for the class of insulators we consider. Thus we need only consider the former, which can be decomposed into “site” polarization and magnetization fields, from which “site multipole moments” can be constructed. Macroscopic polarization and magnetization fields follow, and we identify the relevant contributions to them; for electromagnetic fields varying little over a lattice constant these are the electric and magnetic dipole moments per unit volume, and the electric quadrupole moment per unit volume. A description of optical activity and related magneto-optical phenomena follows from the response of these macroscopic quantities to the electromagnetic field and, while in this paper we work within the independent particle and frozen-ion approximations, both optical rotary dispersion and circular dichroism can be described with this strategy. Earlier expressions describing the magnetoelectric effect are recovered as the zero frequency limit of our more general equations. Since our site quantities are introduced with the use of Wannier functions, the site multipole moments and their macroscopic analogs are generally gauge dependent. However, the resulting macroscopic charge and current densities, together with the optical effects to which they lead, are gauge invariant, as would be physically expected.

Using a semianalytic guided-mode expansion technique, we present theory and analysis of intrinsic propagation losses for topological photonic crystal slab waveguide structures with modified honeycomb lattices of circular or triangular holes. Although conventional photonic crystal waveguide structures, such as the W1 waveguide, have been designed to have lossless propagation modes, they are prone to disorder-induced losses and backscattering. Topological structures have been proposed to help mitigate this effect as their photonic edge states may allow for topological protection. However, the intrinsic propagation losses of these structures are not well understood and the concept of the light line can become blurred. For four example topological edge state structures, photonic band diagrams, loss parameters, and electromagnetic fields of the guided modes are computed. Two of these structures, based on armchair edge states, are found to have significant intrinsic losses for modes inside the photonic bandgap, more than 100 dB/cm, which is comparable to or larger than typical disorder-induced losses using slow-light modes in conventional photonic crystal waveguides, while the other two structures, using the valley Hall effect and inversion symmetry, are found to have a good bandwidth for exploiting lossless propagation modes below the light line (at least in the absence of disorder).

We study the effect of the competition between disorder and stress enhancement in fracture processes using the local load sharing fiber bundle model, a model that hovers on the border between analytical tractability and numerical accessibility. We implement a disorder distribution with one adjustable parameter. The model undergoes a localization transition as a function of this parameter. We identify an order parameter for this transition and find that the system is in the localized phase over a finite range of values of the parameter bounded by a transition to the nonlocalized phase on both sides. The transition is of first order at one side and of second order at the other. The critical exponents characterizing the second-order transition are close to those characterizing the percolation transition. We determine the spatiotemporal correlation function in the localized phase. It is characterized by two power laws as in invasion percolation. We find exponents that are consistent with the values found in that problem.

We consider a quantum walk where a detector repeatedly probes the system with fixed rate $1/\tau$ until the walker is detected. This is a quantum version of the first-passage problem. We focus on the total probability $P_{\det }$ that the particle is eventually detected in some target state, for example, on a node $r_{\mathrm{d}}$ on a graph, after an arbitrary number of detection attempts. Analyzing the dark and bright states for finite graphs and more generally for systems with a discrete spectrum, we provide an explicit formula for $P_{\det }$ in terms of the energy eigenstates which is generically $\tau$ independent. We find that disorder in the underlying Hamiltonian renders perfect detection, $P_{\det }=1$, and then expose the role of symmetry with respect to suboptimal detection. Specifically, we give a simple upper bound for $P_{\det }$ that is controlled by the number of equivalent (with respect to the detection) states in the system. We also extend our results to infinite systems, for example, the detection probability of a quantum walk on a line, which is $\tau$ dependent and less than half, well below Polya's optimal detection for a classical random walk.