The phrase “scale-free network” has become controversial in recent years, as network scientists debate what it means for a finite degree sequence to fit a power-law distribution. In practical terms, however, most network scientists use the phrase to indicate that a network has hubs, and so it would be useful to be able to talk about such networks without reference to power laws at all. This paper presents the Cooke-Nieboer index (CNI), a nonasymptotic measure of the heavy-tailedness of a network's empirical degree distribution which does not presume a power-law form. The CNI is easy to calculate and is able to distinguish between synthetic networks with power-law, exponential, and symmetric degree distributions. It serves as a complementary measure to the traditional tail-index estimators and reflects certain properties in real-life networks better than the estimators do.

Relativistic hydrodynamics is a powerful tool to simulate the evolution of the quark-gluon plasma in relativistic heavy-ion collisions. Using 10 000 initial and final profiles generated from $(2+1)$-dimensional relativistic hydrodynamics vish$2+1$ with Monte Carlo Glauber (MC-Glauber) initial conditions, we train a deep neural network based on the stacked U-net, and use it to predict the final profiles associated with various initial conditions, including MC-Glauber, MC Kharzeev-Levin-Nardi (MC-KLN), a multiphase transport (AMPT) model, and the reduced thickness event-by-event nuclear topology (TRENTo) model. A comparison with the vish$2+1$ results shows that the network predictions can nicely capture the magnitude and inhomogeneous structures of the final profiles, and creditably describe the related eccentricity distributions $P\left({\varepsilon }_n\right)$ $(n=2, 3, 4)$. These results indicate that a deep learning technique can capture the main features of the nonlinear evolution of hydrodynamics, showing its potential to largely accelerate the event-by-event simulations of relativistic hydrodynamics.

We develop a data-driven model discovery and system identification technique for spatially-dependent boundary value problems (BVPs). Specifically, we leverage the sparse identification of nonlinear dynamics (SINDy) algorithm and group sparse regression techniques with a set of forcing functions and corresponding state variable measurements to yield a parsimonious model of heterogeneous material systems. The technique models forced systems governed by linear or nonlinear operators of the form $L\left[u\right(x\left)\right]=f\left(x\right)$ on a prescribed domain $x\in [a,b]$. We demonstrate the approach on a range of example systems, including Sturm-Liouville operators, beam theory (elasticity), and a class of nonlinear BVPs. The generated data-driven model is used to infer the governing operator and spatially-dependent parameters that describe the heterogenous, physical quantities of the system. Our SINDy-BVP framework enables the characterization of a broad range of systems, including for instance, the discovery of anisotropic materials with heterogeneous variability.

Anisotropic particles are known to exhibit a richer and more complex phase behavior in comparison to their spherical counterpart. While the majority of the existing studies address structural properties, the dynamic behavior of anisotropic particles is a relatively lesser explored avenue. Using multispeckle ultra-small-angle x-ray photon correlation spectroscopy (USA-XPCS), we have carried out a systematic investigation of the structural and dynamic properties of colloidal ellipsoids at the nearest-neighbor length scale. The USA-XPCS measurements have allowed us to probe, as a function of the volume fraction, the $q$-dependent effective structure factor, $S_{\text{eff}}\left(q\right)$, along with the effective long time diffusion coefficient, $D_{\text{eff}}\left(q\right)$, for this anisotropic system. Our results indicate a scaling behavior of $D_{\text{eff}}\left(q\right)$ with $1/S_{\text{eff}}\left(q\right)$ from which we have estimated the effective amplitude function $A_{\text{eff}}\left(q\right)$, which can be directly related to the effective hydrodynamic function $H_{\text{eff}}\left(q\right)$. $A_{\text{eff}}\left(q\right)$ shows a similar $q$ dependence to that of $S\left(q\right)$. Our investigation also allows for the precise determination of the volume fraction corresponding to the arrest transition.

We present a parts-per-million test of quantum electrodynamics (QED) in the ${\text{HD}}^{+}$ molecular hydrogen ion, improving on previous tests based on vibrational and rotational transitions by factors of 76 and 1.4, respectively. The test is performed following a unified statistical approach that also produces improved constraints on physics beyond the standard model. We furthermore show how individual constraints derived from the various degrees of freedom in ${\text{HD}}^{+}$ and antiprotonic helium can be combined to enhance the sensitivity, thus ruling out “fifth forces” on the Ångstrom scale that are ${10}^{11}$ times weaker than the electromagnetic interaction.

Understanding the emergent nonequilibrium dynamics of collective units is crucial for steering and engineering active many-body systems. Here, we explore flow transitions and topological defect dynamics of channel-confined active nematics under chiral boundary anchoring. We discover that the anchoring chirality can engender unanticipated solitonlike defect clusters, where activity-excited topological defects self-localize into small cohesive clusters that unidirectionally propagate as dynamically stable solitons. Defects continuously move, nucleate, and annihilate locally, which causes periodic cluster reconfiguration and energy oscillations, reflecting the structural degeneracy of defect clusters. The boundary anchoring chirality not only determines the direction of background active flows but also remarkably speeds them up, which underlies the emergence of solitonlike defect clusters. We further show that the periodicity and structural reconfiguration of defect clusters can be tuned using specified initial orientation fields. These findings could motivate direct programmatic control strategies for engineered active materials and provide insights into the collective behaviors of living organisms within confining tracks during life processes.

We introduce a response theory for open quantum systems within nonequilibrium steady states subject to a Hamiltonian perturbation. Working in the weak system-bath coupling regime, our results are derived within the Lindblad-Gorini-Kossakowski-Sudarshan formalism. We find that the response of the system to a small perturbation is not simply related to a correlation function within the system, unlike traditional linear response theory in closed systems or expectations from the fluctuation-dissipation theorem. In limiting cases, when the perturbation is small relative to the coupling to the surroundings or when it does not lead to a change of the eigenstructure of the system, a perturbative expansion exists where the response function is related to a sum of a system correlation functions and additional forces induced by the surroundings. Away from these limiting regimes, however, the secular approximation results in a singular response that cannot be captured within the traditional approach but can be described by reverting to a microscopic Hamiltonian description. These findings are illustrated by explicit calculations in coupled qubits and anharmonic oscillators in contact with bosonic baths at different temperatures.

Quantum communication is an important application that derives from the burgeoning field of quantum information and quantum computation. Focusing on secure communication, quantum cryptography has two major directions of development, namely quantum key distribution and quantum encryption. In this work we propose a quantum encryption protocol that utilizes a quantum algorithm to create blocks of ciphertexts based on quantum states. The main feature of our quantum encryption protocol is that the encryption configuration of each block is determined by the previous blocks, such that additional security is provided. We then demonstrate our method by an example model encrypting the English alphabet, with numerical simulation results showing the large error rate of a mock attack by a potential adversary. The safety of the encryption method is further demonstrated against several possible attack models. With the improvements against noises, our quantum encryption protocol is a capable addition to the toolbox of quantum cryptography.

We establish time-resolved high harmonic generation (tr-HHG) as a powerful spectroscopy method for tracking photoinduced dynamics in strongly correlated materials through a detailed investigation of the insulator-to-metal phase transitions in vanadium dioxide. We benchmark the technique by comparing our measurements to established momentum-resolved ultrafast electron diffraction, and theoretical density functional calculations. Tr-HHG allows distinguishing of individual dynamic channels, including a transition to a thermodynamically hidden phase. In addition, the HHG yield is shown to be modulated at a frequency characteristic of a coherent phonon of the equilibrium monoclinic phase over a wide range of excitation fluences. These results demonstrate that tr-HHG is capable of tracking complex dynamics in solids through its sensitivity to the band structure.

In social networks, interaction patterns typically change over time. We study opinion dynamics on tie-decay networks in which tie strength increases instantaneously when there is an interaction and decays exponentially between interactions. Specifically, we formulate continuous-time Laplacian dynamics and a discrete-time DeGroot model of opinion dynamics on these tie-decay networks, and we carry out numerical computations for the continuous-time Laplacian dynamics. We examine the speed of convergence by studying the spectral gaps of combinatorial Laplacian matrices of tie-decay networks. First, we compare the spectral gaps of the Laplacian matrices of tie-decay networks that we construct from empirical data with the spectral gaps for corresponding randomized and aggregate networks. We find that the spectral gaps for the empirical networks tend to be smaller than those for the randomized and aggregate networks. Second, we study the spectral gap as a function of the tie-decay rate and time. Intuitively, we expect small tie-decay rates to lead to fast convergence because the influence of each interaction between two nodes lasts longer for smaller decay rates. Moreover, as time progresses and more interactions occur, we expect eventual convergence. However, we demonstrate that the spectral gap need not decrease monotonically with respect to the decay rate or increase monotonically with respect to time. Our results highlight the importance of the interplay between the times that edges strengthen and decay in temporal networks.

We predict the existence of the Einstein-de Haas effect in topological magnon insulators. Temperature variation of angular momentum in the topological state shows a sign change behavior, akin to the low temperature thermal Hall conductance response. This manifests itself as a macroscopic mechanical rotation of the material hosting topological magnons. We show that an experimentally observable Einstein-de Haas effect can be measured in the square-octagon, the kagome, and the honeycomb lattices. Albeit, the effect is the strongest in the square-octagon lattice. We treat both the low and the high temperature phases using spin wave and Schwinger boson theory, respectively. We propose an experimental set up to detect our theoretical predictions. We suggest candidate square-octagon materials where our theory can be tested.

Coherent control of quantum transitions—indispensable in quantum technology—generally relies on the interaction of quantum systems with electromagnetic radiation. Here, we theoretically demonstrate that the nonradiative electromagnetic near field of a temporally modulated free-space electron beam can be utilized for coherent control of quantum systems. We show that such manipulation can be performed with only classical control over the electron beam itself and is readily realizable with current technology. This approach may provide a pathway toward spectrally selective quantum control with nanoscale spatial resolution, harnessing the small de Broglie wavelength of electrons.

In the Hamiltonian-based quantum dynamics, to estimate Hamiltonians from the measured data is a vital topic. In this work, we propose a recurrent neural network to learn the target Hamiltonians from the temporal records of single-qubit measurements, which does not require the ground states and only measures single-qubit observables. It is applicable on both time-independent and time-dependent Hamiltonians and can simultaneously capture the magnitude and sign of Hamiltonian parameters. Taking the Hamiltonians with the nearest-neighbor interactions as numerical examples, we trained our recurrent neural networks to learn different types of Hamiltonians with high accuracy. The study also shows that our method has good robustness against the measurement noise and decoherence effect. Therefore, it has widespread applications in estimating the parameters of quantum devices and characterizing the Hamiltonian-based quantum dynamics.

We investigate the effects of interaction for the stripe phase of a homogeneous one-dimensional Bose gas with laser-induced Raman spin-orbit coupling (SOC) and Zeeman splitting, for a wide range of densities. In order to account for quantum fluctuations, important in one dimension for low densities close to the Tonks-Girardeau limit, we use a variational method based on the hypernetted-chain Euler-Lagrange optimization of a Jastrow-Feenberg ansatz for the many-body wave function. For strong coupling we observe significant deviations from mean-field results not only quantitatively but also qualitatively. The main interest of this paper lies in the interplay and competition between interaction-induced pair correlations and the SOC-induced density oscillations of the stripe phase. We explain the increase in wave number of this density oscillation with increasing interaction due to an effective attraction between particles in the many-body system.

The variational quantum eigensolver (VQE) is an algorithm to find eigenenergies and eigenstates of systems in quantum chemistry and quantum many-body physics. The VQE is one of the most promising applications of near-term quantum devices to investigate such systems. Here we propose an extension of the VQE to calculate the nonadiabatic couplings of molecules in quantum chemical systems and Berry's phase in quantum many-body systems. Both quantities play an important role in understanding the properties of a system beyond the naive adiabatic picture, e.g., nonadiabatic dynamics and topological phase of matter. We provide quantum circuits and classical postprocessings to calculate the nonadiabatic couplings and Berry's phase. Specifically, we show that the evaluation of the nonadiabatic couplings reduces to that of expectation values of observables while that of Berry's phase also requires one additional Hadamard test. Furthermore, we simulate the photodissociation dynamics of a lithium fluoride molecule using the nonadiabatic couplings evaluated on a real quantum device. Our proposal widens the applicability of the VQE and the possibility of near-term quantum devices to study molecules and quantum many-body systems.

The canonical commutation relation is the hallmark of quantum theory, and Heisenberg's uncertainty relation is a direct consequence of it. Although various formulations of uncertainty relations have been tested in experiments a direct test of the commutation relation has hitherto not been performed. The reason for this is that whereas in quantum mechanics, observables are usually represented by Hermitian operators, the product of two noncommuting observables as occurring in the commutator relation is, in general, non-Hermitian. Here, we present a theoretical scheme for a direct test of the commutation relation and report its experimental realization. More precisely, we provide an experimental verification of the canonical commutation relation between two qubit observables based on a measurement scheme widely known as “weak measurement.” In our neutron interferometric setup, we perform the measurement of a single anomalous weak value of a relevant path-qubit observable where the coupled spin-energy degree of freedom serves as an ancilla.

We consider the wave-structure coupling between an acoustic orbital angular momentum beam and a rapidly rotating disk, and present a new configuration exhibiting the wave amplification effect known as rotational superradiance. While initially envisioned in terms of the scattering of an incident wave directed perpendicular to an object's rotation axis, we demonstrate in the context of acoustomechanics that superradiant amplification can also occur with a vortex beam directed parallel to the rotation axis. We propose two different experimental routes: one must either work with rotations high enough that the tangential velocity at the outer edge of the disk exceeds the speed of sound, or use evanescent sound waves. We argue that the latter possibility is more promising, and provides the opportunity to probe a previously unexamined parameter regime in the acoustics of rotating porous media.

Given the rapidly evolving landscape of linguistic prevalence, whereby a majority of the world's existing languages are dying out in favor of the adoption of a comparatively fewer set of languages, the factors behind this phenomenon have been the subject of vigorous research. The majority of approaches investigate the temporal evolution of two competing languages in the form of differential equations describing their behavior at a large scale. In contrast, relatively few consider the spatial dimension of the problem. Furthermore while much attention has focused on the phenomena of language shift—the adoption of majority languages in lieu of minority ones—relatively less light has been shed on linguistic coexistence, where two or more languages persist in a geographically contiguous region. Here, we study the geographical component of language spread on a discrete medium to monitor the dispersal of language species at a microscopic level. Language dynamics is modeled through a reaction-diffusion system that occurs on a heterogeneous network of contacts based on population flows between urban centers. We show that our framework accurately reproduces empirical linguistic trends driven by a combination of the Turing instability, a mechanism for spontaneous pattern-formation applicable to many natural systems, the heterogeneous nature of the contact network, and the asymmetries in how people perceive the status of a language. We demonstrate the robustness of our formulation on two datasets corresponding to linguistic coexistence in the northwestern part of Spain and the southern part of Austria.

The EMC effect in deuterium and helium-3 is studied using a convolution formalism that allows isolating the impact of high-momentum nucleons in short-ranged correlated (SRC) pairs. We assume that the modification of the structure function of bound nucleons is given by a universal (i.e., nucleus independent) function of their virtuality, and find that the effect of such modifications is dominated by nucleons in SRC pairs. This SRC-dominance of nucleon modifications is observed despite the fact that the bulk of the nuclear inelastic scattering cross-section comes from interacting with low-momentum nucleons. These conclusions are found to be robust to model details including nucleon modification function parametrization, free nucleon structure function, and treatment of nucleon motion effects. While existing data cannot discriminate between such model details, we present predictions for measured, but not yet published, tritium EMC effect and tagged nucleon structure functions in deuterium that are sensitive to the neutron structure functions and bound nucleon modification functions.