We observe a set of three replica luminescent peaks at ∼21.4 meV below the dark exciton, and negative and positive dark trions (or exciton polarons) in monolayer $\mathrm{WS}{\mathrm{e}}_2$. The replica redshift energy matches the energy of the zone-center $E^{\prime \prime }$-mode optical phonons. The phonon replicas exhibit a parallel gate dependence and the same $g$-factors as the dark excitonic states, but follow the valley selection rules of the bright excitonic states. While the dark states exhibit an out-of-plane transition dipole and valley-independent linearly polarized emission in the in-plane directions, their phonon replicas exhibit an in-plane transition dipole and valley-dependent circularly polarized emission in the out-of-plane directions. Our results and symmetry analysis show that the $K$-valley dark exciton decays into a left-handed chiral phonon and a right-handed photon, whereas the $K^{\prime }$-valley dark exciton decays into a right-handed chiral phonon and a left-handed photon. Such valley selection rules of chiral phonon replicas can be utilized to identify the valleys of the dark excitonic states and explore their chiral interactions with phonons.

The information convex allows us to look into certain information-theoretic constraints in two-dimensional topological orders. We provide a derivation of the topological contribution $ln{d}_a$ to the von Neumann entropy, where $d_a$ is the quantum dimension of anyon $a$. This value emerges as the only value consistent with strong subadditivity, assuming a certain topological dependence of the information convex structure. In particular, it is assumed that the fusion multiplicities are coherently encoded in a two-hole disk. A similar contribution ($ln{d}_{\alpha }$) is derived for gapped boundaries. This method further allows us to identify the fusion probabilities and certain constraints on the fusion theory. We also derive a linear bound on the circuit depth of unitary non-Abelian string operators and discuss how it generalizes and changes in the presence of a gapped boundary.

We show that the failure time ${\tau }_f$ in the fiber bundle model, taken as a prototype of heterogeneous materials, depends crucially on the strength of the disorder $\delta$ and the stress release range $R$ in the model. In the mean-field limit, the distribution of ${\tau }_f$ is log-normal. In this limit, the average failure time shows the variation ${\tau }_f\sim L^{\alpha \left(\delta \right)}$, where $L$ is the system size. The exponent $\alpha$ has a constant value above a critical disorder ${\delta }_c$ ($=1/6$), while it is an increasing function of $\delta$ in the region $\delta <{\delta }_c$. On the other hand, in the limit where the local stress concentration plays a crucial role, we observe the scaling ${\tau }_f\sim L^{\alpha \left(\delta \right)}\mathrm{\Phi }(R/L^{1-\alpha \left(\delta \right)})$, where $R$ is the stress release range. We find that the crossover length scale $R_c$, between the above two limiting cases, scales as $R_c\sim L^{1-\alpha \left(\delta \right)}$.

Strong coupling of electric transition dipoles with optical or plasmonic resonators modifies their light-matter interaction and, therefore, their optical spectra. Semiconducting $\mathrm{W}{\mathrm{S}}_2$ nanotubes intrinsically provide the dipoles through their excitonic resonances, and the optical cavity via their cylindrical shape. We investigate the nonequilibrium light-matter interaction in $\mathrm{W}{\mathrm{S}}_2$ nanotubes in the time domain using femtosecond transient extinction spectroscopy. We develop a phenomenological coupled oscillator model with time-dependent parameters to describe the transient extinction spectra, allowing us to extract the underlying nonequilibrium electron dynamics. We find that the exciton and trion resonances shift due to many-body effects of the photogenerated charge carriers and their population dynamics on the femto- and picosecond timescale. Our results show that the time-dependent phenomenological model quantitatively reproduces the nonequilibrium optical response of strongly coupled systems.

We report on a chiral observable upon ionization of a chiral molecule (methyloxirane) by a strong elliptically polarized laser field: a rotation of the photoelectron momentum distribution, which is enantiosensitive and forward/backward asymmetric. We explain this forward/backward asymmetric rotation of the count maxima to be equivalent to a dependence of the photoelectron circular dichroism on the electron emission angle in the plane of polarization.

There is a remarkable interest in the study of out-of-time ordered correlators (OTOCs) that goes from many-body theory and high-energy physics to quantum chaos. In the latter case there is a special focus on the comparison with the traditional measures of quantum complexity such as the spectral statistics. The exponential growth has been verified for many paradigmatic maps and systems. However, less is known for multipartite cases. On the other hand, the recently introduced Wigner separability entropy (WSE) and its classical counterpart provide a complexity measure that treats equally quantum and classical distributions in phase space. We compare the behavior of these measures in a system consisting of two coupled and perturbed cat maps with different dynamics: double hyperbolic, double elliptic, and mixed. In all cases, we find that the OTOCs and the WSE have essentially the same behavior, providing a complete characterization in generic bipartite systems and at the same time revealing them as very good measures of quantum complexity for phase-space distributions. Moreover, we establish a relation between both quantities by means of a recently proven theorem linking the second Rényi entropy and OTOCs.

We study the dynamics and pairwise interactions of dark soliton stripes in the two-dimensional defocusing nonlinear Schrödinger equation. By employing a variational approach we reduce the dynamics for dark soliton stripes to a set of coupled one-dimensional “filament” equations of motion for the position and velocity of the stripe. The method yields good qualitative agreement with the numerical results for the transverse instability of the stripes. We propose a phenomenological amendment that also significantly improves the quantitative agreement of the method with the computations. Subsequently, the method is extended for a pair of symmetric dark soliton stripes that include the mutual interactions between the filaments. The reduced equations of motion are compared with a recently proposed adiabatic invariant method and its corresponding findings and are found to provide a more adequate representation of the original full dynamics for a wide range of cases encompassing perturbations with long and short wavelengths, and combinations thereof.

Community structure and interaction delays are common features of ensembles of network coupled oscillators, but their combined effect on the emergence of synchronization has not been studied in detail. We study the transitions between macroscopic states in coupled oscillator systems with community structure and time delays. We show that the combination of these two properties gives rise to nonmonotonic transitions, whereby increasing the global coupling strength can both inhibit and promote synchronization, yielding both desynchronization and synchronization transitions. For relatively wide parameter choices, we also observe asymmetric suppression of synchronization, where communities compete to suppress one another's synchronization properties until one or more win, totally suppressing the others to effective incoherence. Using the ansatz of Ott and Antonsen, we provide analytical descriptions for these transitions that confirm numerical simulations.

In this paper, a Fréedericksz-like positional transition is found for a spherical microdroplet suspended in a nematic liquid crystal cell in the presence of an external electric field. Based on the numerical calculation of elastic energy using the Green's function method, the equilibrium position of the microdroplet is decided through a competition between the buoyant force and the effective force built by the elastic energy gradient existing inside the nematic liquid crystal cell. It is shown that elastic energy dominates the kinetics of the microdroplet until the external field applied reaches a critical value large enough to flatten the elastic energy contour in the central region, which provides a “fast lane” enabling the asymmetric buoyant force to drive the liquid droplet abruptly from the cell midplane to a new equilibrium position, triggering a positional transition. It is also found that such a threshold value of external field depends on thickness $L$ and Frank elastic constant $K$, in a Fréedericksz-like manner, but multiplied by a factor of $3\sqrt{\pi }$. An explicit formula proposed for the critical electric field agrees extremely well with the numerical calculation.

The continuous-spontaneous-localization dynamical collapse structure, adapted to the relativistically invariant model where the collapse-generating operator is a one-dimensional scalar field $\widehat{\varphi }(x,t)$ (mass $m$) is discussed. A complete solution for the density matrix is given, for an initial state $|\psi ,0\rangle =\frac{1}{\sqrt{2}}\left[\right|L\rangle +|R\rangle ]$ when the Hamiltonian $\widehat{H}$ is set equal to 0, and when $\widehat{H}$ is the free field Hamiltonian. Here $|L\rangle ,|R\rangle$ are coherent states which represent clumps of particles, with mean particle number density $N{\chi }_i^2\left(x\right)$, where ${\chi }_1\left(x\right),{\chi }_2\left(x\right)$ are Gaussians of width $\sigma \gg m^{-1}$ with mean positions separated by distance $\gg \sigma$. It is shown that, with high probability, the solution for $\widehat{H}=0$ (identical to the short time solution for $\widehat{H}\ne 0$) favors collapse toward eigenstates of the scalar field whose eigenvalues are close to $\sim {\chi }_i\left(x\right)$. Thus, this collapse dynamics results in essentially one clump of particles. However, eventually particle production dominates the density matrix since, as is well known, the collapse generates energy/sec-volume of every particle momentum in equal amounts. Because of the particle production, this is not an experimentally viable physical theory but, as is emphasized by the discussion, it is a sound relativistic collapse model, with sensible collapse behavior.

Topology has rapidly become one of the central topics in modern physics because of its ability to explain various interesting phenomena, especially in condensed matter physics. Topological invariants, serving as indicators for different topological phases, have been widely studied in various quantum systems. Generally, topological invariants are defined in (quasi)equilibrium systems through their ground-state manifold and are used to classify different topological phases. Recently, topological invariants in quantum systems far from equilibrium have been taken into account theoretically in quite different ways. Here, the dynamical Chern number, originally introduced in quenches of static systems, is extended to the quenches of periodically driven systems. Moreover, experimental measurements of dynamical topological invariants appearing in different quantum quenches are reported. The results show that the dynamical Chern number offers an intrinsic way to classify quenched quantum walks, and they demonstrate further its relation to quasiequilibrium topological bulk invariants associated with quenched quantum walks between different topological phases. The classifications by the dynamical Chern number are also compared with the classifications by the behavior of the dynamical topological order parameter. The platform used in this study provides an ideal way to investigate the topology in nonequilibrium quantum systems.

The thermodynamic properties of the Shastry-Sutherland model have posed one of the longest-lasting conundrums in frustrated quantum magnetism. Over a wide range on both sides of the quantum phase transition (QPT) from the dimer-product state to the plaquette-based ground state, neither analytical nor any available numerical methods have come close to reproducing the physics of the excited states and thermal response. We solve this problem in the dimer-product phase by introducing two qualitative advances in computational physics. One is the use of thermal pure quantum (TPQ) states to augment dramatically the size of clusters amenable to exact diagonalization. The second is the use of tensor-network methods, in the form of infinite projected entangled-pair states (iPEPS), for the calculation of finite-temperature quantities. We demonstrate convergence as a function of system size in TPQ calculations and of bond dimension in our iPEPS results, with complete mutual agreement even extremely close to the QPT. Our methods reveal a remarkably sharp and low-lying feature in the magnetic specific heat, whose origin appears to lie in a proliferation of excitations composed of two-triplon bound states. The surprisingly low energy scale and apparently extended spatial nature of these states explain the failure of less refined numerical approaches to capture their physics. Both of our methods will have broad and immediate application in addressing the thermodynamic response of a wide range of highly frustrated magnetic models and materials.

In turbulent Rayleigh-Bénard convection, the boundary layers are nonsteady with fluctuations, the time-averaged large-scale circulating velocity vanishes far away from the top and bottom plates, and the motion arises from buoyancy. In this paper, we derive the full set of boundary layer equations for both the temperature and velocity fields from the Boussinesq equations for a quasi-two-dimensional flow above a heated plate, taking into account all the above effects. By solving these boundary layer equations, both the time-averaged temperature and velocity boundary layer profiles are obtained.

The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain range of dynamics on complex graphs, higher-dimensional coins are necessary to unleash the full potential of discrete-time quantum walks. In this work, we present an experimental realization of a discrete-time quantum walk on a line graph that, instead of two-dimensional, exhibits a four-dimensional coin space. Making use of the extra degree of freedom we observe multiple ballistic propagation speeds specific to higher-dimensional coin operators. By implementing a scalable technique, we demonstrate quantum walks on circles of various sizes, as well as on an example of a Husimi cactus graph. The quantum walks are realized via time-multiplexing in a Michelson interferometer loop architecture, employing as the coin degrees of freedom the polarization and the traveling direction of the pulses in the loop. Our theoretical analysis shows that the platform supports implementations of quantum walks with arbitrary $4\times 4$ unitary coin operations, and usual quantum walks on a line with various periodic and twisted boundary conditions.

We demonstrate a trap that confines polarizable particles around the antinode of a standing-wave microwave field. The trap relies only on the polarizability of the particles far from any resonances and so can trap a wide variety of atoms and molecules in a wide range of internal states, including the ground state. The trap has a volume of about $10{\mathrm{cm}}^3$ and a depth approaching $1\mathrm{K}$ for many polar molecules. We measure the trap properties using ${}^7\mathrm{Li}$ atoms, showing that when the input microwave power is $610\mathrm{W}$, the atoms remain trapped with a $1/e$ lifetime of $1.76\left(12\right)\mathrm{s}$, oscillating with an axial frequency of $28.55\left(5\right)\mathrm{Hz}$ and a radial frequency of $8.81\left(8\right)\mathrm{Hz}$. The trap could be loaded with slow molecules from a range of available sources and is particularly well suited to sympathetic cooling and evaporative cooling of molecules.

We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying distributions that are widely used in statistics and other fields. This definition allows the distribution to deviate from a pure power law arbitrarily but without affecting the power-law tail exponent. We then identify three estimators of these exponents that are proven to be statistically consistent—that is, converging to the true value of the exponent for any regularly varying distribution—and that satisfy some additional niceness requirements. In contrast to estimators that are currently popular in network science, the estimators considered here are based on fundamental results in extreme value theory, and so are the proofs of their consistency. Finally, we apply these estimators to a representative collection of synthetic and real-world data. According to their estimates, real-world scale-free networks are definitely not as rare as one would conclude based on the popular but unrealistic assumption that real-world data come from power laws of pristine purity, void of noise, and deviations.

Simulation of fermionic many-body systems on a quantum computer requires a suitable encoding of fermionic degrees of freedom into qubits. Here we revisit the superfast encoding introduced by Kitaev and one of the authors. This encoding maps a target fermionic Hamiltonian with two-body interactions on a graph of degree $d$ to a qubit simulator Hamiltonian composed of Pauli operators of weight $O\left(d\right)$. A system of $m$ Fermi modes gets mapped to $n=O\left(md\right)$ qubits. We propose generalized superfast encodings (GSEs) which require the same number of qubits as the original one but have more favorable properties. First, we describe a GSE such that the corresponding quantum code corrects any single-qubit error provided that the interaction graph has degree $d\ge 6$. In contrast, we prove that the original superfast encoding lacks the error correction property for $d\le 6$. Second, we describe a GSE that reduces the Pauli weight of the simulator Hamiltonian from $O\left(d\right)$ to $O(logd)$. The robustness against errors and a simplified structure of the simulator Hamiltonian offered by GSEs can make simulation of fermionic systems within the reach of near-term quantum devices. As an example, we apply the new encoding to the fermionic Hubbard model on a 2D lattice.

Molecular dynamics (MD) simulations have been widely recognized as a promising tool for investigating dynamical processes with an atomic resolution. The time span accessible to MD simulations is, however, extremely limited, which makes it difficult to simulate dynamical events on a timescale of milliseconds or longer while maintaining the microscopic-level resolution. Here, we present an approach that allows us to accelerate the dynamical processes (infrequent events) by introducing an additional bias potential and to describe these events on the correct timescale. To this end, we utilize a reparametrization of time (generalized Poincaré time transformation), which leads to the accelerated dynamics and the biased sampling in phase space. The direct link between the timescale and biased sampling demonstrated in this study makes it possible to extend the timescale in MD simulations without invoking the approximation of the transition state theory. A general form of the bias potential is also introduced, which is easily constructed and straightforwardly applied to various systems. The present approach, Poincaré boost dynamics, is applied to the diffusion process of an impurity atom in an amorphous matrix and to conformational changes of a model protein for demonstrating its validity and versatility.

Motivated by recent advances in the fabrication of Josephson junctions in which the weak link is made of a low-dimensional nonsuperconducting material, we present here a systematic theoretical study of the local density of states (LDOS) in a clean two-dimensional normal metal (N) coupled to two $s$-wave superconductors (S). To be precise, we employ the quasiclassical theory of superconductivity in the clean limit, based on Eilenberger's equations, to investigate the phase-dependent LDOS as a function of factors such as the length or the width of the junction, a finite reflectivity, and a weak magnetic field. We show how the spectrum of Andreev bound states that appear inside the gap shape the phase-dependent LDOS in short and long junctions. We discuss the circumstances when a gap appears in the LDOS and when the continuum displays a significant phase dependence. The presence of a magnetic flux leads to a complex interference behavior, which is also reflected in the supercurrent-phase relation. Our results agree qualitatively with recent experiments on graphene SNS junctions. Finally, we show how the LDOS is connected to the supercurrent that can flow in these superconducting heterostructures and present an analytical relation between these two basic quantities.

We describe a technique which minimizes the amount of neurons in the hidden layer of a random recurrent neural network (rRNN) for time series prediction. Merging Takens-based attractor reconstruction methods with machine learning, we identify a mechanism for feature extraction that can be leveraged to lower the network size. We obtain criteria specific to the particular prediction task and derive the scaling law of the prediction error. The consequences of our theory are demonstrated by designing a Takens-inspired hybrid processor, which extends a rRNN with virtual nodes. Virtual nodes are defined as time-delayed versions of real network nodes. Our hybrid architecture is therefore designed including both real and virtual nodes. Via this symbiosis, we show performance of the hybrid processor by stabilizing an arrhythmic neural model. Thanks to our obtained design rules, we can reduce the stabilizing neural network's size by a factor of 15 with respect to a standard system.