Interactions of large numbers of spiking neurons give rise to complex neural dynamics with fluctuations occurring at multiple scales. Understanding the dynamical mechanisms underlying such complex neural dynamics is a long-standing topic of interest in neuroscience, statistical physics and nonlinear dynamics. Conventionally, fluctuating neural dynamics are formulated as balanced, uncorrelated excitatory and inhibitory inputs with Gaussian properties. Yet heterogeneous, non-Gaussian properties have been widely observed in both neural connections and neural dynamics. Based on balanced neural networks with heterogeneous, non-Gaussian features, our analysis reveals that synaptic inputs possess power-law fluctuations in the limit of large network size, leading to a remarkable relation between complex neural dynamics and the fractional diffusion formalisms of nonequilibrium physical systems. We derive a fractional Fokker-Planck equation with analytically tractable boundary conditions for the network, uniquely accounting for the leapovers caused by the fluctuations of spiking activity. This body of formalisms represents a fractional diffusion theory of heterogeneous neural networks and results in an exact description of the network activity states. In particular, the fractional diffusion theory identifies a dynamical state at which the neural response is maximized as a function of structural connectivity. This state is then implemented in a balanced spiking neural network and displays rich, nonlinear response properties, providing a unified account of a variety of experimental findings on neural dynamics at the individual neuron and network levels, including fluctuations of membrane potentials and population firing rates. Our theory and its network implementations provide a framework for investigating complex neural dynamics emerging from large networks of spiking neurons and their functional roles in neural processing.

We report experimental results on three-dimensional momentum-imaging measurements of anions generated via dissociative electron attachment to gaseous formamide. From the momentum images, we analyze the angular and kinetic-energy distributions for $\mathrm{N}{\mathrm{H}}_2{}^{-}$, ${\mathrm{O}}^{-}$, and ${\mathrm{H}}^{-}$ fragments and discuss the possible electron attachment and dissociation mechanisms for multiple resonances for two ranges of incident electron energies, from 5.3 to 6.8 eV and from 10.0 to 11.5 eV. Ab initio theoretical results for the angular distributions of the $\mathrm{N}{\mathrm{H}}_2{}^{-}$ anion for $\sim 6$-eV incident electrons, when compared with the experimental results, strongly suggest that one of the two resonances producing this fragment is a ${}^2\mathrm{A}^{\prime \prime }$ Feshbach resonance.

The spin-orbit interaction lies at the heart of quantum computation with spin qubits, research on topologically nontrivial states, and various applications in spintronics. Hole spins in Ge/Si core/shell nanowires experience a spin-orbit interaction that has been predicted to be both strong and electrically tunable, making them a particularly promising platform for research in these fields. We experimentally determine the strength of spin-orbit interaction of hole spins confined to a double quantum dot in a Ge/Si nanowire by measuring spin-mixing transitions inside a regime of spin-blockaded transport. We find a remarkably short spin-orbit length of $\sim 65\mathrm{nm}$, comparable to the quantum dot length and the interdot distance. We additionally observe a large orbital effect of the applied magnetic field on the hole states, resulting in a large magnetic field dependence of the spin-mixing transition energies. Strikingly, together with these orbital effects, the strong spin-orbit interaction causes a significant enhancement of the $g$ factor with magnetic field. The large spin-orbit interaction strength demonstrated is consistent with the predicted direct Rashba spin-orbit interaction in this material system and is expected to enable ultrafast Rabi oscillations of spin qubits and efficient qubit-qubit interactions, as well as provide a platform suitable for studying Majorana zero modes.

We use a combination of computer simulations and isoflux tension propagation (IFTP) theory to investigate the translocation dynamics of a flexible linear polymer through a nanopore into an environment composed of repulsive active rods in two dimensions. We demonstrate that the rod activity induces a crowding effect on the polymer, leading to a time-dependent effective net force that facilitates translocation into the active environment. Incorporating this force into the IFTP theory for pore-driven translocation allows us to characterize translocation dynamics in detail and derive a scaling form for the average translocation time as $\tilde{\tau }\sim N_{01}^{1+\nu }{\tilde{L}}_{\text{r}}^{\nu }/{\tilde{F}}_{\text{SP}}$, where $N_{01},$ ${\tilde{L}}_{\text{r}},$ and ${\tilde{F}}_{\text{SP}}$ are the initial contour length of the cis-side subchain, rod length, and self-propelling force acting on the rods, respectively, and $\nu$ is the equilibrium Flory scaling exponent.

A focused acoustic standing wave creates a Hookean potential well for a small sphere and can levitate it stably against gravity. Exposing the trapped sphere to a second transverse traveling sound wave imposes an additional acoustic force that drives the sphere away from its mechanical equilibrium. The driving force is shaped by interference between the standing trapping wave and the traveling driving wave. If, furthermore, the traveling wave is detuned from the standing wave, the driving force oscillates at the difference frequency. Far from behaving like a textbook-driven harmonic oscillator, however, the wave-driven harmonic oscillator instead exhibits a remarkably rich variety of dynamical behaviors. These include oscillations at both harmonics and subharmonics of the driving frequency, period-doubling routes to chaos, and Fibonacci cascades. This model system therefore illustrates opportunities for dynamic acoustic manipulation based on spectral, rather than spatial, control of the sound field.

We develop a method based on tensor networks to create localized single-particle excitations on top of strongly correlated quantum spin chains. In analogy to the problem of creating localized Wannier modes, this is achieved by optimizing the gauge freedom of momentum excitations on top of matrix product states. The corresponding wave packets propagate almost dispersionlessly. The time-dependent variational principle is used to scatter two such wave packets, and we extract the phase shift from the collision data. We also study reflection and transmission coefficients of a wave packet impinging on an impurity.

Realizing the promise of quantum information processing remains a daunting task given the omnipresence of noise and error. Adapting noise-resilient classical computing modalities to quantum mechanics may be a viable path towards near-term applications in the noisy intermediate-scale quantum era. Here, we propose continuous variable quantum reservoir computing in a single nonlinear oscillator. Through numerical simulation of our model we demonstrate quantum-classical performance improvement and identify its likely source: the nonlinearity of quantum measurement. Beyond quantum reservoir computing, this result may impact the interpretation of results across quantum machine learning. We study how the performance of our quantum reservoir depends on Hilbert space dimension, how it is impacted by injected noise, and briefly comment on its experimental implementation. Our results show that quantum reservoir computing in a single nonlinear oscillator is an attractive modality for quantum computing on near-term hardware.

Quantum key distribution (QKD) protocols with threshold detectors are driving high-performance QKD demonstrations. The corresponding security proofs usually assume that all physical detectors have the same detection efficiency. However, the efficiencies of the detectors used in practice might show a mismatch depending on the manufacturing and setup of these detectors. A mismatch can also be induced as the different spatial-temporal modes of an incoming signal might couple differently to a detector. Here we develop a method that allows to provide security proofs without the usual assumption. Our method can take the detection-efficiency mismatch into account without having to restrict the attack strategy of the adversary. Especially, we do not rely on any photon-number cutoff of incoming signals such that our security proof is directly applicable to practical situations. We illustrate our method for a receiver that is designed for polarization encoding and is sensitive to a number of spatial-temporal modes. In our detector model, the absence of quantum interference between any pair of spatial-temporal modes is assumed. For a QKD protocol with this detector model, we can perform a security proof with characterized efficiency mismatch and without photon-number cutoff assumption. Our method also shows that in the absence of efficiency mismatch in our detector model, the key rate increases if the loss due to detection inefficiency is assumed to be outside of the adversary's control, as compared to the view where for a security proof this loss is attributed to the action of the adversary.

We introduce a perturbative method to calculate all moments of the first passage time distribution in stochastic one-dimensional processes which are subject to both white and colored noise. This class of non-Markovian processes is at the center of the study of thermal active matter, that is self-propelled particles subject to diffusion. The perturbation theory about the Markov process considers the effect of self-propulsion to be small compared to that of thermal fluctuations. To illustrate our method, we apply it to the case of active thermal particles (i) in a harmonic trap and (ii) on a ring. For both we calculate the first-order correction of the moment-generating function of first passage times, and thus to all its moments. Our analytical results are compared to numerics.

Machine learning methods have been recently applied to learning phases of matter and transitions between them. Of particular interest is the topological phase transition, such as in the XY model, whose critical points can be difficult to be obtained by using unsupervised learning, such as the principal component analysis. Recently, the authors of [Nat. Phys. 15, 790 (2019)] employed the diffusion map method for identifying topological orders and were able to determine the Berezinskii-Kosterlitz-Thouless (BKT) phase transition of the XY model, specifically via the intersection of the average cluster distance $\overline{D}$ and the within-cluster dispersion parameter $\overline{\sigma }$ (when the different clusters vary from separation to mixing together). However, sometimes it is not easy to find the intersection if $\overline{D}$ or $\overline{\sigma }$ does not change too much due to topological constraint. In this paper, we propose to use the Calinski-Harabaz (ch) index, defined roughly as the ratio $\overline{D}/\overline{\sigma }$, to determine the critical points at which the ch index reaches a maximum or minimum value or jumps sharply. We examine the ch index in several statistical models, including ones that contain a BKT phase transition. For the Ising model, the peaks of the quantity ch or its components are consistent with the position of the specific-heat maximum. For the XY model, both on the square and on the honeycomb lattices, our results of the ch index show the convergence of the peaks over a range of parameters $\varepsilon /{\varepsilon }_0$ in the Gaussian kernel. We also examine the generalized XY model with $q=2$ and $q=8$ and study the phase transition using the fractional 1/2-vortex or 1/8-vortex constraint, respectively. The global phase diagram can be obtained by our method, which does not use the label of configuration needed by supervised learning, nor a crossing from two curves $\overline{D}$ and $\overline{\sigma }$. Our method is, thus, useful to both topological and nontopological phase transitions and can achieve accuracy as good as supervised learning methods previously used in these models and may be used for searching phases from experimental data.

The Collatz conjecture, perhaps the most elementary unsolved problem in mathematics, claims that for all positive integers $n$, the map $n\mapsto n/2$ ($n$ even) and $n\mapsto 3n+1$ ($n$ odd) reaches 1 after a finite number of iterations. We examine the Collatz map's orbits, known as hailstone sequences, to determine whether or not they exhibit scale-invariant behavior, in analogy with certain processes observed in real physical systems. We develop an efficient way to generate orbits for extremely large $n$ (e.g., higher than $n\sim {10}^{3000}$), allowing us to statistically analyze very long sequences. We find strong evidence of a scale-free power law for the Collatz map. We analytically derive the scaling exponents, displaying excellent agreement with the numerical estimations. The scale-free sequences seen in the Collatz dynamics are consistent with geometric Brownian motion with drift, which is compatible with the validity of the Collatz conjecture. Our results lead to another conjecture (conceivably testable through direct, nonetheless very time consuming, numerical simulations): Given an initial $n$, the average number of iterations needed to reach 1 is proportional, to lowest order, to $log\left[n\right]$ (basis 10).

We study internal dynamics of exciton-polariton condensates created by the nonresonant optical pump in a cylindrical pillar microcavity with an ensemble of embedded quantum wells. The polariton condensates are intrinsically nonequilibrium systems: Their dissipative nature together with a spatial inhomogeneity of a potential landscape and localized pumping leads to formation of steady polariton flows. The gain-loss engineering consisting of a deliberate breaking of the rotational symmetry of the system makes the polariton flows controllable. We demonstrate the switching between the polariton current states characterized by both integer and fractional orbital angular momenta (OAM) by tuning the position and ellipticity of the pump spot. At a weak shift and a small ellipticity, the phase rather than the density of the exciton-polariton condensate is significantly affected. Then the polariton condensate is characterized by an integer OAM per particle coinciding with the topological charge of the polariton vortex state. We demonstrate experimentally the polariton current states with the topological charges from $-3$ to $+2$. The further shift of the pump spot perturbs the azimuthal distribution of the polariton density and causes a jump of the phase of the condensate at the density deep. The mean orbital angular momentum characterizing such polariton condensate acquires fractional values. To describe the experimentally observed polariton current states, we propose a model based on the Gross-Pitaevskii equation projected onto the azimuthal states of the ring trap which treats the formation of fractional OAM states as a result of the coherent superposition of integer OAM states sustained due to the gain-loss balance in the system with a broken rotational symmetry.

Recently, we have experimentally observed signatures of sharp exciton peaks in the photoluminescence spectra of bundles of monoatomic carbon chains stabilized by gold nanoparticles and deposited on a glass substrate. Here we estimate the characteristic energies of excitonic transitions in this complex quasi-one-dimensional nanosystem with use of the variational method. We show that the characteristic energy scale for the experimentally observed excitonic fine structure is governed by the interplay between the hopping energy in a Van der Waals quasicrystal formed by parallel carbon chains, neutral-charged exciton splitting, and positive-negative trion splitting. These three characteristic energies are an order of magnitude lower than the direct exciton binding energy.

Online social networks have significantly changed global communication dynamics. Despite the complexity of such dynamics, emergent patterns from empirical microblogging data on hashtag usage, such as meme popularity power-law distributions, have been observed. However, going beyond empirical or simulation-based studies, highlighting and distinguishing fundamental mechanisms at the origin of such patterns are still open problems. Herein, inspired by the neutral theory of ecology, we provide an analytical formalism capable of capturing the competition for attention in online social systems and explaining several emergent patterns observed in the context of information ecosystems. Specifically, besides meme popularity distributions, we study the persistence distributions of memes within the network and the capacity of the system to sustain several coexisting diverse memes. Such properties have a clear analogy to extinction time and biodiversity in natural ecosystems. In the social network context, diversity of ideas is indeed an identifying characteristic of the “health” of the communication process. We show how our theoretical framework is successful in explaining real data collected from the Twitter online social network. The proposed framework introduced here provides both insight into the roles played by competition and network structure on meme diversity and persistence, and an applicable null model to be tested against real data.

New ideas for low-mass dark matter direct detection suggest that narrow band gap materials, such as Dirac semiconductors, are sensitive to the absorption of meV dark matter or the scattering of keV dark matter. Here we propose spin-orbit semiconductors—materials whose band gap arises due to spin-orbit coupling—as low-mass dark matter targets owing to their $O$(10 meV) band gaps. We present three material families that are predicted to be spin-orbit semiconductors using density functional theory (DFT), assess their electronic and topological features, and evaluate their use as low-mass dark matter targets. In particular, we find that the tin pnictide compounds are especially suitable having a tunable range of meV-scale band gaps with anisotropic Fermi velocities allowing directional detection. Finally, we address the pitfalls in the DFT methods that must be considered in the ab initio prediction of narrow-gapped materials, including those close to the topological critical point.

Continuous-variable encoding of quantum information in the optical domain has recently yielded large temporal and spectral entangled states instrumental for quantum computing and quantum communication. We introduce a protocol for the generation of spatial multipartite entanglement based on phase-matching of a propagation eigenmode in a monolithic photonic device: the array of quadratic nonlinear waveguides. We theoretically demonstrate in the spontaneous parametric downconversion regime the generation of large multipartite entangled states useful for multimode quantum networks. Our protocol is remarkably simple and robust as it does not rely on specific values of coupling, nonlinearity, or length of the sample.

Strong anomalous diffusion is characterized by asymptotic power-law growth of the moments of displacement, with exponents that do not depend linearly on the order of the moment. The exponents concerning small-order moments are dominated by random motion, while higher-order exponents grow by faster trajectories, such as ballistic excursions or “light fronts.” Often such a situation is characterized by two linear dependencies of the exponents on their order. Here, we introduce a simple exactly solvable model, the fly-and-die (FnD) model, that sheds light on this behavior and on the consequences of light fronts on displacement autocorrelation functions in transport processes. We present analytical expressions for the moments and derive a scaling form that expresses the long-time asymptotics of the autocorrelation function $\langle x\left(t_1\right)x\left(t_2\right)\rangle$ in terms of the dimensionless time difference $(t_2-t_1)/t_1$. The scaling form provides a faithful collapse of numerical data for vastly different systems. This is demonstrated here for the Lorentz gas with infinite horizon, polygonal billiards with finite and infinite horizon, the Lévy-Lorentz gas, the slicer map, and Lévy walks. Our analysis also captures the system-specific corrections to scaling.

FeSeTe has recently emerged as a leading candidate material for the two-dimensional topological superconductivity (TSC). Two reasons for the excitement are the high $T_c$ of the system and the fact that the Majorana zero modes (MZMs) inside the vortex cores live on the exposed surface rather than at the interface of a heterostructure as in the proximitized topological insulators. However, the recent scanning tunneling spectroscopy data have shown that, contrary to the theoretical expectation, the MZM does not exist inside every vortex core. Hence there are “full” vortices with MZMs and “empty” vortices without MZMs. Moreover, the fraction of “empty” vortices increases with an increase in the magnetic field. We propose the possibility of two distinct gapped states competing for the topological surface states in FeSeTe: the TSC and half quantum anomalous Hall (hQAH). The latter is promoted by a magnetic field through the alignment of impurity magnetic moments such as Fe interstitials. When hQAH takes over the topological surface state, the surface will become transparent to scanning tunneling microscopy and the nature of the vortices in such regions will appear identical to what is expected of the vortices in the bulk, i.e., empty. The unmistakable signature of the proposed mechanism for empty vortices will be the existance of chiral Majorana modes(CMM) at the domain wall between an hQAH region and a TSC region. Such CMMs should be observable by measuring local density of states along a line connecting an empty vortex to a nearby full vortex.

We present a method to construct pseudo-BCS wave functions from the one-body density matrix. The resulting many-body wave function, which can be produced for any fermion systems, including those with purely repulsive interactions, has the form of a number-projected BCS form, or antisymmetrized geminal power (AGP). Such wave functions provide a better ansatz for correlated fermion systems than a single Slater determinant, and often better than a linear combination of Slater determinants (for example from a truncated active space calculation). We describe a procedure to build such a wave function conveniently from a given reduced density matrix of the system, rather than from a mean-field solution (which gives a Slater determinant for repulsive interactions). The pseudo-BCS wave function thus obtained reproduces the density matrix or minimizes the difference between the input and resulting density matrices. One application of the pseudo-BCS wave function is in auxiliary-field quantum Monte Carlo (AFQMC) calculations as the trial wave function to control the sign/phase problem. AFQMC is often among the most accurate general methods for correlated fermion systems. We show that the pseudo-BCS form further reduces the constraint bias and leads to improved accuracy compared to the usual Slater determinant trial wave functions, using the two-dimensional Hubbard model as an example. Furthermore, the pseudo-BCS trial wave function allows a new systematically improvable self-consistent approach, with pseudo-BCS trial wave function iteratively generated by AFQMC via the one-body density matrix.

We present a theorem describing stable solutions for a driven quantum system. The theorem, coined inertial theorem, is applicable for fast driving, provided the acceleration rate is small. The theorem states that in the inertial limit eigenoperators of the propagator remain invariant throughout the dynamics, accumulating dynamical and geometric phases. The proof of the theorem utilizes the structure of Liouville space and a closed Lie algebra of operators. We demonstrate applications of the theorem by studying three explicit solutions of a harmonic oscillator, two-level and three-level system models. These examples demonstrate that the inertial solution is superior to that obtained with the adiabatic approximation. Inertial protocols can be combined to generate a family of solutions. The inertial theorem is then employed to extend the validity of the Markovian master equation to strongly driven open quantum systems. In addition, we explore the consequence of geometric phases associated with the driving parameters.