Nonlocal Coupling Research Articles

Controlling photons by phonons via giant atom in a waveguide QED setup.

We investigate the single photon scattering in a phonon-photon hybrid system in the waveguide quantum electrodynamics (QED) scheme. In our consideration, an artificial giant atom, which is dressed by the phonons in a surface acoustic wave resonator, interacts with a coupled resonator waveguide (CRW) nonlocally via two connecting sites. Together with the interference effect by the nonlocal coupling, the phonon serves as a controller to the transport of the photon in the waveguide. On the one hand, the coupling strength between the giant atom and the surface acoustic wave resonator modulates the width of the transmission valley or window in the near resonant regime. On the other hand, the two reflective peaks induced by the Rabi splitting degrade into a single one when the giant atom is large detuned from the surface acoustic resonator, which implies an effective dispersive coupling. Our study paves the way for the potential application of giant atoms in the hybrid system.

Synchronization of Phase Oscillators Due to Nonlocal Coupling Mediated by the Slow Diffusion of a Substance

Many systems of physical and biological interest are characterized by assemblies of phase oscillators whose interaction is mediated by a diffusing chemical. The coupling effect results from the fact that the local concentration of the mediating chemical affects both its production and absorption by each oscillator. Since the chemical diffuses through the medium in which the oscillators are embedded, the coupling among oscillators is non-local; it considers all the oscillators depending on their relative spatial distances. We considered a mathematical model for this coupling, when the diffusion time is arbitrary with respect to the characteristic oscillator periods, yielding a system of coupled nonlinear integro-differential equations which can be solved using Green functions for appropriate boundary conditions. In this paper, we show numerical solutions of these equations for three finite domains: a linear one-dimensional interval, a rectangular, and a circular region, with absorbing boundary conditions. From the numerical solutions, we investigate phase and frequency synchronization of the oscillators, with respect to changes in the coupling parameters for the three considered geometries.

Dynamics of a Chain of Interacting Neurons with Nonlocal Coupling, Given by Laplace Operator of Fractional and Variable Orders with Nonlinear Hindmarsh–Rose Model Functions

Dynamics of a Chain of Interacting Neurons with Nonlocal Coupling, Given by Laplace Operator of Fractional and Variable Orders with Nonlinear Hindmarsh–Rose Model Functions

In-phase and anti-phase bursting dynamics and synchronisation scenario in neural network by varying coupling phase.

We have analysed the synchronisation scenario and the rich spatiotemporal patterns in the network of Hindmarsh-Rose neurons under the influence of self, mixed and cross coupling of state variables which are realised by varying coupling phase. We have introduced a coupling matrix in the model to vary coupling phase. The excitatory and inhibitory couplings in the membrane potential induce in-phase and anti-phase bursting dynamics, respectively, in the two coupled system. When the off-diagonal elements of the matrix are zero, the system shows self coupling of the three variables, which helps to attain synchrony. The off-diagonal elements give cross interactions between the variables, which reduces synchrony. The stability of the synchrony attained is analysed using Lyapunov function approach. In our study, we found that self coupling in three variables is sufficient to induce chimera states in non-local coupling. The strength of incoherence and discontinuity measure validates the existence of chimera and multichimera states. The inhibitor self coupling in local interaction induces interesting patterns like Mixed Oscillatory State and clusters. The results may help in understanding the spatiotemporal communications of the brain, within the limitations of the size of the network analysed in this study.

Spectral features of polaronic excitations in a superconducting analog simulator

We investigate spectral properties of polaronic excitations within the framework of an analog quantum simulator based on inductively coupled superconducting transmon qubits and microwave resonators. This system emulates a lattice model that describes a nonlocal coupling of an itinerant spinless-fermion excitation to dispersionless (Einstein-type) phonons through the Peierls and breathing-mode interaction mechanisms. The model is characterized by a sharp, level-crossing transition at a critical value of the effective excitation-phonon coupling strength; above the transition point, the ground state of this model corresponds to a heavily dressed (small-polaron) excitation. Using the kernel-polynomial method, we evaluate the momentum-frequency resolved spectral function of this system for a broad range of parameters. In particular, we underscore the ramifications of the fact that the zero-quasimomentum Bloch state of a bare excitation represents the exact eigenstate of the Hamiltonian of this system for an arbitrary excitation-phonon coupling strength. We also show that -- based on the numerically evaluated spectral function and its well-known relation with the survival probability of the initial, bare-excitation Bloch state (the Loschmidt echo) -- one can make predictions about the system dynamics following an excitation-phonon interaction quench. To make contact with anticipated experimental realizations, we utilize a previously proposed method for extracting dynamical-response functions in systems with local (single-qubit) addressability using the multiqubit (many-body) version of the Ramsey interference protocol.

Causal deep learning models for studying the Earth system

Abstract. Earth is a complex non-linear dynamical system. Despite decades of research and considerable scientific and methodological progress, many processes and relations between Earth system variables remain poorly understood. Current approaches for studying relations in the Earth system rely either on numerical simulations or statistical approaches. However, there are several inherent limitations to existing approaches, including high computational costs, uncertainties in numerical models, strong assumptions about linearity or locality, and the fallacy of correlation and causality. Here, we propose a novel methodology combining deep learning (DL) and principles of causality research in an attempt to overcome these limitations. On the one hand, we employ the recent idea of training and analyzing DL models to gain new scientific insights into relations between input and target variables. On the other hand, we use the fact that a statistical model learns the causal effect of an input variable on a target variable if suitable additional input variables are included. As an illustrative example, we apply the methodology to study soil-moisture–precipitation coupling in ERA5 climate reanalysis data across Europe. We demonstrate that, harnessing the great power and flexibility of DL models, the proposed methodology may yield new scientific insights into complex non-linear and non-local coupling mechanisms in the Earth system.

Ergodic Mean-Field Games with aggregation of Choquard-type

We consider second-order ergodic Mean-Field Games systems in the whole space RN with coercive potential and aggregating nonlocal coupling, defined in terms of a Riesz interaction kernel. These MFG systems describe Nash equilibria of games with a large population of indistinguishable rational players attracted toward regions where the population is highly distributed. Equilibria solve a system of PDEs where an Hamilton-Jacobi-Bellman equation is combined with a Kolmogorov-Fokker-Planck equation for the mass distribution. Due to the interplay between the strength of the attractive term and the behavior of the diffusive part, we will obtain three different regimes for the existence and non existence of classical solutions to the MFG system. By means of a Pohozaev-type identity, we prove nonexistence of regular solutions to the MFG system without potential in the Hardy-Littlewood-Sobolev-supercritical regime. On the other hand, using a fixed point argument, we show existence of classical solutions in the Hardy-Littlewood-Sobolev-subcritical regime at least for masses smaller than a given threshold value. In the mass-subcritical regime we show that actually this threshold can be taken to be +∞.

Analysis of ideal models of real nonlocal acoustic and elastic metamaterials

Nonlocal coupling in acoustic and elastic systems has received growing attention for its potential to expand the capabilities of active metamaterials. Previously, we have shown experimentally how nonlocality imposed through action at a distance, where signals from disturbances at one location are used to drive actuators at separate locations, gives rise to unique scattering characteristics, namely highly nonreciprocal transmission. We showed how the mathematical models for these experimental systems were excellent predictors for real system behavior, and as such, represented powerful experimental design tools. However, these models were elaborate, incorporating the characteristics of real sensors and actuators, electronic controllers, and material properties and geometries, consequently obscuring the underlying nonlocal physics responsible for their unique behavior. Here, we present simplified models of these real systems that feature closed form expressions for system scattering characteristics, allowing for the identification of relevant dimensionless quantities and revealing how the interactions of those quantities affect both system performance and stability. We compare and contrast ideal models for both acoustic and elastodynamic nonlocal systems, highlighting how each ideal model is qualitatively representative of its real counterpart, thus providing a pathway to a deeper understanding and further exploration of nonlocality in wave-bearing systems.

Asymmetric spiral chimeras on a spheric surface of nonlocally coupled phase oscillators.

The spiral chimera state shows a remarkable spatiotemporal pattern in a two-dimensional array of oscillators for which the coherent spiral arms coexist with incoherent cores. In this work, we report on an asymmetric spiral chimera having incoherent cores of different sizes on the spherical surface of identical phase oscillators with nonlocal coupling. This asymmetric spiral chimera exhibits a strongly symmetry-broken state in the sense that not only the coherent and incoherent domains coexist, but also their incoherent cores are nonidentical, although the underlying coupling structure is symmetric. On the basis of analyses along the Ott-Antonsen invariant manifold, the bifurcation conditions of asymmetric spiral chimeras are derived, which reveals that the asymmetric spiral chimera state emerges via a supercritical symmetry-breaking bifurcation from the symmetric spiral chimera. For the coupling function composed of two Legendre modes, rigorous stability analyses are carried out to present a complete stability diagram for different types of spiral chimeras, including the stationary symmetric and asymmetric spiral chimeras as well as breathing asymmetric spiral chimera. For the general coupling scheme the asymmetric spiral chimera occurs as a result of competition between the odd and even Legendre modes of the coupling function. Our theoretical findings are verified by using extensive numerical simulations of the model system.

Collective Dynamical Behaviors of Nonlocally Coupled Brockett Oscillators

In this study, we consider a network of nonlocally coupled Brockett oscillators (BOs) with attractive and repulsive (AR) couplings to illustrate the existence of diverse collective dynamical behaviors, whereas previous studies solely concentrated on synchronization. In the absence of coupling, the individual BO oscillator shows stable periodic oscillations (POs) or stable steady state (SS) depending on the critical values of the parameters. We first begin by examining the collective dynamics by setting the critical value of the parameters at the active (PO) region. A diverge collective dynamical states are manifested for a fixed nonlocal coupling range with rising coupling magnitude. Notably, the lower coupling strength exhibits two distinct dynamical patterns at lower and higher transients. At lesser transients, for example, transient dynamics of desynchronization, chimera, and traveling wave states are observed. At larger time periods, the transient dynamics disappear with the emergence of a synchronized state. Increasing the coupling strength results in a unique state of traveling wave or synchronized state for smaller and larger time periods depending on the coupling strength. Increasing the coupling strength further gives rise to clustering behaviors. Importantly, the considered system attains cluster oscillation death (COD) through a cluster oscillatory state (COS). Finally, there exists a chimera death at a larger coupling strength. The observed dynamical transitions are further demonstrated through the two‐parameter analysis by setting different critical thresholds.

Nonlocal Impacts of Soil Moisture Variability in South America: Linking Two Land–Atmosphere Coupling Hot Spots

Abstract The land–atmosphere interactions play an important role in modulating climate variability at different spatial and temporal scales. In South America, two recognized hot spots of soil moisture–atmosphere coupling are located in southeastern South America (SESA) and eastern Brazil. Soil moisture variability may not only alter the climate locally but may also have nonlocal impacts through changes in the regional circulation. Here we explore how these two local coupling hot spots interact with each other, how soil moisture variability modulates the regional circulation, and what is the consequent nonlocal impact on precipitation. To this end, we analyze numerical experiments, performed with a regional climate model for the period October–March of 1983–2012, that allow us to isolate the influence of the soil moisture interannual variability on the regional climate. When the soil moisture–atmosphere interaction is enabled, we find a nonlocal coupling mechanism that links both hot spots at different temporal scales, favoring precipitation in eastern Brazil to the detriment of the precipitation in SESA through shifts in the regional circulation, when compared with a simulation with constrained soil moisture–atmosphere interaction. In northeastern Argentina, a subregion of SESA located at the exit of the South American low-level jet, it was found that the amount of nighttime precipitation is modulated by the proposed nonlocal coupling mechanism. A better understanding of the variability of precipitation due to the influence of land–atmosphere interaction processes may contribute to improving the predictability of precipitation and the interpretation of climate projections.

Sensing the Local Magnetic Environment through Optically Active Defects in a Layered Magnetic Semiconductor.

Atomic-level defects in van der Waals (vdW) materials are essential building blocks for quantum technologies and quantum sensing applications. The layered magnetic semiconductor CrSBr is an outstanding candidate for exploring optically active defects because of a direct gap, in addition to a rich magnetic phase diagram, including a recently hypothesized defect-induced magnetic order at low temperature. Here, we show optically active defects in CrSBr that are probes of the local magnetic environment. We observe a spectrally narrow (1 meV) defect emission in CrSBr that is correlated with both the bulk magnetic order and an additional low-temperature, defect-induced magnetic order. We elucidate the origin of this magnetic order in the context of local and nonlocal exchange coupling effects. Our work establishes vdW magnets like CrSBr as an exceptional platform to optically study defects that are correlated with the magnetic lattice. We anticipate that controlled defect creation allows for tailor-made complex magnetic textures and phases with direct optical access.

Synchronization of phase oscillators with chemical coupling: Removal of oscillators and external feedback control

In many applications of biological interest spatially localized phase oscillators present a non-local coupling characterized by the diffusion of a mediating chemical. The latter is both produced and absorbed by the phase oscillators according to their dynamical behavior. We investigate numerically phase and frequency synchronization in a model for chemical coupling of uniform phase oscillators with natural frequencies randomly distributed according to some statistical distribution. We study the effect of removal of oscillators, caused by lesions, on the synchronization properties of the network. The partial or complete suppression of synchronization is also investigated through the influence of a time-delayed feedback external signal.

Periodic orbits in the Ott–Antonsen manifold

In their seminal paper (2008 Chaos 18 037113), Ott and Antonsen showed that large groups of phase oscillators driven by a certain type of common force display low dimensional long-term dynamics, which is described by a small number of ordinary differential equations. This fact was later used as a simplifying reduction technique in many studies of synchronisation phenomena occurring in networks of coupled oscillators and in neural networks. Most of these studies focused mainly on partially synchronised states corresponding to the equilibrium-type dynamics in the so called Ott–Antonsen manifold. Going beyond this paradigm, here we propose a universal approach for the efficient analysis of partially synchronised states with non-equilibrium periodic collective dynamics. Our method is based on the observation that the Poincaré map of the complex Riccati equation, which describes the dynamics in the Ott–Antonsen manifold, coincides with the well-known Möbius transformation. To illustrate the possibilities of our method, we use it to calculate a complete bifurcation diagram of travelling chimera states in a ring network of phase oscillators with asymmetric nonlocal coupling.

Non-local multi-fields coupling response of a piezoelectric semiconductor nanofiber under shear force

Based on the nonlocal piezoelectric semiconductor theory, the transient multi-fields coupling response of a nanosized piezoelectric semiconductor composite fiber is studied. The one-dimensional phenomenological theory of piezoelectric semiconductors is used to derive the coupling constitutive relation. Combining nonlocal piezoelectric semiconductor theory and coupling constitutive relation, the size-dependent governing equations for bending, the charge equation of electrostatics and the conservation of charge for electrons are obtained, and the multi-fields coupling response of the nanofiber under shear force is solved. The bending vibration, the electric potential, and the concentration of electrons along the nanofiber with different nonlocal effects are analyzed. It is found that the change of electric potential and concentration from positive and negative in the nanofiber can be used to control the performance of electronic devices.

Prediction of chimera in coupled map networks by means of deep learning

Chimera states are Spatio-temporal patterns in coupled oscillator arrays, in which incoherent domains coexist with coherent ones. To characterize chimeras, however, is a nontrivial problem since it is difficult to distinguish between coherent domains and incoherent domains. A useful tool for this task is machine learning, in particular deep learning techniques like reservoir computing and multilayer perceptrons. In this work we use these quantifiers in order to identify chimera states in logistic map lattices with non-local coupling. We compare our results from machine learning techniques with more conventional characterizations, such as Lyapunov exponents and a local order parameter.

A first-principles study of magnetic switching and hysteresis effect in the ferromagnetic Fe metal

The first-principles calculation method used in this study has an extended Hamiltonian, which contains both spin states, so that the spin magnetic moment per unit cell, m , and magnetization vector, M , can be obtained via the spinors of atomic orbitals. Both spin- and orbital- B -field couplings are considered. The magnetic field, B , induces not only components of m and M along their directions, which vanish when the field is cut off, but also bi-stable spontaneous z components, m z and M z . This study reveals that the spin- B -field coupling is energetically too weak to reverse m z / M z directly. The B field is found to reverse the spin polarization of itinerant s p electrons first when B reaches a threshold, which then triggers the reversal of m z / M z via nonlocal exchange interactions with localized d electrons. The hysteresis effect is found to be due to the existence of bi-stable m z / M z and that without a reversed B the spin-polarization of itinerant s p electrons won’t be reversed to trigger magnetic switching. • The first use of spinors to obtain the 3-D magnetization vector in Fe. • The conventional magnetic field is energetically too weak to cause magnetic switching directly. • The magnetic field reverses spin polarization of sp electrons first, which then triggers reversal of magnetization through nonlocal exchange couplings. • The relationship between the calculated magnetization and the magnetic field is hysteresis-loop-like. • The magnetic switching can be assisted by an accompanying strong transverse magnetic field.

Spiral wave chimeras in populations of oscillators coupled to a slowly varying diffusive environment

Chimera states are firstly discovered in nonlocally coupled oscillator systems. Such a nonlocal coupling arises typically as oscillators are coupled via an external environment whose characteristic time scale τ is so small (i.e., τ → o) that it could be eliminated adiabatically. Nevertheless, whether the chimera states still exist in the opposite situation (i.e., τ ≫ 1) is unknown. Here, by coupling large populations of Stuart—Landau oscillators to a diffusive environment, we demonstrate that spiral wave chimeras do exist in this oscillator-environment coupling system even when τ is very large. Various transitions such as from spiral wave chimeras to spiral waves or unstable spiral wave chimeras as functions of the system parameters are explored. A physical picture for explaining the formation of spiral wave chimeras is also provided. The existence of spiral wave chimeras is further confirmed in ensembles of FitzHugh—Nagumo oscillators with the similar oscillator-environment coupling mechanism. Our results provide an affirmative answer to the observation of spiral wave chimeras in populations of oscillators mediated via a slowly changing environment and give important hints to generate chimera patterns in both laboratory and realistic chemical or biological systems.

Local and Nonlocal Energy-Based Coupling Models

In this paper we study two different ways of coupling a local operator with a nonlocal one in such a way that the resulting equation is related to an energy functional. In the first strategy the coupling is given via source terms in the equation and in the second one a flux condition in the local part appears. For both models we prove existence and uniqueness of a solution that is obtained via direct minimization of the related energy functional. In the second part of this paper we extend these ideas to deal with local/nonlocal elasticity models in which we couple classical local elasticity with nonlocal peridynamics.

Local and Nonlocal Two-Electron Tunneling Processes in a Cooper Pair Splitter.

We measure the rates and coupling coefficients for local Andreev, nonlocal Andreev, and elastic cotunneling processes. The nonlocal Andreev process, giving rise to Cooper pair splitting, exhibits the same coupling coefficient as the elastic cotunneling whereas the local Andreev process is more than 2 orders of magnitude stronger than the corresponding nonlocal one. Theory estimates describe the findings and explain the large difference in the nonlocal and local coupling arising from competition between electron diffusion in the superconductor and tunnel junction transparency.