Effects Of Nonlocal Interactions Research Articles

Stability and spatiotemporal patterns of a memory-based diffusion equation with nonlocal interaction

In this paper, we investigate the spatiotemporal dynamics driven by the memory delay and nonlocal interaction for the memory-based diffusion equation, where the nonlocal interaction is characterized by the given Green function. It has been shown that this kind of nonlocal interaction can lead to inhomogeneous steady states with any modes, and the joint effect of nonlocal interaction and memory delay can lead spatially inhomogeneous Hopf bifurcation and Turing–Hopf bifurcation.

The effect of nonlocal interaction on chaotic dynamics, Turing patterns, and population invasion in a prey-predator model.

Pattern formation is a central process that helps to understand the individuals' organizations according to different environmental conditions. This paper investigates a nonlocal spatiotemporal behavior of a prey-predator model with the Allee effect in the prey population and hunting cooperation in the predator population. The nonlocal interaction is considered in the intra-specific prey competition, and we find the analytical conditions for Turing and Hopf bifurcations for local and nonlocal models and the spatial-Hopf bifurcation for the nonlocal model. Different comparisons have been made between the local and nonlocal models through extensive numerical investigation to study the impact of nonlocal interaction. In particular, a legitimate range of nonlocal interaction coefficients causes the occurrence of spatial-Hopf bifurcation, which is the emergence of periodic patterns in both time and space from homogeneous periodic solutions. With an increase in the range of nonlocal interaction, the whole Turing pattern suppresses after a certain threshold, and no pure Turing pattern exists for such cases. Specifically, at low diffusion rates for the predators, nonlocal interaction in the prey population leads to the extinction of predators. As the diffusion rate of predators increases, impulsive wave solutions emerge in both prey and predator populations in a one-dimensional spatial domain. This study also includes the effect of nonlocal interaction on the invasion of populations in a two-dimensional spatial domain, and the nonlocal model produces a patchy structure behind the invasion where the local model predicts only the homogeneous structure for such cases.

Chemically coupled Hindmarsh–Rose neurons with cross interactions between membrane potential and magnetic flux

In this work, we have analysed the synchronous dynamics and pattern formation in Hindmarsh–Rose neurons with cross interactions between membrane potential and magnetic flux, in the chemical mode. The self, mixed and cross interactions are realised by varying coupling phase. The magnetic flux induces plateau bursting and amplitude death in the network. The self chemical coupling induces synchrony, whereas, the cross coupling is incapable of it. However, the cross coupling acts along with self coupling to form mixed coupling and induces synchrony in the system. The stability of the synchronous state has been studied by master stability approach. The parameter space reveals the bifurcation point at which cross coupling overrides self coupling effects. The synchronising ability of interactions are justified in a network of neurons as well. The statistical factor of synchronisation quantifies the amount of synchrony in the network in different interaction modes. The combined effect of non local interactions and mixed coupling of variables initiates the emergence of chimera and multichimera states. However, in cross-coupled systems, only incoherent states are present. The existence of chimera and multichimera states are confirmed by calculating the strength of incoherence and discontinuity measure. The analysis of spatiotemporal patterns reveals the presence of travelling chimeras within the network. The Hamilton energy function indicate that a greater amount of energy is required to sustain coherent neurons at higher potential. This work may enhance the understanding of chimera states and improve its applicability to real-world systems.

Non-local interaction effects in models of interacting populations

We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka–Volterra’s classical equations. The main feature of this work is that the interaction terms are non local and the interactions occur within a bounded range. These terms include the competitive intraspecific interaction among individuals and the interspecific terms for which we consider two cases: Competition and predation. The results show that not only the non-locality induces spatial structures but also allows for the survival of the species when due to predation or the competitive exclusion extinction was expected, and even promotes spatio-temporal patterns not linked to eventual temporal oscillations in the local case. In this work, we also explore some interesting details about the behavior of the population dynamics that shows spatial patterns that interfere in a way that leads to non-trivial results. In this way, we complement and extend some results obtained in previous works.

Effects of nonlocal interactions in describing V centers of MgO

The electronic structure and optical absorption spectrum of V 0 and center in MgO are investigated based on the density functional theory. The V-type centers are well described when the local symmetry around Mg vacancy is destroyed by using the nonlocal hybrid functionals. It is demonstrated that the holes are trapped on one (or two) O atoms around Mg vacancy for (or V 0) center. The defect states are separated from the valence bands due to the nonlocal exchange interactions involved in the hybrid functionals, which is the key to describing the optical properties correctly. At ambient condition, the absorption peaks ∼2.5 eV and ∼2.6 eV are assigned to V 0 and center, respectively, and they exhibit blue shift with increasing pressure.

Tunneling density of states in a Luttinger liquid in proximity to a superconductor: Effect of nonlocal interaction

A recent study have shown that it is possible to have enhancement, in contrast to an expected suppression, in tunneling density of states (TDOS) in a Luttinger liquid (LL) which is solely driven by the non-local density-density interactions. Also, it is well known that a LL in proximity to a superconductor (SC) shows enhancement in TDOS in the vicinity of the junction in the zero energy limit. In this paper, we study the interplay of nonlocal density-density interaction and superconducting correlations in the TDOS in the vicinity of the SC-LL junction, where the LL maybe realized on the edge of an integer or a fractional quantum Hall state. We show that the TDOS enhancement in a LL quantum wire (QW) due to superconducting correlation at the junction can be farther amplified in presence of appropriate choice of non-local interaction parameters, which is demonstrated through a neat algebraic expression in the weak interaction limit. We also show that, in the full parameter regime comprising both the local and the non-local interaction, the region of enhanced TDOS for LL junction with "superconducting" boundary condition and that of "non-superconducting charge conserving" boundary condition (discussed in Phys. Rev. B 104, 045402 (2021)) are mutually exclusive. We show that this fact can be understood in terms of symmetry relation established between the superconducting and non-superconducting sectors of the theory. We compare the dependence of the proximity induced pair potential and TDOS as a function of distance $x$ from the junction. We demonstrate that the dependence of the spatial power law exponent for the `TDOS(x)/TDOS(x -> 0)' and the `pair-potential(x)/pair-potential(x -> 0)' are distinct function of the various local and non-local interaction parameters, which implies that the TDOS enhancement can not be directly attributed to the proximity induced pair potential in the LL.

Nonlocality-induced surface localization in Bose-Einstein condensates of light

The ability to create and manipulate strongly correlated quantum many-body states is of central importance to the study of collective phenomena in several condensed-matter systems. In the last decades, a great amount of work has been focused on ultracold atoms in optical lattices, which provide a flexible platform to simulate peculiar phases of matter both for fermionic and bosonic particles. The recent experimental demonstration of Bose-Einstein condensation (BEC) of light in dye-filled microcavities has opened the intriguing possibility to build photonic simulators of solid-state systems, with potential advantages over their atomic counterpart. A distinctive feature of photon BEC is the thermo-optical nature of the effective photon-photon interaction, which is intrinsically nonlocal and can thus induce interactions of arbitrary range. This offers the opportunity to systematically study the collective behaviour of many-body systems with tunable interaction range. In this paper, we theoretically study the effect of nonlocal interactions in photon BEC. We first present numerical results of BEC in a double-well potential, and then extend our analysis to a short one-dimensional lattice with open boundaries. By resorting to a numerical procedure inspired by the Newton-Raphson method, we simulate the time-independent Gross-Pitaevskii equation and provide evidence of surface localization induced by nonlocality, where the condensate density is localized at the boundaries of the potential. Our work paves the way towards the realization of synthetic matter with photons, where the interplay between long-range interactions and low dimensionality can lead to the emergence of unexplored nontrivial collective phenomena.

Fractional-order structural stability: Formulation and application to the critical load of nonlocal slender structures

This study presents a framework to perform stability analysis of nonlocal solids whose behavior is described according to the fractional-order continuum theory. In this formulation, space fractional-order operators are used to capture the nonlocal response of the medium by means of nonlocal kinematic relations. We use the geometrically nonlinear fractional-order kinematic relations within an energy based approach to establish the Lagrange-Dirichlet stability criteria for nonlocal structures. This energy based approach to nonlocal structural stability is possible due to a positive-definite and thermodynamically consistent definition of the deformation energy enabled by the fractional-order kinematic formulation. The Rayleigh-Ritz coefficient for critical load is also derived for linear buckling conditions. The fractional-order formulation is finally used to determine critical loads for buckling of the slender nonlocal beams and plates using a dedicated fractional-order finite element solver. Results establish that, in contrast to existing studies, the effect of nonlocal interactions is observed on both the material and the geometric stiffness, when using the fractional-order kinematics approach. These observations are supported quantitatively via the solution of case studies that focus on the critical buckling response of fractional-order nonlocal slender structures, and a direct comparison of the fractional-order approach with classical nonlocal approaches.

Second harmonic generation theory for a helical macromolecule with high sensitivity to structural disorder.

Microscopic theory for the second harmonic generation in a helical molecular system is developed in the minimal coupling representation including non-local interaction effects. At the second order to the field we find a compact expression which combines dipolar, quadrupolar and magnetic contributions. A detailed derivation of the response is performed to specifically isolate the quadratic coupling terms, which we denote as the K coupling. Applying the theory to a helical macromolecule we find that the dipolar and quadrupolar contributions reflect the symmetry properties of the system and its homogeneity, while the K coupling contribution reveals inhomogeneities of the system.

Collective modes in excitonic insulators: Effects of electron-phonon coupling and signatures in the optical response

We consider a two-band spinless model describing an excitonic insulator (EI) on the two-dimensional square lattice with anisotropic hopping parameters and electron-phonon (el-ph) coupling, inspired by the EI candidate Ta$_2$NiSe$_5$. We systematically study the nature of the collective excitations in the ordered phase which originates from the interband Coulomb interaction and the el-ph coupling. When the ordered phase is stabilized only by the Coulomb interaction (pure EI phase), its collective response exhibits a massless phase mode in addition to the amplitude mode. We show that in the BEC regime, the signal of the amplitude mode becomes less prominent and that the anisotropy in the phase mode velocities is relaxed compared to the model bandstructure. Through coupling to the lattice, the phase mode acquires a mass and the signal of the amplitude mode becomes less prominent. Importantly, character of the softening mode at the boundary between the normal semiconductor phase and the ordered phase depends on the parameter condition. In particular, we point out that even for el-ph coupling smaller than the Coulomb interaction the mode that softens to zero at the boundary can have a phonon character. We also discuss how the collective modes can be observed in the optical conductivity. Furthermore, we study the effects of nonlocal interactions on the collective modes and show the possibility of realizing a coexistence of an in-gap mode and an above-gap mode split off from the single amplitude mode in the system with the local interaction only.

Nonlocal Coulomb interaction and spin-freezing crossover as a route to valence-skipping charge order

Multiorbital systems away from global half-filling host intriguing physical properties promoted by Hund’s coupling. Despite increasing awareness of this regime dubbed Hund’s metal, effect of nonlocal interaction is still elusive. Here we study a three-orbital model with 1/3 filling (two electrons per site) including the intersite Coulomb interaction (V). Using the GW plus extended dynamical mean-field theory, the valence-skipping charge order transition is shown to be driven by V. Most interestingly, the instability to this transition is significantly enhanced in the spin-freezing crossover regime, thereby lowering the critical V to the formation of charge order. This behavior is found to be closely related to the population profile of the atomic multiplet states in the spin-freezing regime. In this regime, maximum spin states are dominant in each total charge subspace with substantial amount of one- and three-electron occupations, which leads to almost equal population of one- and the maximum spin three-electron state. Our finding unveils another feature of the Hund’s metal and has potential implications for the broad range of multiorbital systems as well as the recently discovered charge order in iron pnictides.

Photoenhanced excitonic correlations in a Mott insulator with nonlocal interactions

We investigate the effect of nonlocal interactions on the photo-doped Mott insulating state of the two-dimensional Hubbard model using a nonequilibrium generalization of the dynamical cluster approximation. In particular, we compare the situation where the excitonic states are lying within the continuum of doublon-holon excitations to a set-up where the excitons appear within the Mott gap. In the first case, the creation of nearest-neighbor doublon-holon pairs by excitations across the Mott gap results in enhanced excitonic correlations, but these excitons quickly decay into uncorrelated doublons and holons. In the second case, photo-excitation results in long-lived excitonic states. While in a low-temperature equilibrium state, excitonic features are usually not evident in single-particle observables such as the photoemission spectrum, we show that the photo-excited nonequilibrium system can exhibit in-gap states associated with the excitons. The comparison with exact-diagonalization results for small clusters allows us to identify the signatures of the excitons in the photo-emission spectrum.

The influence of nonlocal interactions on valence transitions and formation of excitonic bound states in the generalized Falicov–Kimball model

We use the density-matrix-renormalization-group (DMRG) method to study the combined effects of nonlocal interactions on valence transitions and the formation of excitonic bound states in the generalized Falicov-Kimball model. In particular, we consider the nearest-neighbour Coulomb interaction $U_{nn}$ between two $d$, two $f$, $d$ and $f$ electrons as well as the so-called correlated hopping term $U_{ch}$ and examine their effects on the density of conduction $n_d$ (valence $n_f$) electrons and the excitonic momentum distribution $N(q)$. It is shown that $U_{nn}$ and $U_{ch}$ exhibit very strong and fully different effects on valence transitions and the formation (condensation) of excitonic bound states. While the nonlocal interaction $U_{nn}$ suppresses the formation of zero momentum condensate ($N(q$=$0)$) and stabilizes the intermediate valence phases with $n_d \sim 0.5, n_f \sim 0.5$, the correlated hopping term $U_{ch}$ significantly enhances the number of excitons in the zero-momentum condensate and suppresses the stability region of intermediate valence phases. The physically most interesting results are observed if both $U_{nn}$ and $U_{ch}$ are nonzero, when the combined effects of $U_{nn}$ and $U_{ch}$ are able to generate discontinuous changes in $n_f$, $N(q$=$0)$ and some other ground-state quantities.

Pattern formation in a diffusive intraguild predation model with nonlocal interaction effects

In this paper, we investigate the spatiotemporal pattern formation in a diffusive intraguild predation (IGP) model with a nonlocal interaction term in the growth of the shared resource, which extends previous studies of local reaction-diffusion IGP model. We first perform the stability and Hopf bifurcation analyses for the unique positive equilibrium of the corresponding non-spatial system, and give analytical formulas to determine the direction and stability of the bifurcating periodic solutions. Then the linear stability analysis for the nonlocal model shows that the nonlocal interaction is a key mechanism for the formation of Turing patterns. Numerical simulations show that low conversion rate from resource to IG predator can induce stationary Turing patterns, intermediate conversion rate can induce regular oscillatory patterns, and high conversion rate can induce irregular spatiotemporal chaotic patterns for certain diffusive rate. The impact of nonlocal interaction on the resulting patterns with certain diffusive rate is further explored by numerical simulations, which show that nonlocal interaction can induce pattern transition from stationary Turing patterns to non-stationary oscillatory patterns, and even to spatiotemporal chaotic patterns with the increase of the nonlocal interaction tensity. In addition, spatiotemporal chaotic patterns are found in the Turing-Hopf parametric space, which enrich pattern dynamics for diffusive IGP models with nonlocal interactions.

Generation of atypical hopping and interactions by kinetic driving

We study the effect of time-periodically varying the hopping amplitude in a one-dimensional Bose–Hubbard model, such that its time-averaged value is zero. Employing Floquet theory, we derive a static effective Hamiltonian in which nearest-neighbor single-particle hopping processes are suppressed, but all even higher-order processes are allowed. Unusual many-body features arise from the combined effect of nonlocal interactions and correlated tunneling. At a critical value of the driving, the system passes from a Mott insulator to a superfluid formed by two quasi-condensates with opposite non-zero momenta. This work shows how driving of the hopping energy provides a novel form of Floquet engineering, which enables atypical Hamiltonians and exotic states of matter to be produced and controlled.

Effect of non-local interactions on the vortex solution in Bose-Einstein Condensates

We consider the Gross-Pitaevskii (GP) model of a Bose-Einstein Condensate (BEC) to study a single vortex line in the presence of non-local repulsive s-wave scattering. We show that in addition to the vortex solution with core width of the order of the healing length, there exists a vortex solution whose width is a microscopic length scale of the order of s-wave scattering length and is independent of the healing length. We compare the two classes of vortex solution and show the region where one can possibly observe the vortex whose width is of the order of scattering length.

Dynamical effects of nonlocal interactions in discrete-time growth-dispersal models with logistic-type nonlinearities

The paper is devoted to the study of discrete time and continuous space models with nonlocal resource competition and periodic boundary conditions. We consider generalizations of logistic and Ricker's equations as intraspecific resource competition models with symmetric nonlocal dispersal and interaction terms. Both interaction and dispersal are modeled using convolution integrals, each of which has a parameter describing the range of nonlocality. It is shown that the spatially homogeneous equilibrium of these models becomes unstable for some kernel functions and parameter values by performing a linear stability analysis. To be able to further analyze the behavior of solutions to the models near the stability boundary, weakly nonlinear analysis, a well-known method for continuous time systems, is employed. We obtain Stuart–Landau type equations and give their parameters in terms of Fourier transforms of the kernels. This analysis allows us to study the change in amplitudes of the solutions with respect to ranges of nonlocalities of two symmetric kernel functions. Our calculations indicate that supercritical bifurcations occur near stability boundary for uniform kernel functions. We also verify these results numerically for both models.

Spatio-temporal pattern formation in Rosenzweig–MacArthur model: Effect of nonlocal interactions

Spatio-temporal pattern formation in reaction–diffusion models of interacting populations is an active area of research due to various ecological aspects. Instability of homogeneous steady-states can lead to various types of patterns, which can be classified as stationary, periodic, quasi-periodic, chaotic, etc. The reaction–diffusion model with Rosenzweig–MacArthur type reaction kinetics for prey–predator type interaction is unable to produce Turing patterns but some non-Turing patterns can be observed for it. This scenario changes if we incorporate non-local interactions in the model. The main objective of the present work is to reveal possible patterns generated by the reaction–diffusion model with Rosenzweig–MacArthur type prey–predator interaction and non-local consumption of resources by the prey species. We are interested in the existence of Turing patterns in this model and in the effect of the non-local interaction on the periodic travelling wave and spatio-temporal chaotic patterns. Global bifurcation diagrams are constructed to describe the transition from one pattern to another one.

Capturing nonlocal interaction effects in the Hubbard model: Optimal mappings and limits of applicability

We investigate the Peierls-Feynman-Bogoliubov variational principle to map Hubbard models with nonlocal interactions to effective models with only local interactions. We study the renormalization of the local interaction induced by nearest-neighbor interaction and assess the quality of the effective Hubbard models in reproducing observables of the corresponding extended Hubbard models. We compare the renormalization of the local interactions as obtained from numerically exact determinant Quantum Monte Carlo to approximate but more generally applicable calculations using dual boson, dynamical mean field theory, and the random phase approximation. These more approximate approaches are crucial for any application with real materials in mind. Furthermore, we use the dual boson method to calculate observables of the extended Hubbard models directly and benchmark these against determinant Quantum Monte Carlo simulations of the effective Hubbard model.

Deformation mechanism of graphene in amorphous polyethylene: A molecular dynamics based study

The current paper focuses on investigating deformation mechanism of graphene sheets in a graphene reinforced polyethylene (Gn–PE) nanocomposite. Classical molecular dynamics (MD) simulation was conducted on large Gn–PE systems. Different spatial arrangements of graphene sheets were considered in order to study the effect of nonlocal interaction among the graphenes. In all the cases 5% weight concentration of graphene was considered in order to prepare atomistic models for Gn–PE. As expected, graphene seemed to enhance the overall Young’s modulus and tensile strength of the Gn–PE nanocomposite. Randomly oriented graphenes with strong nonlocal interaction were observed to be comparatively preferable than the other spatial arrangements of graphenes. The high strength and stiffness of graphene sheets can be properly utilized if the graphenes are randomly oriented and have strong long range interactions. Finally, the failure mechanism of the graphene and role of voids in the polymer were discussed both qualitatively and quantitatively. It was seen that the randomly oriented graphenes were firstly pulled out from the polyethylene matrix during deformation prior to breaking into pieces. This can explain the loss of stiffness and strength in graphene sheets embedded in the polymer matrix. From the current work it is clearly understood that the necessity of the long range graphene–graphene interaction is important in both elastic as well as plastic regime of the deformation.