Nonlocal Interactions Research Articles

Su-Schrieffer-Heeger-Hubbard model at quarter filling: Effects of magnetic field and nonlocal interactions

Su-Schrieffer-Heeger-Hubbard model at quarter filling: Effects of magnetic field and nonlocal interactions

Arrest behavior of local resonators connected by nonlocal interaction in elastic wave metamaterials with machine learning prediction

Arrest behavior of local resonators connected by nonlocal interaction in elastic wave metamaterials with machine learning prediction

Onset of global instability in a premixed annular V-flame

We investigate self-excited axisymmetric oscillations of a lean premixed methane–air V-flame in a laminar annular jet. The flame is anchored near the rim of the centrebody, forming an inverted cone, while the strongest vorticity is concentrated along the outer shear layer of the annular jet. Consequently, the reaction and vorticity dynamics are largely separated, except where they coalesce near the flame tip. The global eigenmodes corresponding to the linearised reacting flow equations around the steady base state are computed in an axisymmetric setting. We identify an arc branch of eigenmodes exhibiting strong oscillations at the flame tip. The associated eigenvalues are robust with respect to domain truncation and numerical discretisation, and they become destabilised as the Reynolds number increases. The frequency of the leading eigenmode is found to correspond to the Lagrangian disturbance advection time from the nozzle outlet to the flame tip. The essential role of this convective mechanism is also supported by resolvent analysis, which finds that the same flame-tip disturbance structure and frequency are optimally amplified when the flame is subjected to external white noise forcing. Strong non-modal effects in the form of pseudo-resonance are not found. Nonlinear time-resolved simulation further reveals notable hysteresis phenomena in the subcritical regime prior to instability. Hence, even when the flame is linearly stable, perturbations of sufficient amplitude can trigger limit-cycle oscillations and higher-dimensional dynamics sustained by nonlinear feedback. A Monte Carlo simulation of passive tracers in the unsteady flame suggests a nonlinear non-local instability mechanism. Notably, linear analysis of the subcritical time-averaged limit-cycle state yields eigenvalues that do not match the nonlinear periodic oscillation frequencies. This mismatch is attributed to the fundamentally nonlinear dynamics of the subcritical V-flame instability, where the dichromatic, non-local interaction between the heat release rate along the flame surface and the vortex dynamics in the jet shear layer cannot be approximated as a simple distortion of the mean flow.

Cavity-modified local and non-local electronic interactions in molecular ensembles under vibrational strong coupling.

Resonant vibrational strong coupling (VSC) between molecular vibrations and quantized field modes of low-frequency optical cavities constitutes the conceptual cornerstone of vibro-polaritonic chemistry. In this work, we theoretically investigate the role of complementary nonresonant electron-photon interactions in the cavity Born-Oppenheimer (CBO) approximation. In particular, we study cavity-induced modifications of local and non-local electronic interactions in dipole-coupled molecular ensembles under VSC. Methodologically, we combine CBO perturbation theory (CBO-PT) [E. W. Fischer and P. Saalfrank, J. Chem. Theory Comput. 19, 7215 (2023)] with non-perturbative CBO Hartree-Fock (HF) and coupled cluster (CC) theories. In a first step, we derive up to second-order CBO-PT cavity potential energy surfaces, which reveal non-trivial intra- and inter-molecular corrections induced by the cavity. We then introduce the concept of a cavity reaction potential (CRP), minimizing the electronic energy in the cavity subspace to discuss vibro-polaritonic reaction mechanisms. We present reformulations of CBO-HF and CBO-CC approaches for CRPs and derive second-order approximate CRPs from CBO-PT for unimolecular and bimolecular scenarios. In the unimolecular case, we find small local modifications of molecular potential energy surfaces for selected isomerization reactions dominantly captured by the first-order dipole fluctuation correction. Excellent agreement between CBO-PT and non-perturbative wave function results indicates minor VSC-induced state relaxation effects in the single-molecule limit. In the bimolecular scenario, CBO-PT reveals an explicit coupling of interacting dimers to cavity modes besides cavity-polarization dependent dipole-induced dipole and van der Waals interactions with enhanced long-range character. An illustrative CBO-coupled cluster theory with singles and doubles-based numerical analysis of selected molecular dimer models provides a complementary non-perturbative perspective on cavity-modified intermolecular interactions under VSC.

Existence of subsonic periodic traveling waves in discrete Klein-Gordon type equations with nonlocal interaction

Existence of subsonic periodic traveling waves in discrete Klein-Gordon type equations with nonlocal interaction

Topological features of trajectories of virtual photons and their effective interaction under multiple scattering in a system of conductive nanoparticles

It is shown that in conditions of strong light localization in a system of Rayleigh's resonance scatterers, effective photon–photon interaction appears. This interaction is associated with neither nonlinearity of medium nor nonlocal interaction of polarization-entangled photon pairs. It is related to complex topology of photon trajectories due to multiple scattering. Because of this interaction, acts of simultaneous elastic scattering of pair of photons in the considered system cease to be independent processes. The differential cross section of this cooperative process contains only an extra degree of small Rayleigh's factor in comparison with the classical scattering cross section of a single photon. This opens up the possibility of control of light fluxes by means of alternative low-intensity light fluxes without using slow optoelectronic converters. Light localization that provides the effective photon–photon interaction is considered in the framework of a new formalism different from traditional one. Equation of the Bethe–Salpeter for two-photon propagator is resolved directly in coordinate representation without traditional reducing of this equation to some transport equation. This allows in a new light to look on reason of weak light localization and to show that weak localization is one of consequences of strong localization.

Analysis of multi-term arbitrary order implicit differential equations with variable type delay

Due to their capacity to simulate intricate dynamic systems containing memory effects and non-local interactions, fractional differential equations have attracted a great deal of attention lately. This study examines multi-term fractional differential equations with variable type delay with the goal of illuminating their complex dynamics and analytical characteristics. The introduction to fractional calculus and the justification for its use in many scientific and technical domains sets the stage for the remainder of the essay. It describes the importance of including variable type delay in differential equations and then applying it to model more sophisticated and realistic behaviours of real-world phenomena. The research study then presents the mathematical formulation of variable type delay and multi-term fractional differential equations. The system’s novelty stems from its unique combination of variable delay, generalized multi terms fractional differential operators (n and m), and integral implicit parameters, and studying the stability of the the newly formulated system as compared to the work in the existing literature. While the variable type delay is introduced as a function of time to describe instances where the delay is not constant, the fractional order derivatives are generated using the Caputo approach. The existence, uniqueness, and stability of solutions are the main topics of the theoretical analysis of the suggested differential equations. In order to establish important mathematical features, the inquiry makes use of spectral techniques, and fixed-point theorems. The study finishes by summarizing the major discoveries and outlining potential future research avenues in this developing field. It highlights the potential contribution of multi-term fractional differential equations with variable type delay to improving the control and design of complex systems. Overall, this study adds to the growing body of knowledge in the field of fractional calculus and provides insightful information about the investigation of multi-term fractional differential equations with variable type delay, making it pertinent for academics and practitioners from a variety of fields.

Revisiting the earliest hyperscanning study: power and functional connectivity in the alpha band may link brains far apart.

This brief report revisits the earliest known hyperscanning study published in 1965, which examined simultaneous EEG recordings of identical twins separated by six meters. The original study's findings suggested that eye closure in one twin elicited alpha activity in the other, despite physical separation. Leveraging contemporary signal processing techniques, we reanalyzed the digitized data to validate their findings. Spectral analysis confirmed alpha activity in the twins' EEG signals, aligning with the original observations. Multitapering along with background noise subtraction also revealed the alpha activity in the unrelated subject, which could not be observed by visual inspection alone. Coherence analysis revealed significant alpha band synchrony between a twin and an unrelated subject, differing from the initial study's conclusions. Our findings indicate that even historical data can yield new insights when revisited with contemporary data analysis tools and highlight the potential for future large-scale studies using advanced techniques to explore nonlocal brain interactions.

Multi-functional periodically heterogeneous structures for energy harvesting and vibration attenuation-effects of piezoelectricity and shunting circuits

Abstract We explore a kind of metamaterial plate structures intended for simultaneous energy harvesting and vibration control. These structures are designed using a periodically perforated piezoelectric plate (the matrix) with elastic inclusions situated in the holes and serving for the resonators. The design options comprise two- and three-phase configurations related to the mechanical connection between the matrix and inclusions. By introducing a singularity—the focal spot created as a defect in the perfectly periodic structure and using the theory of super-cell, an enhanced piezoelectric energy harvester is obtained. It is observed that such a meta-structure serves as a dual-purpose system: efficiently capturing vibrational energy at a focal spot while maintaining the overall vibration attenuation throughout the structure. The band gap analysis based on the Bloch’s wave decomposition theory shows that by concentrating energy and halting vibration propagation, approximately 10 times energy harvesting enhancement and a remarkable 100 dB reduction in vibrations are achieved simultaneously. Besides the passive response of these meta-structures, we consider its extension by an external electric circuit (EC). Such modified configurations enable to exploit ‘actively’ the piezoelectric plate property to transmit the mechanical response between two, or more distant locations. Due to nonlocal interactions introduced by means the controllable EC, we consider optimization of the EC impedance to reduce the vibrations at a selected location of the whole structure without any external energy supply. The computational study discovers perspectives and benefits of designing such active self-powered meta-structures.

On the Identifiability of Nonlocal Interaction Kernels in First-Order Systems of Interacting Particles on Riemannian Manifolds

On the Identifiability of Nonlocal Interaction Kernels in First-Order Systems of Interacting Particles on Riemannian Manifolds

Nonperturbative RG for the weak interaction corrections to the magnetic moment

We analyze, by rigorous renormalization group methods, a Fermi model for weak forces with a single family of leptons, one massless and the other with mass m=Me−β, with M the gauge boson mass, a quartic nonlocal interaction with coupling λ2, and a momentum cutoff Λ. The magnetic moment is written as a series in λ2, with n-th coefficients bounded by Cn(m2M2)β2n(Λ2M2)(1+0+)(n−1) if C is a constant; this implies convergence and provides nonperturbative bounds on the higher order contributions. The fact that the magnetic moment is associated with a dimensionally irrelevant quantity requires the implementation of cancellations in the multiscale analysis. Published by the American Physical Society 2024

Variations in non-local interaction range lead to emergent chase-and-run in heterogeneous populations.

In a chase-and-run dynamic, the interaction between two individuals is such that one moves towards the other (the chaser), while the other moves away (the runner). Examples can be found in both interacting cells and animals. Here, we investigate the behaviours that can emerge at a population level, for a heterogeneous group that contains subpopulations of chasers and runners. We show that a wide variety of patterns can form, from stationary patterns to oscillatory and population-level chase-and-run, where the latter describes a synchronized collective movement of the two populations. We investigate the conditions under which different behaviours arise, specifically focusing on the interaction ranges: the distances over which cells or organisms can sense one another's presence. We find that when the interaction range of the chaser is sufficiently larger than that of the runner-or when the interaction range of the chase is sufficiently larger than that of the run-population-level chase-and-run emerges in a robust manner. We discuss the results in the context of phenomena observed in cellular and ecological systems, with particular attention to the dynamics observed experimentally within populations of neural crest and placode cells.

Review of approximation formulas for fractional derivatives of variable order

Fractional differential equations of variable order, depending on a time or space variable, are successfully used to study time and/or spatial dynamics. The purpose of this review is to consider the latest research and results related to the basic definitions and approximation formulas for fractional derivatives of variable order. The review begins with an examination of existing definitions based on various physical and practical knowledge. The following are formulas for discretizing fractional derivatives, since they play a key role in numerical modeling, providing an effective means of describing complex systems with long-term memory, heterogeneous parameters and non-local interactions. Their use not only improves the accuracy of models, but also facilitates the numerical solution of differential equations, which is essential for analyzing and predicting the behavior of real processes in various fields of science and engineering. This review is intended to help readers select appropriate definitions and discretization formulas to effectively solve specific physical and engineering problems.

Transitions between Localised Patterns with Different Spatial Symmetries in Non-Local Hyperbolic Models for Self-Organised Biological Aggregations

Pattern formation in biological aggregations is a topic of great interest, due to the complex spatial structure of various aggregations of cells/bacteria/animals that can be observed in nature. While many such aggregations look similar at the macroscopic level, they might differ in their microscopic spatial structure. However, the complexity of the non-linear and sometimes non-local interactions among individuals inside these aggregations makes it difficult to investigate these spatial structures. In this study, we investigate numerically the transitions between different spatial patterns of animal aggregations with various symmetries (even, odd or no symmetry) that characterise the microscopic distribution of individuals inside these aggregations. To this end, we construct a bifurcation diagram starting with perturbations of spatially homogeneous solutions with low, medium, and high amplitudes. For perturbations with low amplitudes, the bifurcating structures show transitions among even-symmetric, odd-symmetric, and non-symmetric solutions. For perturbations with large amplitudes, there are wide parameter regions with non-convergent solutions, characterised by oscillatory transitions between different relatively similar solutions. These numerical results emphasize: (i) the effect of nonlinear and non-local interactions on the microscopically different symmetric/non-symmetric structures of macroscopically similar ecological aggregations; (ii) the difficulty of developing continuation algorithms for this class of non-local models.

Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems

We introduce a novel method of efficiently simulating the non-equilibrium steady state of large many-body open quantum systems with highly non-local interactions, based on a variational Monte Carlo optimization of a matrix product operator ansatz. Our approach outperforms and offers several advantages over comparable algorithms, such as an improved scaling of the computational cost with respect to the bond dimension for periodic systems. We showcase the versatility of our approach by studying the phase diagrams and correlation functions of the dissipative quantum Ising model with collective dephasing and long-ranged power law interactions for spin chains of up to N=100 spins.

Damage analysis of OC4 jacket subjected to cyclic loading by peridynamic approach

Catastrophic structural failure caused by fatigue damage under cyclic loads can be avoided by identifying critical locations of the damage initiation and the fatigue life during the design stage. Peridynamic (PD) theory defines structure as a collection of material points with non-local bond interactions where the structural discontinuity due to fatigue represented by instantaneous bond breakage is estimated through cumulative decrement of the bond’s life at each load cycle. In this work, we model a reference jacket presented under the Offshore Code Comparison Collaboration Continuation project (OC4) through peridynamic beam formulation. Initially, the static deformations of the beam and deformations of the OC4 jacket under static, harmonic, and irregular point loads are validated with ABAQUS results in all six degrees of freedom. Thereby, the PD fatigue parameters of the jacket’s steel material are calibrated from the experimental data of the corresponding material with a trial simulation for fatigue damage analysis. Later, different load cases from regular waves interacting with the jacket are generated in the PD framework by adopting linear wave theory. Based on the PD cyclic energy release rate model, a comparative study of all load cases to identify critical damage locations with the failure load cycles for damage initiation and fracture is performed for the considered OC4 jacket.

Maximizers of nonlocal interactions of Wasserstein Type

We characterize the maximizers of a functional that involves the minimization of the Wasserstein distance between sets of equal volume. We prove that balls are the only maximizers by combining a symmetrization-by-reflection technique with the uniqueness of optimal transport plans. Further, in one dimension, we provide a sharp quantitative refinement of this maximality result.

Unconventional superconductivity and paramagnetic Meissner response triggered by nonlocal pairing interaction in proximitized heterostructures

Unconventional superconductivity and paramagnetic Meissner response triggered by nonlocal pairing interaction in proximitized heterostructures

Boundary-localized many-body bound states in the continuum

Bound states in the continuum (BICs), referring to spatially localized bound states with energies falling within the range of extended modes, have been extensively investigated in single-particle systems, leading to diverse applications in photonics, acoustics, and other classical-wave systems. Recently, there has been theoretical interest in exploring many-body BICs in interacting quantum systems, which necessitate the careful design of impurity potentials or spatial profiles of interaction. Here, we propose a type of many-body BICs localized at boundaries, which can be purely induced by the uniform onsite interaction without requiring any specific design of impurity potential or nonlocal interaction. We numerically show that three or more interacting bosons can concentrate on the boundary of a homogeneous one-dimensional lattice, which is absent at single- and two-particle counterparts. Moreover, the eigenenergy of multi-boson bound states can embed within the continuous energy spectra of extended scattering states, thereby giving rise to interaction-induced boundary many-body BICs. Furthermore, by mapping Fock states of three and four bosons to nonlinear circuit networks, we experimentally simulate boundary many-body BICs. Our findings enrich the comprehension of correlated BICs beyond the single-particle level, and have the potential to inspire future investigations on exploring many-body BICs.

Spread complexity and quantum chaos for periodically driven spin chains.

The complexity of quantum states under dynamical evolution can be investigated by studying the spread with time of the state over a predefined basis. It is known that this complexity is minimized by choosing the Krylov basis, thus defining the spread complexity. We study the dynamics of spread complexity for quantum maps using the Arnoldi iterative procedure. The main illustrative quantum many-body model we use is the periodically kicked Ising spinchain with nonintegrable deformations, a chaotic system where we look at both local and nonlocal interactions. In the various cases, we find distinctive behavior of the Arnoldi coefficients and spread complexity for regular versus chaotic dynamics: suppressed fluctuations in the Arnoldi coefficients as well as larger saturation value in spread complexity in the chaotic case. We compare the behavior of the Krylov measures with that of standard spectral diagnostics of chaos. We also study the effect of changing the driving frequency on the complexity saturation.