Nonlocal Coupling Research Articles

Anomalous quantum dynamics in a lossy nonlocal system

Abstract The non-Hermitian skin effect and non-Hermitian edge burst reflect the vital role of the spatial boundary in non-Hermitian systems from both static and dynamic perspectives. Here, we study a non-Hermitian dissipative lattice with nonlocal coupling and demonstrate many interesting static and dynamic phenomena. In the case of a global coupling with all sites coupled with each other, we observe an anomalous hopping resonance, at which a quantum walker initially placed at one single site almost completely escape from the boundary of the system regardless of its initial position. In the case of the non-global, but still infinite-range coupling, the interplay between nonlocal hopping and non-Hermitian skin effect leads to the emergence of local bulk modes presenting multi-partite density distribution. The presence of local bulk modes induce nontrivial dynamics of a quantum walker, featuring multiple peaks of lost probability in spatially separated domains. Our findings demonstrate unique properties induced by nonlocal coupling in non-Hermitian systems.

Singlet, triplet, and mixed all-to-all pairing states emerging from incoherent fermions

The electron-electron and electron-phonon coupling in complex materials can be more complicated than simple density-density interactions, involving intertwined dynamics of spin, charge, and spatial symmetries. This motivates studying universal models with complex interactions and whether BCS-type singlet pairing is still the “natural” fate of the system. To this end, we construct a Yukawa-SYK model with nonlocal couplings in both spin and charge channels. Furthermore, we provide for time-reversal-symmetry breaking dynamics by averaging over the Gaussian unitary ensemble rather than the orthogonal ensemble. We find that the ground state of the system can be an orbitally nonlocal superconducting state arising from incoherent fermions with no BCS-like analog. The superconductivity has an equal tendency to triplet and singlet pairing states separated by a non-Fermi liquid phase. We further study the fate of the system within the superconducting phase and find that the expected ground state, away from the critical point, is a mixed singlet/triplet state. Finally, we find that, while at Tc the triplet and singlet transitions are dual to one another, below Tc the duality is broken, with the triplet state more susceptible to orbital fluctuations just by its symmetry. Our results indicate that such fluctuation-induced mixed states may be an inherent feature of strongly correlated materials. Published by the American Physical Society 2024

Shape optimization for high efficiency metasurfaces: theory and implementation

Complex non-local behavior makes designing high efficiency and multifunctional metasurfaces a significant challenge. While using libraries of meta-atoms provide a simple and fast implementation methodology, pillar to pillar interaction often imposes performance limitations. On the other extreme, inverse design based on topology optimization leverages non-local coupling to achieve high efficiency, but leads to complex and difficult to fabricate structures. In this paper, we demonstrate numerically and experimentally a shape optimization method that enables high efficiency metasurfaces while providing direct control of the structure complexity through a Fourier decomposition of the surface gradient. The proposed method provides a path towards manufacturability of inverse-designed high efficiency metasurfaces.

Broadband acoustic metamaterial absorber

Constrained by the causality nature, it is a challenge to achieve low-frequency broadband efficient absorption via passive materials. By coupling local resonances as many as possible, broadband metamaterial absorbers can be realized. In this scenario, the coupling effect is crucial for improving the absorption efficiency. Here, we demonstrate a kind of acoustic metamaterial absorber capable of high-efficiency broadband absorption by optimizing the non-local coupling effect. Cascade neck-embedded Helmholtz resonator is designed as the subunit of the metamaterial absorber. By coupling 36 subunits, a metamaterial absorber is constructed with the aid of optimization algorithm. The simulation results suggest that strong non-locality is induced in the near field, which effectively suppresses the impedance oscillations and absorption dips at the antiresonance frequencies. Eventually, the presented metamaterial absorber realizes impedance matching to the air from 320 Hz to 6400 Hz, leading to efficient broadband absorption performance. The results and methodologies in this work reveal the significance of non-local coupling effect in coupled-resonant metamaterials.

Efficient simulation of open quantum systems coupled to a reservoir through multiple channels.

It is challenging to simulate open quantum systems that are connected to a reservoir through multiple channels. For example, vibrations may induce fluctuations in both energy gaps and electronic couplings, which represent two independent channels of system-bath couplings. Systems of this kind are ubiquitous in the processes of excited state radiationless decay. Combined with density matrix renormalization group (DMRG) and matrix product states (MPS) methods, we develop an interaction-picture chain mapping strategy for vibrational reservoirs to simulate the dynamics of these open systems, resulting in time-dependent spatially local system-bath couplings in the chain-mapped Hamiltonian. This transformation causes the entanglement generated by the system-bath interactions to be restricted within a narrow frequency window of vibrational modes, enabling efficient DMRG/MPS dynamical simulations. We demonstrate the utility of this approach by simulating singlet fission dynamics using a generalized spin-boson Hamiltonian with both diagonal and off-diagonal system-bath couplings. This approach generalizes an earlier interaction-picture chain mapping scheme, allowing for efficient and exact simulation of systems with multi-channel system-bath couplings using matrix product states, which may further our understanding of nonlocal exciton-phonon couplings in exciton transport and the non-Condon effect in energy and electron transfer.

Death transitions in attractive–repulsive coupled oscillators with higher-order interactions

The first-order phase transition from oscillation to steady state, known as explosive death (ED), is prevalent in various dynamical models. However, previous studies on ED have predominantly focused on interactions between pairs of elements. In this work, we investigate how death transitions occur when both pairwise and three-body interactions are present in an extended Van der Pol oscillator network with attractive–repulsive coupling. By examining both global and non-local interaction mechanisms, the impact of higher-order interactions on ED and the differences in the transition process are comprehensively analyzed. Firstly, we construct a diagram of the global dynamics in the context of higher-order and first-order coupling strengths, identifying that the higher-order interactions promote the onset of ED with a contribution comparable to that of first-order interactions. Specifically, for global coupling, the theoretical backward critical curves matching the numerical results are derived through linear stability analyses, showcasing a linear correlation with a slope of -1 between the higher-order and first-order coupling strengths. Under non-local coupling, fitting the numerically obtained backward critical curves likewise yields a consistent quantitative relationship. Additionally, during the transition process of ED, we discover intriguing coexisting states in the hysteresis area under non-local coupling, including the coexistence of chimera states with coherent or incoherent oscillation, and the coexistence of chimera states with oscillation death. This is attributed to symmetry breaking induced by non-local action. These findings enhance the understanding of higher-order interactions in complex systems and provide a fresh perspective for studying multi-stability behavior in biochemical and physical systems.

Real-time methods in JT/SYK holography

Abstract We study the conventional holographic recipes and its real-time extensions in the context of the correspondence between SYK quantum mechanics and JT gravity. We first observe that only closed contours are allowed to have a 2d space-time holographic dual. Thus, in any real-time formulation of the duality, the boundaries of a classical connected geometry are a set of closed curves, parameterized by a complex \emph{closed} time contour as in the Schwinger-Keldysh framework. Thereby, a consistent extension of the standard holographic formulas is proposed, in order to describe the correspondence between gravity and boundary quantum models that include averaging on the coupling constants. We investigate our prescription in different AdS
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 solutions with Schwinger-Keldysh boundary condition, dual to a boundary quantum theory at finite temperature defined on a complex time contour, and consider also classical, asymptotically AdS solutions (wormholes) with two disconnected boundaries. In doing this, we revisit the so-called factorization problem, and its resolution in conventional holography by virtue of some (non-local) coupling between disconnected boundaries, and we show how in specific contexts, the averaging proposal by-passes the paradox as well, since it induces a similar effective coupling.

Reconstructing the Pseudo-2-Dimensional (p2D) Model in Comsol Multiphysics Using Mathematical Interfaces

The classic ‘pseudo-2-dimensional’ (p2D) model of Newman and co-workers (also known as the DFN model), with its different efficient implementations, is the state-of-the-art physics-based electrochemical model for lithium-ion batteries. COMSOL Multiphysics (COMSOL) is a popular modeling software for multiphysics simulations, and its Battery Design Module for Li-ion batteries is widely used in the battery modeling community. This work presents a step-wise model development for reconstructing the detailed p2D model equations. This includes variable model parameters and weak-form implementation for the solid-phase diffusion, eliminating the need for non-local couplings and approximations for modeling the pseudo radial-dimension in the solid-phase.To model and understand the effect of capacity degradation on lithium-ion cells, the battery models in COMSOL need to incorporate additional degradation mechanisms. In this work, we have followed the approach of equation-based modeling in COMSOL, which enables us to formulate the p2D model using the mathematical PDE interfaces. This approach provides us with a lot of flexibility in terms of battery degradation model formulation and helps develop a clearer understanding of the p2D model equation in light of the assumptions involved.The steps in the model development involved writing the conservation equations in the generic mathematics interfaces coupled with the additional equations for the degradation mechanisms. The efforts were centered on developing cycling simulations based on Events for practically relevant operating conditions. This custom model was validated against the results from COMSOL’s Battery Interface, in-house codes, and baseline cycle data from the experiments and further developed as a physicochemical degradation model for automotive, large-format Lithium-ion batteries.This equation-based COMSOL model with cycling works without the requirement for Battery Design Module, LiveLink and Application Builder and can be adopted for a variety of electrochemical modeling applications by the electrochemical modeling community.

Physics-based discrete models for magneto-mechanical metamaterials

Magneto-mechanical metamaterials are emerging smart materials whose mechanical responses can be tailored through structure architecture and magnetic interactions. The latter provides additional freedom in the material design space and leads to novel behaviors due to its nonlocal nature. The enriched functionalities open new possibilities in various applications, such as actuators, energy absorbers, and soft robots. However, the nonlinear and nonlocal coupling between elastic and magnetic forces poses a great challenge in the modeling and simulation of these systems, further hindering theory-based rational design strategies. Here, we focus on a class of magneto-mechanical metamaterials comprising elastic solids embedded with rigid permanent magnets. The clear separation between elastic and magnetic forces simplifies the design and fabrication process, yet their nonlocal interplay still allows for complex behaviors. We present a simulation framework for such magneto-mechanical metamaterials by combining a lattice spring model for the elastic solid with the dipole model for the magnetic interactions and implementing it in the LAMMPS molecular dynamics software. We demonstrate the capabilities of our framework by simulating a few representative structures, including shape-locking lattice metamaterials, a soft cellular solid with controllable buckling, and a metamaterial chain with phase-transforming behavior. For the shape-locking lattice metamaterials, we successfully capture the magnetic-actuation-driven reconfiguration and the nonlinear mechanical response of the curved lattices. For the soft cellular solid, we identify its buckling patterns under external non-uniform magnetic fields and simulate a buckling evolution process consistent with experiments. For the metamaterial chain, we include the strong long-range interactions among the embedded magnets and reproduce the controllable phase transitions in the experiments. Our work provides a simple yet versatile simulation methodology to investigate the nonlinear mechanical behaviors in the presence of strong external and internal magnetic forces, which will facilitate the design and analysis of magneto-mechanical materials. It can also be applied to other magnetically-driven smart structures, such as soft robots.

Roles of nonlocal electron-phonon coupling on the electrical conductivity and Seebeck coefficient: A time-dependent DMRG study

Roles of nonlocal electron-phonon coupling on the electrical conductivity and Seebeck coefficient: A time-dependent DMRG study

Theory of acoustic polarons in the two-dimensional SSH model applied to the layered superatomic semiconductor Re6Se8Cl2.

Layered superatomic semiconductors, whose building blocks are atomically precise molecular clusters, exhibit interesting electronic and vibrational properties. In recent work [Tulyagankhodjaev et al., Science 382, 438 (2023)], transient reflection microscopy revealed quasi-ballistic exciton dynamics in Re6Se8Cl2, which was attributed to the formation of polarons due to coupling with acoustic phonons. Here, we characterize the electronic, excitonic, and phononic properties with periodic density functional theory. We further parameterize a polaron Hamiltonian with nonlocal (Su-Schrieffer-Heeger) coupling to an acoustic phonon to study the polaron ground state binding energy and dispersion relation with variational wavefunctions. We calculate a polaron binding energy of about 10meV at room temperature, and the maximum group velocity of our polaron dispersion relation is 1.5 km/s, which is similar to the experimentally observed exciton transport velocity.

Impact of Local and Nonlocal Vibronic Coupling on the Absorption and Emission Spectra of J- and H-Dimers.

The impact of exciton-vibrational (EV) coupling involving low-energy ("slow") intermolecular vibrations and higher-energy ("fast") intramolecular vibrations on the absorption and emission spectra of H- and J-dimers is studied theoretically for a pair of chromophores with excitonic coupling dominated by transition dipole-dipole coupling, JC. Exact quantum-mechanical solutions based on a Frenkel-Holstein-Peierls Hamiltonian reveal a fascinating interplay between the two coupling sources in determining the spectral line widths, Stoke shifts and radiative decay rates. It is shown that the ratio rules derived from the vibronic progression of the fast mode in molecular dimers remain valid under the influence of slow-mode EV coupling under most conditions. However, a highly unusual aggregate behavior occurs when the product of local and nonlocal couplings, |gLgNL|, exceeds 2ℏωs|JC|, where ℏωs is the energy of the slow mode. In this regime and when gL and gNL are in-phase, an H-dimer (JC > 0) becomes strongly emissive and can even be super-radiant, while a J-dimer (JC < 0) with out-of-phase gL and gNL values becomes subradiant. Such behaviors are in marked contrast to the predictions of Kasha theory and demonstrate the richness of the photophysical behavior resulting from EV coupling involving inter- and intramolecular vibrations.

On the Quadratic Convergence of Newton’s Method for Mean Field Games with Non-separable Hamiltonian

AbstractWe analyze asymptotic convergence properties of Newton’s method for a class of evolutive Mean Field Games systems with non-separable Hamiltonian arising in mean field type models with congestion. We prove the well posedness of the Mean Field Game system with non-separable Hamiltonian and of the linear system giving the Newton iterations. Then, by forward induction and assuming that the initial guess is sufficiently close to the solution of problem, we show a quadratic rate of convergence for the approximation of the Mean Field Game system by Newton’s method. We also consider the case of a nonlocal coupling, but with separable Hamiltonian, and we show a similar rate of convergence.

An energy-efficient GMRES–multigrid solver for space-time finite element computation of dynamic poroelasticity

We present and analyze computationally Geometric MultiGrid (GMG) preconditioning techniques for Generalized Minimal RESidual (GMRES) iterations to space-time finite element methods (STFEMs) for a coupled hyperbolic–parabolic system modeling, for instance, flow in deformable porous media. By using a discontinuous temporal test basis, a time marching scheme is obtained. Higher order approximations that offer the potential to inherit most of the rich structure of solutions to the continuous problem on computationally feasible grids increase the block partitioning dimension of the algebraic systems, comprised of generalized saddle point blocks. Our V-cycle GMG preconditioner uses a local Vanka-type smoother. Its action is defined in an exact mathematical way. Due to nonlocal coupling mechanisms of 348 unknowns, the smoother is applied on patches of elements. This ensures damping of higher order error frequencies. By numerical experiments of increasing complexity, the efficiency of the solver for STFEMs of different polynomial order is illustrated and confirmed. Its parallel scalability is analyzed. Beyond this study of classical performance engineering, the solver’s energy efficiency is investigated as an additional and emerging dimension in the design and tuning of algorithms on the hardware.

Inverse-designed metasurfaces with facile fabrication parameters

Optical metasurfaces are planar nanostructured devices that are industrially attractive in part because they utilize high-throughput microelectronic fabrication techniques for implementation. It is therefore critical to develop design paradigms that can balance the realization of highly efficient wavefront responses together with device manufacturability. We introduce a gradient-based design framework for freeform metasurfaces in which nanoscale elements are explicitly constrained to feature basic shapes, nearly uniform feature sizes, and exceptionally low aspect ratios. In spite of the apparent uniformity of the metasurface geometric features, the devices are able to utilize nonlocal near-field optical coupling to achieve highly efficient and extreme wavefront scattering beyond conventional design methodologies. Utilizing this approach, we design facile high-numerical-aperture devices such as beam deflectors and large-area metalenses capable of diffraction-limited focusing. We anticipate that these concepts can facilitate the design and integration of metasurfaces into monolithic optical systems.

Emergence of chimera states in neural networks with distance-dependent mean field coupling

The emergence of chimera states in neural networks has been an interesting area of research in the past few years and aims to explore the complex brain functions. Even though the presence of chimera states in systems with nonlocal interaction is well known, its emergence in networks with global and local interactions is least explored. Different techniques like introducing distance dependent interactions and restricting initial conditions to certain classes are adopted to induce chimera states in such network. This work analyzes methods to induce chimera or multichimera states in a network of mean field coupled Hindmarsh–Rose neurons in ring topology. The interaction schemes in the network, viz., global, nonlocal and local are realized by limiting the number of neurons involved in coupling and the power law exponent gives a distance gradient effect to them. The studies have shown that, in global interaction, power law exponent induces chimera states and reduces the amount of synchrony in the network. The nonlocal coupling is self-capable of inducing chimera states and power law exponent enhances the capability. When the value of power law exponent is high, the synchrony level is independent of the number of neurons taking part in the coupling. The traveling chimera states are induced in the local (nearest neighbor) coupling by modifying the initial conditions.

Studies on Dual Helmholtz Resonators and Asymmetric Waveguides for Ventilated Soundproofing.

Achieving the simultaneity of ventilation and soundproofing is a significant challenge in applied acoustics. Ventilated soundproofing relies on the interplay between local resonance and nonlocal coupling of acoustic waves within a sub-wavelength structure. However, previously studied structures possess limited types of fundamental resonators and lack modifications from the basic arrangement. These constraints often force the specified position of each attenuation peak and low absorption performance. Here, we suggest the in-duct-type sound barrier with dual Helmholtz resonators, which are positioned around the symmetry-breaking waveguides. The numerical simulations for curated dimensions and scattered fields show the aperiodic migrations and effective amplifications of the two absorptive domains. Collaborating with the subsequent reflective domains, the designed structure holds two effective attenuation bands under the first Fabry-Pérot resonance frequency. This study would serve as a valuable example for understanding the local and non-local behaviors of sub-wavelength resonating structures. Additionally, it could be applied in selective noise absorption and reflection more flexibly.

Hybrid variable exponent model for image denoising: A nonstandard high-order PDE approach with local and nonlocal coupling

In this paper, we propose a novel hybrid model combining local and nonlocal methods for effective image denoising. The model utilizes variable exponents p(x) to achieve adaptive diffusion behavior and preserve image features. Nevertheless, the coupling structure of our proposed process, along with the spatial dependence of p(x), poses challenges in theoretical analysis. To address this, we investigate the existence and uniqueness of the solution using the Faedo-Galerkin approximation, a priori estimates, and compactness considerations. Through these theoretical investigations, we demonstrate the existence of a weak solution for the coupled parabolic system. Overall, our model outperforms existing methods in noise reduction and image quality preservation.

Cluster synchronization in a semiconductor laser

Cluster synchronization is a general phenomenon in a network of non-locally coupled oscillators. Here, we show that cluster synchronization occurs in semiconductor lasers, where the beat notes between the pairs of adjacent longitudinal modes of the laser cavity constitute a collection of coupled phase oscillators. Non-local coupling arises from the standing-wave nature of the cavity with finite mirror reflectivities, which we can actively control. Varying the coupling, we can bring the laser into a state of cluster synchronization where the two beat note families oscillate at two distinct collective frequencies. Using a coherent beat note detection technique, we show that the beat notes within the two families are synchronized in the opposite configurations—in-phase and antiphase.

Hyperscaling in the Coherent Hyperspin Machine.

Classical and quantum systems are used to simulate the Ising Hamiltonian, an essential component in large-scale optimization and machine learning. However, as the system size increases, devices like quantum annealers and coherent Ising machines face an exponential drop in their success rate. Here, we introduce a novel approach involving high-dimensional embeddings of the Ising Hamiltonian and a technique called "dimensional annealing" to counteract the decrease in performance. This approach leads to an exponential improvement in the success rate and other performance metrics, slowing down the decline in performance as the system size grows. A thorough examination of convergence dynamics in high-performance computing validates the new methodology. Additionally, we suggest practical implementations using technologies like coherent Ising machines, all-optical systems, and hybrid digital systems. The proposed hyperscaling heuristics can also be applied to other quantum or classical Ising devices by adjusting parameters such as nonlinear gain, loss, and nonlocal couplings.