Attractive Coupling Research Articles

Chimera-like behavior in a heterogeneous Kuramoto model: The interplay between attractive and repulsive coupling.

Interaction within an ensemble of coupled nonlinear oscillators induces a variety of collective behaviors. One of the most fascinating is a chimera state that manifests the coexistence of spatially distinct populations of coherent and incoherent elements. Understanding of the emergent chimera behavior in controlled experiments or real systems requires a focus on the consideration of heterogeneous network models. In this study, we explore the transitions in a heterogeneous Kuramoto model under the monotonical increase of the coupling strength and specifically find that this system exhibits a frequency-modulated chimera-like pattern during the explosive transition to synchronization. We demonstrate that this specific dynamical regime originates from the interplay between (the evolved) attractively and repulsively coupled subpopulations. We also show that the above-mentioned chimera-like state is induced under weakly non-local, small-world, and sparse scale-free coupling and suppressed in globally coupled, strongly rewired, and dense scale-free networks due to the emergence of the large-scale connections.

Chimera States mediated by nonlocally attractive-repulsive coupling in FitzHugh–Nagumo neural networks

The spontaneous occurrence of heterogeneous behaviors in homogeneous systems is an intriguing phenomenon. Recently, a remarkable heterogeneous behavior, called “chimera states”, which consists of spatially coherent and incoherent domains, has been studied in a great variety of systems including physical, chemical, biological, or optical. In this paper, chimera states in FitzHugh–Nagumo (FHN) neural networks are investigated. The identical FHN neurons are assigned in a ring and nonlocally coupled by attractive and repulsive couplings. We show that, the chimera states can be induced by the cooperation of nonlocally attractive and repulsive interactions between these neurons. Moreover, depending on the strength and range of attractive or repulsive couplings, the neural networks display different spatiotemporal behaviors, including chimera states, multi-cluster (MC) chimera states, traveling waves, traveling coherent states, solitary states, bursting synchronizations, and synchronizations. These results suggest that attractive and repulsive couplings may play a crucial role in mediating dynamic behavior of neural networks, and these results could be useful in understanding and predicting the rich dynamics of neural networks.

Emergent behaviors of a first-order particle swarm model on the hyperboloid

We study the emergent dynamics of a first-order particle swarm model (PSM) on the hyperboloid with a constant negative curvature that corresponds to the special case (p, q) = (1, d) of the PSM on the indefinite special orthogonal group SO(p, q) in the work of Ritchie et al. [Chaos 28, 053116 (2018)]. For the proposed PSM on the hyperboloid, we first establish the global existence of a solution via the extension of a local solution to a global one by the continuity argument and then show that the solutions are uniformly bounded by a quantity only depending on the initial data and the coupling strength although the underlying manifold is not compact. In this paper, we consider both attractive and repulsive couplings. For an attractive regime, we show that the complete synchronization occurs for all initial data, whereas for a repulsive regime, we show that distances between particles diverge to infinity, as time goes on. Finally, we present several numerical results consistent with our theoretical results.

Many-body quantum dynamics and induced correlations of Bose polarons

We study the ground state properties and non-equilibrium dynamics of two spinor bosonic impurities immersed in a one-dimensional bosonic gas upon applying an interspecies interaction quench. For the ground state of two non-interacting impurities we reveal signatures of attractive induced interactions in both cases of attractive or repulsive interspecies interactions, while a weak impurity–impurity repulsion forces the impurities to stay apart. Turning to the quench dynamics we inspect the time-evolution of the contrast unveiling the existence, dynamical deformation and the orthogonality catastrophe of Bose polarons. We find that for an increasing postquench repulsion the impurities reside in a superposition of two distinct two-body configurations while at strong repulsions their corresponding two-body correlation patterns show a spatially delocalized behavior evincing the involvement of higher excited states. For attractive interspecies couplings, the impurities exhibit a tendency to localize at the origin and remarkably for strong attractions they experience a mutual attraction on the two-body level that is imprinted as a density hump on the bosonic bath.

From 2D to 3D solids: stacking of transition metal nitroprusside layers through intermolecular physical interactions

This contribution reports the preparation and study of a series of hybrid inorganic-organic solids obtained by intercalation of pyridine molecules between neighboring layers of 2D transition metal nitroprussides, T[Fe(CN)5NO]. The pyridine molecule coordinated to the axial positions for the metal (T) linked at the N ends of the equatorial CN ligands. From such regular pyridine molecule disposition at the layer and the attractive dispersive interactions and dipole-dipole coupling between neighboring molecules in the interlayer region, the formation of a long range 3D framework results. The refined crystal structure and the magnetic measurements shed light on the interaction between intercalated neighboring molecules. In the resulting 3D framework, the hybrid material preserves its 2D identity because no formation of chemical bonds is involved in the stacking process. Such structural features are properly supported by the refined crystal structures and computational studies for the interaction of the organic molecule with the metal (T) center. This series of hybrid solids crystallizes with an orthorhombic unit cell in the Ic2m space group. The unit cell volume shows a slight dependence of the metal (T), Ni < Co < Zn < Mn, which is related to the metal polarizing power and follows the order found for the T-NCN and T-NPy bond distances. The results herein discussed are relevant for hybrid inorganic-organic materials design, preparation and applications.

Renormalization Group Study of the Mixed Spin-1 and Spin-3/2 Blume-Emery-Griffiths Model with Attractive Biquadratic Coupling

The mixed spin-1 and spin-3/2 Blume-Emery-Griffiths model with attractive biquadratic coupling is investigated in the framework of the Migdal-Kadanoff Renormalization Group method. By changing the ratio R > 0 of biquadratic and bilinear exchange interactions and according to the different values of crystal field interactions, we have determined six main types of phase diagrams. The full flow in the parameters space of the Hamiltonian was established and the fixed points obtained are drawn up in a table. In addition, we have determined the eigenvalues of the transformation of the group in the vicinity of the critical points. Finally, the introduction of a positive biquadratic interaction was discussed.

Quantum-Granularity Effect in the Formation of Supermixed Solitons in Ring Lattices

We investigate a notable class of states peculiar to a bosonic binary mixture featuring repulsive intraspecies and attractive interspecies couplings. We evidence that, for small values of the hopping amplitudes, one can access particular regimes marked by the fact that the interwell boson transfer occurs in a jerky fashion. This property is shown to be responsible for the emergence of a staircase-like structure in the phase diagram of a mixture confined in a ring trimer and to resemble the mechanism of the superfluid-Mott insulator transition strongly. Under certain conditions, in fact, we show that it is possible to interpret the interspecies attraction as an effective chemical potential and the supermixed soliton as an effective particle reservoir. Our investigation is developed both within a fully quantum approach based on the analysis of several quantum indicators and by means of a simple analytical approximation scheme capable of capturing the essential features of this ultraquantum effect.

Is Higgsium a possibility in 2HDMs?

We investigate the possibility of a Higgs-Higgs bound state in the two Higgs doublet model. Specifically we look for the effect of dimension six operators, generated by new physics at a scale of a few TeV, on the self-couplings of the heavy CP even scalar field in the model. Following the pioneering work of Grinstein and Trott [1], we construct an effective field theory formalism to examine the physics of the Higgs sector. The magnitudes of the attractive and repulsive coupling strengths are compared to estimate the possibility of the formation of the H−H bound state. Another way to check if a bound state is formed or not is from the formation and decay times of the bound state. The possibilities in various types of two Higgs doublet models have been discussed elaborately in the paper. The bound state energy has been evaluated and the allowed parameter space has been studied in the linear and non-linear realizations.

Prediction of Attractive Level Crossing via a Dissipative Mode.

The new field of spin cavitronics focuses on the interaction between the magnon excitation of a magnetic element and the electromagnetic wave in a microwave cavity. In the strong interaction regime, such an interaction usually gives rise to the level anticrossing for the magnonic and the electromagnetic mode. Recently, the attractive level crossing has been observed, and it is explained by a non-Hermitian model Hamiltonian. However, the mechanism of such attractive coupling is still unclear. We reveal the secret by using a simple model with two harmonic oscillators coupled to a third oscillator with large dissipation. We further identify this dissipative third party as the invisible cavity mode with large leakage in cavity-magnon experiments. This understanding enables one to design dissipative coupling in all sorts of coupled systems.

The dynamics of two coupled Van der Pol oscillators with attractive and repulsive coupling

We consider a variant of two coupled Van der Pol oscillators with both attractive and repulsive mean-field interactions. In the presence of attractive coupling, the system is in the complete synchrony, while repulsive coupling shows anti-synchronization state leading to suppression of oscillations with increasing interaction strength. The coupled system with both attractive and repulsive interactions shows competitive tendencies of being complete synchronization and anti-synchronization resulting in the stabilization of the fixed point. We have also studied the effect of the damping coefficient of the VdP oscillator on the nature of the transition from oscillatory to a steady-state. These oscillators stabilize to unstable equilibrium point or coupling dependent inhomogeneous steady state via second or first-order transitions respectively depending upon the damping coefficient and coupling strength. These transitions are analyzed in the parameter plane by analytical and numerical studies of the two coupled Van der Pol oscillators.

Sub-decibel silicon grating couplers based on L-shaped waveguides and engineered subwavelength metamaterials

The availability of low-loss optical interfaces to couple light between standard optical fibers and high-index-contrast silicon waveguides is essential for the development of chip-integrated nanophotonics. Input and output couplers based on diffraction gratings are attractive coupling solutions. Advanced grating coupler designs, with Bragg or metal mirror underneath, low- and high-index overlays, and multi-level or multi-layer layouts, have proven less useful due to customized or complex fabrication, however. In this work, we propose a rather simpler in design of efficient off-chip fiber couplers that provide a simulated efficiency up to 95% (-0.25 dB) at a wavelength of 1.55 µm. These grating couplers are formed with an L-shaped waveguide profile and synthesized subwavelength grating metamaterials. This concept jointly provides sufficient degrees of freedom to simultaneously control the grating directionality and out-radiated field profile of the grating mode. The proposed chip-to-fiber couplers promote robust sub-decibel coupling of light, yet contain device dimensions (> 120 nm) compatible with standard lithographic technologies presently available in silicon nanophotonic foundries. Fabrication imperfections are also investigated. Dimensional offsets of ± 15 nm in shallow-etch depth and ± 10 nm in linewidth's and mask misalignments are tolerated for a 1-dB loss penalty. The proposed concept is meant to be universal, which is an essential prerequisite for developing reliable and low-cost optical couplers. We foresee that the work on L-shaped grating couplers with sub-decibel coupling efficiencies could also be a valuable direction for silicon chip interfacing in integrated nanophotonics.

Inhomogeneous to homogeneous dynamical states through symmetry breaking dynamics

We explore the dynamical transitions facilitated by the symmetry breaking dynamical states in a directly coupled limit-cycle oscillators, when the oscillators are interacting through attractive and repulsive couplings. Initially, we show that the transition from out-of-phase synchronized (OPS) state to in-phase synchronized (IPS) state is mediated by the onset of symmetry breaking oscillatory (SBO) state using two coupled systems. Similarly, we find the emergence of symmetry breaking oscillation death (AOD) state when the system transits from oscillation death (OD) state to nontrivial amplitude death (NAD) state. Further, we deduce the analytical stability conditions for all the observed dynamical states, namely the IPS, OPS, NAD, OD, including SBO and AOD states. Additionally, the investigation on symmetry breaking dynamics in a ring of unidirectionally coupled oscillators reveals that the breaking of symmetry leads to the traveling chimera (TC) and symmetry breaking incoherent oscillation death states. We also report that the transient nature of TC state obeys a power-law relation near the stable TC region as a function of the coupling strength. From the results, it is evident that the trade-off between the attractive and the repulsive couplings induces the symmetry breaking dynamics in the entire range of the system frequency.

Triggered incommensurate transition in PbHfO3

We report a type of structural phase transitions in dielectric materials: the triggered incommensurate (IC) transition. We demonstrate evidence for such a transition in the perovskite antiferroelectric ${\mathrm{PbHfO}}_{3}$ by means of single-crystal x-ray diffraction, diffuse, and inelastic-scattering experiments, which we interpret using the Landau theory of phase transitions. This transition is not driven by an IC soft mode, as is the case for the majority of IC dielectrics, but by the soft mode associated with a different, coexisting order parameter related to antiferrodistortive (AFD) tilts of the oxygen octahedra. When cooling from the high-temperature cubic phase these two order parameters are established simultaneously and discontinuously at ${T}_{\text{IC}}\ensuremath{\approx}468$ K. Two lattice instabilities are present in the cubic phase: AFD instability with critical temperature ${T}_{0}\ensuremath{\approx}441$ K and ferroelectric instability with ${T}_{0}\ensuremath{\approx}408$ K. The IC instability is absent. The analysis of the transition mechanism within the Landau theory of coupled order parameters indicates that the transition is of triggered character, conditioned upon the attractive biquadratic coupling between the IC modulation and the AFD octahedral tilts, and is driven by the AFD soft mode.

Emergent behaviors of the Cucker–Smale ensemble under attractive–repulsive couplings and Rayleigh frictions

In this paper, we revisit an interaction problem of two homogeneous Cucker–Smale (in short CS) ensembles with attractive–repulsive couplings, possibly under the effect of Rayleigh friction, and study three sufficient frameworks leading to bi-cluster flocking in which two sub-ensembles evolve to two clusters departing from each other. In the previous literature, the interaction problem has been studied in the context of attractive couplings. In our interaction problem, inter-ensemble and intra-ensemble couplings are assumed to be repulsive and attractive, respectively. When the Rayleigh frictional forces are turned on, we show that the total kinetic energy is uniformly bounded so that spatially mixed initial configurations evolve toward the bi-cluster configuration asymptotically fast under some suitable conditions on system parameters, communication weight functions and initial configurations. In contrast, when Rayleigh frictional forces are turned off, the flocking analysis is more delicate mainly due to the possibility of an exponential growth of the kinetic energy. In this case, we employ two mutually disjoint frameworks with constant inter-ensemble communication function and exponentially localized inter-ensemble communication functions, respectively, and prove the bi-clustering phenomenon in both cases. This work extends the previous work on the interaction problem of CS ensembles. We also conduct several numerical experiments and compare them with our theoretical results.

General Synthesis of Industrial Cephalosporin‐Based Antibiotics Through Amidation with Tosyl Chloride as a Coupling Reagent

In this contribution we demonstrate the feasibility of a recently developed amidation method for a general synthesis of industrially important semi‐synthetic cephalosporin antibiotics starting from readily available 7‐aminocephalosporanic acid and derivatives thereof. The amidation process is based on the use of 4‐toluene‐sulfonyl chloride as an economically attractive coupling reagent in combination with methanol or ethyl acetate as one of the solvent components. A broad reaction scope was shown by the successful synthesis of three further cephalosporin antibiotics with different functionalities, which were obtained in high yields of 82–95 % in the reactions even under non‐optimized conditions. It is noteworthy that also different oxime functionalities in the side chain of the 7′‐position are tolerated as well as an ester moiety in 4′‐position and a cationic functionality in 3′‐position. Thus, this amidation process through an activated anhydride formed by means of 4‐toluenesulfonyl chloride is a broadly applicable methodology for the synthesis of industrial semi‐synthetic cephalosporin antibiotics.

Attractive Dipolar Coupling between Stacked Exciton Fluids

The interaction between aligned dipoles is long-ranged and highly anisotropic: it changes from repulsive to attractive depending on the relative positions of the dipoles. We report on the observation of the attractive component of the dipolar coupling between excitonic dipoles in stacked semiconductor bilayers. We show that the presence of a dipolar exciton fluid in one bilayer modifies the spatial distribution and increases the binding energy of excitonic dipoles in a vertically remote layer. The binding energy changes are explained by a many-body polaron model describing the deformation of the exciton cloud due to its interaction with a remote dipolar exciton. The results open the way for the observation of theoretically predicted new and exotic collective phases, the realization of interacting dipolar lattices in semiconductor systems as well as for engineering and sensing their collective excitations.

Hamiltonian quantum computing with superconducting qubits

We consider how the Hamiltonian Quantum Computing scheme introduced in (2016 New J. Phys. 18 023042) can be implemented using a 2D array of superconducting transmon qubits. We show how the scheme requires the engineering of strong attractive cross-Kerr and weak flip-flop or hopping interactions and we detail how this can be achieved. Our proposal uses a new electric circuit for obtaining the attractive cross-Kerr coupling between transmons via a dipole-like element. We discuss and numerically analyze the forward motion and execution of the computation and its dependence on coupling strengths and their variability. We extend (2016 New J. Phys. 18 023042) by explicitly showing how to construct a direct Toffoli gate, thus establishing computational universality via the Hadamard and Toffoli gate or via controlled-Hadamard, Hadamard and CNOT.

A graphical approach to estimate the critical coupling strength for Kuramoto networks.

The Kuramoto model is an archetypal model for studying synchronization in groups of nonidentical oscillators. Each oscillator is imbued with its own personal inherent driving frequency and experiences attractive coupling forces toward all the other oscillators in the system. As the coupling increases, there exists a minimal coupling strength called the critical coupling beyond which the system moves in a collective rhythm. A unified approach for creating approximations of the critical coupling is created. It is based on an interpretation of a measurement of phase synchronization among the oscillators (the order parameter) as a function of the coupling strength. The approach allows a graphical way to develop new approximations that are provably, strict lower bounds. It is shown that several of the critical coupling bounds that have been previously studied can be interpreted in this unified framework. In addition, a process based on fixed point sampling is introduced that converts upper bounds for the critical coupling into associated lower bounds.

Revisiting the replica theory of the liquid to ideal glass transition.

The replica theory of the "Random First Order Transition" (RFOT) from a supercooled liquid to an "ideal" glass of a system of "soft spheres" is revisited. Following the seminal work of Mézard and Parisi [J. Chem. Phys. 111, 1076 (1999)], the number m of weakly interacting replicas of the system is varied continuously from m = 2 to m < 1. Relevant order parameters and the free energy of the liquid and glass phases are calculated using the hypernetted chain (HNC) approximation for the pair correlation functions. The scenario observed for all m confirms the existence of two glass branches G1 and G2. The latter has the lowest free energy for all m > 1, while the former has a lower free energy for m < 1 but is shown to be unstable against spinodal decomposition for any nonzero value of the attractive inter-replica coupling. The critical temperature Tcr of the RFOT turns out to depend on m, which may be a by-product of the approximation inherent in the HNC closure. The RFOT is predicted to be weakly first order, characterized by a small jump in density between the coexisting liquid and G2 phases for all m > 1. Estimating Tcr in the limit m → 1 requires a proper extrapolation of high resolution HNC calculations. The present protocol explores the behavior of the free energy of the ideal glass phase below Tcr as a function of m.

Leap-frog patterns in systems of two coupled FitzHugh-Nagumo units.

We study a system of two identical FitzHugh-Nagumo units with a mutual linear coupling in the fast variables. While an attractive coupling always leads to synchronous behavior, a repulsive coupling can give rise to dynamical regimes with alternating spiking order, called leap-frogging. We analyze various types of periodic and chaotic leap-frogging regimes, using numerical path-following methods to investigate their emergence and stability, as well as to obtain the complex bifurcation scenario which organizes their appearance in parameter space. In particular, we show that the stability region of the simplest periodic leap-frog pattern has the shape of a locking cone pointing to the canard transition of the uncoupled system. We also discuss the role of the timescale separation in the coupled FitzHugh-Nagumo system and the relation of the leap-frog solutions to the theory of mixed-mode oscillations in multiple timescale systems.