Critical Value Of Coupling Research Articles

What lies beyond the horizon of a holographic p-wave superconductor

We study the planar anti-de Sitter black hole in the p-wave holographic superconductor model. We identify a critical coupling value which determines the type of phase transition. Beyond the horizon, at specific temperatures flat spacetime emerges. Numerical analysis close to these temperatures demonstrates the appearance of a large number of alternating Kasner epochs.

Shiba states in systems with density of states singularities

Magnetic impurities placed in the superconductor can lead to emergence of the Yu-Shiba-Rusinov bound states. Coupling between the impurity and the substrate depends on density of states (DOS) at the Fermi level and can be tuned by DOS singularities. In this paper, we study the role of DOS singularities using the real space Bogoliubov-de Gennes equations for chosen lattice models. To uncover the role of these singularities (Dirac point, van Hove singularity, or the flat band), we study honeycomb, kagome, and Lieb lattices. We show that the properties of the Shiba state strongly depends on the type of lattice. Nevertheless some behaviors are generic, e.g. dependence of the critical magnetic coupling on the DOS at the Fermi level. However, the Shiba states realized in the Lieb lattice exhibit extraordinary properties, which can be explained by the presence of a few nonequivalent sublattices. Depending on the location of the magnetic impurity in the chosen sublattice, the value of critical magnetic coupling $J_\text{c}$ can be reduced or enhanced when the flat band is located at the Fermi level. In this context, we also present differences in the local DOS and coherence lengths for different sublattices in the Lieb lattice.

Transition to Fully or Partially Arrested State in Coupled Logistic Maps on a Ladder

Layered structures are an object of interest for theoretical and experimental reasons. In this work, we study coupled map lattice on a ladder. The ladder consists of two one-dimensional chains coupled at every point. We study linearly and nonlinearly coupled logistic maps in this system and study transition to nonzero persistence, in particular. We coarse-grain the variable value by assigning spin [Formula: see text] ([Formula: see text]) to sites that have value greater (less) than the fixed point and compute the number of sites that have not changed their spin values at all even times till the given time [Formula: see text]. The fraction of such sites at a given time [Formula: see text] is known as persistence. In our system, we observe a power-law of persistence at the critical value of coupling. This transition is also accompanied by long-range antiferromagnetic ordering for nonlinear coupling and long-range ferromagnetic ordering for linear coupling. The number of domain walls decay as [Formula: see text] at the critical point in both cases. The persistence exponent is 0.375 for a nonlinear case with two layers which is an exponent for the voter model on the ladder as well as for the Ising model at zero temperature or voter model in 1D. For linear coupling, we obtain a smaller persistence exponent.

The 2D non self-dual Ising lattices: An exact renormalization group treatment

In this work, an exact renormalization group treatment of honeycomb lattice leading to an exact relation between the coupling strengths of the honeycomb and the triangular lattices is presented. Using the honeycomb and the triangular duality relation, the critical coupling values of honeycomb and triangular lattices are calculated exactly by the simultaneous solution of the renormalized relation and the duality relation, without using the so-called star-triangular transformation. Apparently, the obtained coupling relation is unique. It not only takes place the role of the star triangular relation, but it is also the only exact relation obtained from renormalization group theory other than the 1D Ising chain. An exact pair correlation function expression relating the nearest neighbors and the next nearest neighbor correlation functions are also obtained for the honeycomb lattice. Utilizing this correlation relation, an exact expression of the correlation length of the honeycomb lattice is calculated analytically for the coupling constant values less than the critical value in the realm of the scaling theory. The critical exponents [Formula: see text] and [Formula: see text] are also calculated as [Formula: see text] and [Formula: see text].

Fractional dynamics in nonlinear magnetic metamaterials

We examine the existence of nonlinear modes and their temporal dynamics, in arrays of split-ring resonators, using a fractional extension of the Laplacian in the evolution equation. We find a closed-form expression for the dispersion relation as a function of the fractional exponent as well as an exact expression for the critical coupling between rings, beyond which no fractional magnetoinductive waves can exist. We also find the low-lying families of bulk and surface nonlinear modes and their bifurcation diagrams. Here the phenomenology is similar for all exponents and resembles what has been observed in other discrete evolution equations, such as the DNLS equation. The propagation of an initially localized magnetic excitation is always ballistic, with a ‘speed’ that is computed in exact form as a function of the fractional exponent. For a given exponent, it increases with an increase in coupling up to a critical coupling value, beyond which the ballistic speed could diverge inside the fractional interval [0,1]. Examination of the modulational instability shows that it tends to increase with an increase in the fractional exponent, where the decay proceeds via the formation of filamentary structures that merge eventually and form pure radiation. The dynamical selftrapping around an initially localized excitation increases with the fractional exponent, but it also shows a degree of trapping in the linear limit. This trapping increases with a decrease in the exponent and can be explained by near-degeneracy arguments.

Configurational mean-field reduced transfer matrix method for Ising systems

A mean-field method for the hypercubic nearest-neighbor Ising system is introduced and applications to the method are demonstrated. The main idea of this work is to combine the Kadanoff’s mean-field approach with the model presented by one of us previously. The mean-field approximation is introduced with the replacement of the central spin in Ising Hamiltonian with an average value of particular spin configuration, i.e, the approximation is taken into account within each configuration. This approximation is used in two different mean-field-type approaches. The first consideration is a pure-mean-field-type treatment in which all the neighboring spins are replaced with the assumed configurational average. The second consideration is introduced by the reduced transfer matrix method. The estimations of critical coupling values of the systems are evaluated both numerically and also analytically by the using of saddle point approximation. The analytic estimation of critical values in the first and second considerations are [Formula: see text] and [Formula: see text] respectively. Obviously, both of the considerations have some significant deviation from the exact treatment. In this work, we conclude that the method introduced here is more appropriate physical picture than self-consistent mean-field-type models, because the method introduced here does not presume the presence of the phase transition from the outset. Consequently, the introduced approach potentially makes our research very valuable mean-field-type picture for phase transition treatment.

Composite Nambu–Jona-Lasinio inflation near infrared fixed point of the Hořava-Lifshitz theory

In this work, we first propose a cosmological scenario inherently based on the effective Nambu–Jona-Lasio (NJL) model near the infrared (IR) limit of the Hořava-Lifshitz (HL) theory. Having used the one-loop correction, we employ the NJL framework in the ultraviolet (UV) limit of the HL theory, with critical exponent z=3, to demonstrate in the IR limit that the symmetry of the potential at the critical coupling value is broken at z=1. We also derive the effective Higgs-like potential in the low energy regimes. Here the symmetry of the effective potential will be broken near z=1 at a certain value of the critical coupling. In our scenario, the scalar channel of the NJL model plays the role of a composite inflaton. We find that the Lorentz invariance (LI) appears at the IR regime of the HL theory and employ the standard inflationary (slow-roll) paradigm as a probe of physics at very high energy. We compute inflationary parameters and compare them with recent Planck 2015 data. Interestingly, we discover that the predictions of the model are in perfect agreement with the Planck analysis. Our salient feature is that we used inflation to quantify the IR and UV fixed points of underlying theory. We discover that the IR fixed point of HL gravity is compatible with the grand unified energy scale; whilst the UV fixed point is the Planck energy scale.

Instability of a Reissner-Nordström-AdS black hole under perturbations of a scalar field coupled to the Einstein tensor

We study the instability of a Reissner-Nordstr\"om-AdS (RNAdS) black hole under perturbations of a massive scalar field coupled to Einstein tensor. Calculating the potential of the scalar perturbations we find that as the strength of the coupling of the scalar to Einstein tensor is increasing, the potential develops a negative well outside the black hole horizon, indicating an instability of the background RNAdS. We then investigate the effect of this coupling on the quasinormal modes. We find that there exists a critical value of the coupling which triggers the instability of the RNAdS. We also find that as the charge of the RNAdS is increased towards its extremal value, the critical value of the derivative coupling is decreased.

Neural activity of heterogeneous inhibitory spiking networks with delay.

We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a winner-takes-all mechanism. For sufficiently large transmission delay we observe the emergence of collective oscillations in the system beyond a critical coupling value. Heterogeneity promotes neural inactivation and asynchronous dynamics and its effect can be counteracted by considering longer time delays. In sparse networks, inhibition has the counterintuitive effect of promoting neural reactivation of silent neurons for sufficiently large coupling. In this regime, current fluctuations are on one side responsible for neural firing of subthreshold neurons and on the other side for their desynchronization. Therefore, collective oscillations are present only in a limited range of coupling values, which remains finite in the thermodynamic limit. Out of this range the dynamics is asynchronous and for very large inhibition neurons display a bursting behavior alternating periods of silence with periods where they fire freely in absence of any inhibition.

On the phase structure of vector-matrix scalar model in four dimensions

The leading-order equations of the 1/N – expansion for a vector-matrix model with interaction gphi _a^*phi _bchi _{ab} in four dimensions are investigated. This investigation shows a change of the asymptotic behavior in the deep Euclidean region in a vicinity of a certain critical value of the coupling constant. For small values of the coupling the phion propagator behaves as free. In the strong-coupling region the asymptotic behavior drastically changes – the propagator in the deep Euclidean region tend to some constant limit. The phion propagator in the coordinate space has a characteristic shell structure. At the critical value of coupling that separates the weak and strong coupling regions, the asymptotic behavior of the phion propagator is a medium among the free behavior and the constant-type behavior in strong-coupling region. The equation for a vertex with zero transfer is also investigated. The asymptotic behavior of the solutions shows the finiteness of the charge renormalization constant. In the strong-coupling region, the solution for the vertex has the same shell structure in coordinate space as the phion propagator. An analogy between the phase transition in this model and the re-arrangement of the physical vacuum in the supercritical external field due to the “fall-on-the-center” phenomenon is discussed.

Transient dynamics in strongly nonlinear systems: optimization of initial conditions on the resonant manifold.

We consider a system of two linear and linearly coupled oscillators with ideal impact constraints. Primary resonant energy exchange is investigated by analysis of the slow flow using the action-angle (AA) formalism. Exact inversion of the action-energy dependence for the linear oscillator with impact constraints is not possible. This difficulty, typical for many models of nonlinear oscillators, is circumvented by matching the asymptotic expansions for the linear and impact limits. The obtained energy-action relation enables the complete analysis of the slow flow and the accurate description of the critical delocalization transition. The transition from the localization regime to the energy-exchange regime is captured by prediction of the critical coupling value. Accurate prediction of the delocalization transition requires a detailed account of the coupling energy with appropriate redefinition and optimization of the limiting phase trajectory on the resonant manifold.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

Effect of Total Reflection from a Symmetric Two-Channel Device with Fermion Path Nonanalyticity Points Induced by Rashba Spin-Orbit Coupling

The effect Rashba spin-orbit coupling has on transmission coefficient through a symmetric system with fermion path nonanalyticity points is illustrated using the example of a regular polygon-shaped chain. It is shown that the current passage through a device is blocked at the critical spin-orbit coupling values determined by the system’s geometry. At the near-critical spin-orbit coupling values, electron transport is possible only in a narrow range of energies.

Testing a non-perturbative mechanism for elementary fermion mass generation: lattice setup

In this contribution we lay down a lattice setup that allows for the nonperturbative study of a field theoretical model where a SU(2) fermion doublet, subjected to non-Abelian gauge interactions, is also coupled to a complex scalar field doublet via a Yukawa and an “irrelevant” Wilson-like term. Using naive fermions in quenched approximation and based on the renormalizedWard identities induced by purely fermionic chiral transformations, lattice observables are discussed that enable: a) in theWigner phase, the determinations of the critical Yukawa coupling value where the purely fermionic chiral transformation become a symmetry up to lattice artifacts; b) in the Nambu-Goldstone phase of the resulting critical theory, a stringent test of the actual generation of a fermion mass term of non-perturbative origin. A soft twisted fermion mass term is introduced to circumvent the problem of exceptional configurations, and observables are then calculated in the limit of vanishing twisted mass.

Synchronization of coupled active rotators by common noise.

We study the effect of common noise on coupled active rotators. While such a noise always facilitates synchrony, coupling may be attractive (synchronizing) or repulsive (desynchronizing). We develop an analytical approach based on a transformation to approximate angle-action variables and averaging over fast rotations. For identical rotators, we describe a transition from full to partial synchrony at a critical value of repulsive coupling. For nonidentical rotators, the most nontrivial effect occurs at moderate repulsive coupling, where a juxtaposition of phase locking with frequency repulsion (anti-entrainment) is observed. We show that the frequency repulsion obeys a nontrivial power law.

Diffusion dynamics and synchronizability of hierarchical products of networks.

The hierarchical product of networks represents a natural tool for building large networks out of two smaller subnetworks: a primary subnetwork and a secondary subnetwork. Here we study the dynamics of diffusion and synchronization processes on hierarchical products. We apply techniques previously used for approximating the eigenvalues of the adjacency matrix to the Laplacian matrix, allowing us to quantify the effects that the primary and secondary subnetworks have on diffusion and synchronization in terms of a coupling parameter that weighs the secondary subnetwork relative to the primary subnetwork. Diffusion processes are separated into two regimes: for small coupling the diffusion rate is determined by the structure of the secondary network, scaling with the coupling parameter, while for large coupling it is determined by the primary network and saturates. Synchronization, on the other hand, is separated into three regimes, for both small and large coupling hierarchical products have poor synchronization properties, but is optimized at an intermediate value. Moreover, the critical coupling value that optimizes synchronization is shaped by the relative connectivities of the primary and secondary subnetworks, compensating for significant differences between the two subnetworks.

Influence of electron-phonon interaction on quantum phase transition in a triangular triple quantum dot

We investigate the quantum phase transition in triple quantum dot system with triangular geometry, in which one of the dots is connected to metallic leads and electrons in the dot interact with a local phonon mode. The influence of electron-phonon interaction on the quantum phase transition between local moment phase and Kondo screened strong coupling phase at the particle-hole symmetric point is studied based on the analytical arguments and the numerical renormalization group method. The results show that the critical value of tunnel-coupling between side dots decreases with the increase of electron-phonon coupling in “spin Kondo” regime. Furthermore, at a certain critical value of electron-phonon coupling, there appears only strong coupling phase, irrespective of tunnel-coupling between dots. The study of the influence of electron-phonon interaction on the quantum phase transition in triple quantum dot has the great importance for clarifying the mechanism of Kondo screening in the system.

Conditional Lyapunov exponents and transfer entropy in coupled bursting neurons under excitation and coupling mismatch

This work has a twofold aim: (a) to analyze an alternative approach for computing the conditional Lyapunov exponent (λcmax) aiming to evaluate the synchronization stability between nonlinear oscillators without solving the classical variational equations for the synchronization error dynamical system. In this first framework, an analytic reference value for λcmax is also provided in the context of Duffing master-slave scenario and precisely evaluated by the proposed numerical approach; (b) to apply this technique to the study of synchronization stability in chaotic Hindmarsh-Rose (HR) neuronal models under uni- and bi-directional resistive coupling and different excitation bias, which also considered the root mean square synchronization error, information theoretic measures and asymmetric transfer entropy in order to offer a better insight of the synchronization phenomenon. In particular, statistical and information theoretical measures were able to capture similarity increase between the neuronal oscillators just after a critical coupling value in accordance to the largest conditional Lyapunov exponent behavior. On the other hand, transfer entropy was able to detect neuronal emitter influence even in a weak coupling condition, i.e. under the increase of conditional Lyapunov exponent and apparently desynchronization tendency. In the performed set of numerical simulations, the synchronization measures were also evaluated for a two-dimensional parameter space defined by the neuronal coupling (emitter to a receiver neuron) and the (receiver) excitation current. Such analysis is repeated for different feedback couplings as well for different (emitter) excitation currents, revealing interesting characteristics of the attained synchronization region and conditions that facilitate the emergence of the synchronous behavior. These results provide a more detailed numerical insight of the underlying behavior of a HR in the excitation and coupling space, being in accordance with some general findings concerning HR coupling topologies. As a perspective, besides the synchronization overview from different standpoints, we hope that the proposed numerical approach for conditional Lyapunov exponent evaluation could outline a valuable strategy for studying neuronal stability, especially when realistic models are considered, in which analytical or even Jacobian evaluation could define a laborious or impracticable task.

Symmetry Breaking in Light-Front $${\varvec{\phi }}^\mathbf{4 }$$ ϕ 4 Theory

We consider the symmetric and broken phases of light-front $\phi^4$ theory in two dimensions. In both cases the mass of the lowest state is computed and its dependence on the coupling used to infer critical coupling values. The structure of the eigenstate is examined to determine whether it shows the signs of critical behavior, specifically whether the one-body sector becomes improbable relative to the higher Fock sectors. In attempts to establish this behavior, we consider both sector-independent and sector-dependent constituent masses.

Quantum phase transition in trigonal triple quantum dots: The case of quantum dots deviated from particle–hole symmetric point

We consider a triple quantum dot system in a triangular geometry with one of the dots connected to metallic leads. We investigate quantum phase transition between local moment phase and Kondo screened strong coupling phase in triple quantum dots where energy levels of dots are deviated from the particle–hole symmetric point. The effect of on-site energy of dots on quantum phase transition between local moment phase and Kondo screened strong coupling phase in triple quantum dots is studied based on the analytical arguments and the numerical renormalization group method. The results show that the critical value of tunnel coupling between side dots decreases when the energy level of embedded dot rises up from the symmetric point to the Fermi level and the critical value increases when the energy levels of two side dots rise up. The study of the influence of on-site-energy changes on the quantum phase transitions in triple quantum dots has the importance for clarifying the mechanism of Kondo screening in triple quantum dots where energy levels of dots are deviated from the particle–hole symmetric point.

Breathing dynamics of a trapped impurity in a dipolar Bose gas

With the consideration of impurity-bosons coupling and dipole–dipole interactions (DDI), we study the breathing dynamics of a harmonically trapped impurity interacting with a separately trapped background of dipolar Bose gas. By using the variational approach, the breathing equations, the breathing frequencies and the effective potentials governing the breathing dynamics of the impurity in dipolar gas are obtained. The effects of DDI, impurity-bosons interaction and external trapping potentials on breathing dynamics of impurity are discussed. We find that, because of the anisotropic and long-range characters of DDI, the effects of DDI, impurity-bosons interaction and external trapping potentials on breathing dynamics of impurity are strongly coupled. DDI has significant modification on dynamics, which depends on the external trapping potentials. For spherically symmetric external trapping, DDI makes the impurity more cigar-shaped along axial direction and the breathing oscillation in radial direction is suppressed by DDI. However, the effect of DDI on the breathing dynamics is weakened for cigar-shaped external trapping. Interestingly, for strong external pancake-shaped trapping, the symmetries of the breathing dynamics with respect to attractive and repulsive impurity-bosons coupling recover. Especially, for some critical value of impurity-bosons coupling, the breathing dynamics undergo a sudden quench.