Large Coupling Regime Research Articles

Strong cosmic censorship in charged black-hole spacetimes: As strong as ever

It is proved that dynamically formed Reissner-Nordström-de Sitter (RNdS) black holes, which have recently been claimed to provide counter-examples to the Penrose strong cosmic censorship conjecture, are characterized by unstable (singular) inner Cauchy horizons. The proof is based on analytical techniques which explicitly reveal the fact that charged massive scalar fields in the charged RNdS black-hole spacetime are characterized, in the large-coupling regime, by quasinormal resonant frequencies with ℑωmin<12κ+, where κ+ is the surface gravity of the black-hole event horizon. This result implies that the corresponding relaxation rate ψ∼e−ℑωmint of the collapsed charged fields is slow enough to guarantee, through the mass-inflation mechanism, the instability of the dynamically formed inner Cauchy horizons. Our results reveal the physically important fact that, taking into account the unavoidable presence of charged matter fields in dynamically formed charged spacetimes, non-asymptotically flat RNdS black holes are globally hyperbolic and therefore respect the fundamental strong cosmic censorship conjecture.

Practical Synchronization of Winfree Oscillators in a Random Environment

We present a practical synchronization estimate of Winfree oscillators in a random environment. In a large coupling regime, the deterministic Winfree model exhibits the oscillator death, emerging with a convergence of the phase ensemble. The additive noise, however, is expected to destroy the stability of an equilibrium. In this paper, we estimate the running maximum of the phase processes, and conclude that the escaping probability from a small interval is in the order of $$TN^{-1}\exp (-\kappa /\Vert \varSigma \Vert ^2)$$ over a time interval [0, T], where $$\kappa $$ , N and $$\Vert \varSigma \Vert $$ denote the coupling strength, number of oscillators and noise strength, respectively. This result explains the robustness of the practical synchronization, which indicates that the finite-time emergent behavior from finite oscillators is close to the synchronization phenomena when $$\kappa $$ is large enough. Our approach produces explicit bounds on probabilities, relying on comparisons with the Ornstein–Uhlenbeck processes. It is hence optimal in the sense that the linearized model gives the same order.

A local sensitivity analysis for the kinetic Kuramoto equation with random inputs

We present a local sensivity analysis for the kinetic Kuramoto equation with random inputs in a large coupling regime. In our proposed random kinetic Kuramoto equation (in short, RKKE), the random inputs are encoded in the coupling strength. For the deterministic case, it is well known that the kinetic Kuramoto equation exhibits asymptotic phase concentration for well-prepared initial data in the large coupling regime. To see a response of the system to the random inputs, we provide propagation of regularity, local-in-time stability estimates for the variations of the random kinetic density function in random parameter space. For identical oscillators with the same natural frequencies, we introduce a Lyapunov functional measuring the phase concentration, and provide a local sensitivity analysis for the functional.

On the Relaxation Dynamics of Lohe Oscillators on Some Riemannian Manifolds

We study the collective relaxation dynamics appearing in weakly coupled Lohe oscillators in a large coupling regime. The Lohe models on the unit sphere and unitary group were proposed as a nonabelian generalization of the Kuramoto model on the unit circle and their emergent dynamics has been extensively studied in previous literature for some restricted class of initial data based on the Lyapunov functional approach and order parameter approach. In this paper, we extend the previous partial results to cover a generic initial configuration via the detailed analysis on the order parameter measuring the modulus of the centroid. In particular, we present a detailed relaxation dynamics and structure of the resulting asymptotic states for the Lohe sphere model. We also present new gradient flow formulations for the Lohe matrix models with the same one-body Hamiltonians on some group manifolds. As a direct application of this new formulation, we show that every bounded Lohe flow which originated from any initial configuration converges asymptotically.

Emergent dynamics of the Kuramoto ensemble under the effect of inertia

We study the emergent collective behaviors for an ensemble of identical Kuramoto oscillators under the effect of inertia. In the absence of inertial effects, it is well known that the generic initial Kuramoto ensemble relaxes to the phase-locked states asymptotically (emergence of complete synchronization) in a large coupling regime. Similarly, even for the presence of inertial effects, similar collective behaviors are observed numerically for generic initial configurations in a large coupling strength regime. However, this phenomenon has not been verified analytically in full generality yet, although there are several partial results in some restricted set of initial configurations. In this paper, we present several improved complete synchronization estimates for the Kuramoto ensemble with inertia in two frameworks for a finite system. Our improved frameworks describe the emergence of phase-locked states and its structure. Additionally, we show that as the number of oscillators tends to infinity, the Kuramoto ensemble with infinite size can be approximated by the corresponding kinetic mean-field model uniformly in time. Moreover, we also establish the global existence of measure-valued solutions for the Kuramoto equation and its large-time asymptotics.

Emergent dynamics of Cucker–Smale particles under the effects of random communication and incompressible fluids

We study the dynamics of infinitely many Cucker–Smale (C–S) flocking particles under the interplay of random communication and incompressible fluids. For the dynamics of an ensemble of flocking particles, we use the kinetic Cucker–Smale–Fokker–Planck (CS–FP) equation with a degenerate diffusion, whereas for the fluid component, we use the incompressible Navier–Stokes (N–S) equations. These two subsystems are coupled via the drag force. For this coupled model, we present the global existence of weak and strong solutions in Rd(d=2,3). Under the extra regularity assumptions of the initial data, the unique solvability of strong solutions is also established in R2. In a large coupling regime and periodic spatial domain T2:=R2/Z2, we show that the velocities of C–S particles and fluids are asymptotically aligned to two constant velocities which may be different.

Radially Excited AdS5 Black Holes in Einstein–Maxwell–Chern–Simons Theory

In the large coupling regime of the 5-dimensional Einstein–Maxwell–Chern–Simons theory, charged and rotating cohomogeneity-1 black holes form sequences of extremal and non-extremal radially excited configurations. These asymptotically global Anti-de Sitter (AdS 5 ) black holes form a discrete set of solutions, characterised by the vanishing of the total angular momenta, or the horizon angular velocity. However, the solutions are not static. In this paper, we study the branch structure that contains these excited states, and its relation with the static Reissner–Nordström-AdS black hole. Thermodynamic properties of these solutions are considered, revealing that the branches with lower excitation number can become thermodynamically unstable beyond certain critical solutions that depend on the free parameters of the configuration.

Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions

A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one- and two-dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum adiabatic theorem, are reviewed in a basic framework, which is meant to be accessible to non-specialists. We discuss the Kitaev chain, SSH, and BHZ models. The role of the electromagnetic interaction in the topological insulator theory is addressed in the light of the Pseudo quantum electrodynamics (PQED). The well known parity anomaly for massless Dirac particle is reviewed in terms of the Chern number. Within the continuum limit, a half-quantized Hall conductivity is obtained. Thereafter, by considering the lattice regularization of the Dirac theory, we show how one may obtain the well known quantum Hall conductivity for a single Dirac cone. The renormalization of the electron energy spectrum, for both small and large coupling regime, is derived. In particular, it is shown that massless Dirac particles may, only in the strong correlated limit, break either chiral or parity symmetries. For graphene, this implies the generation of Landau-like energy levels and the quantum valley Hall effect.

Spinning Kerr black holes with stationary massive scalar clouds: the large-coupling regime

We study analytically the Klein-Gordon wave equation for stationary massive scalar fields linearly coupled to spinning Kerr black holes. In particular, using the WKB approximation, we derive a compact formula for the discrete spectrum of scalar field masses which characterize the stationary composed Kerr-black-hole-massive-scalar-field configurations in the large-coupling regime M μ ≫ 1 (here M and μ are respectively the mass of the central black hole and the proper mass of the scalar field). We confirm our analytically derived formula for the Kerr-scalar-field mass spectrum with numerical data that recently appeared in the literature.

Emergent dynamics of Cucker–Smale flocking particles in a random environment

We present a new kinetic Cucker–Smale–Fokker–Planck (CS-FP) type equation with a degenerate diffusion, which describes the dynamics for an ensemble of infinitely many Cucker–Smale particles in a random environment. The asymptotic dynamics of the CS-FP equation exhibits a threshold-like phenomenon depending on the relative strength between the coupling strength and the noise strength. In the small coupling regime, the noise effect becomes dominant, which induces the velocity variance to increase to infinity exponentially fast. In contrast, the velocity alignment effect is strong in the large coupling regime, and the velocity variance tends to zero exponentially fast. We present the global existence of classical solutions to the CS-FP equation for a sufficiently smooth initial datum without smallness in its size. For the kinetic CS-FP equation with a metric dependent communication weight, we provide a uniform-in-time mean-field limit from the stochastic CS-model to the kinetic CS-FP equation without convergence rate.

The Fibonacci Hamiltonian

We consider the Fibonacci Hamiltonian, the central model in the study of electronic properties of one-dimensional quasicrystals, and provide a detailed description of its spectrum and spectral characteristics (namely, the optimal H\"older exponent of the integrated density of states, the dimension of the density of states measure, the dimension of the spectrum, and the upper transport exponent) for all values of the coupling constant (in contrast to all previous quantitative results, which could be established only in the regime of small or large coupling). In particular, we show that the spectrum of this operator is a dynamically defined Cantor set and that the density of states measure is exact-dimensional; this implies that all standard fractal dimensions coincide in each case. We show that all the gaps of the spectrum allowed by the gap labeling theorem are open for all values of the coupling constant. Also, we establish strict inequalities between the four spectral characteristics in question, and provide the exact large coupling asymptotics of the dimension of the density of states measure (for the other three quantities, the large coupling asymptotics were known before). A crucial ingredient of the paper is the relation between spectral properties of the Fibonacci Hamiltonian and dynamical properties of the Fibonacci trace map (such as dimensional characteristics of the non-wandering hyperbolic set and its measure of maximal entropy as well as other equilibrium measures, topological entropy, multipliers of periodic orbits). We establish exact identities relating the spectral and dynamical quantities, and show the connection between the spectral quantities and the thermodynamic pressure function.

Vector resonances in weak-boson-fusion at future pp colliders

We present a first estimate of the reach of future pp colliders, the 14 TeV LHC and a futuristic 100 TeV pp collider, on a vector resonance, specifically a W′, produced via weak-boson-fusion, and decaying dominantly into tb. The analysis is motivated by Composite Higgs, Randall-Sundrum and Little Higgs scenarios, which predict the existence of vector resonances with a large coupling to W and Z longitudinal bosons. In particular, in composite Higgs models with partial compositeness, the standard Drell-Yan production channel is suppressed at large coupling while the weak-boson-fusion is enhanced and could thus provide a unique opportunity to directly test the large coupling regime of the theory. We outline a search strategy for the W′ in the weak-boson-fusion channel and present the reach of future colliders on the W′ mass vs coupling parameter space.

Entanglements in a coupled cavity–array with one oscillating end-mirror**Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91121023), the National Natural Science Foundation of China (Grant Nos. 61378012 and 60978009), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20124407110009), the National Basic Research Program of

We theoretically investigate the entanglement properties in a hybrid system consisting of an optical cavity–array coupled to a mechanical resonator. We show that the steady state of the system presents bipartite continuous variable entanglement in an experimentally accessible parameter regime. The effects of the cavity–cavity coupling strength on the bipartite entanglements in the field–mirror subsystem and in the field–field subsystem are studied. We further find that the entanglement between the adjacent cavity and the movable mirror can be entirely transferred to the distant cavity and mirror by properly choosing the cavity detunings and the coupling strength in the two-cavity case. Surprisingly, such a remote macroscopic entanglement tends to be stable in the large coupling regime and persists for environment temperatures at above 25 K in the three-cavity case. Such optomechanical systems can be used for the realization of continuous variable quantum information interfaces and networks.

Universality in the relaxation dynamics of the composed black-hole-charged-massive-scalar-field system: The role of quantum Schwinger discharge

The quasinormal resonance spectrum {ωn(μ,q,M,Q)}n=0n=∞ of charged massive scalar fields in the charged Reissner–Nordström black-hole spacetime is studied analytically in the large-coupling regime qQ≫Mμ (here {μ,q} are respectively the mass and charge coupling constant of the field, and {M,Q} are respectively the mass and electric charge of the black hole). This physical system provides a striking illustration for the validity of the universal relaxation bound τ×T≥ħ/π in black-hole physics (here τ≡1/ℑω0 is the characteristic relaxation time of the composed black-hole-scalar-field system, and T is the Bekenstein–Hawking temperature of the black hole). In particular, it is shown that the relaxation dynamics of charged massive scalar fields in the charged Reissner–Nordström black-hole spacetime may saturate this quantum time-times-temperature inequality. Interestingly, we prove that potential violations of the bound by light scalar fields are excluded by the Schwinger-type pair-production mechanism (a vacuum polarization effect), a quantum phenomenon which restricts the physical parameters of the composed black-hole-charged-field system to the regime qQ≪M2μ2/ħ.

Emergence of phase-locked states for the Winfree model in a large coupling regime

We study the large-time behavior of the globally coupled Winfree model in a large coupling regime. The Winfree model is the first mathematical model for the synchronization phenomenon in an ensemble of weakly coupled limit-cycle oscillators. For the dynamic formation of phase-locked states, we provide a sufficient framework in terms of geometric conditions on the coupling functions and coupling strength. We show that in the proposed framework, the emergent phase-locked state is the unique equilibrium state and it is asymptotically stable in an $l^1$-norm; further, we investigate its configurational structure. We also provide several numerical simulations, and compare them with our analytical results.

High fidelity quantum state transfer in electromechanical systems with intermediate coupling.

Hybrid quantum systems usually consist of two or more subsystems, which may take the advantages of the different systems. Recently, the hybrid system consisting of circuit electromechanical subsystems have attracted great attention due to its advanced fabrication and scalable integrated photonic circuit techniques. Here, we propose a scheme for high fidelity quantum state transfer between a superconducting qubit and a nitrogen-vacancy center in diamond, which are coupled to a superconducting transmission-line resonator with coupling strength g1 and a nanomechanical resonator with coupling strength g2, respectively. Meanwhile, the two resonators are parametrically coupled with coupling strength J. The system dynamics, including the decoherence effects, is numerical investigated. It is found that both the small () and large () coupling regimes of this hybrid system can not support high fidelity quantum state transfer before significant technique advances. However, in the intermediate coupling regime (J ~ g1 ~ g2), in contrast to a conventional wisdom, high fidelity quantum information transfer can be implemented, providing a promising route towards high fidelity quantum state transfer in similar coupled resonators systems.

Holographic plasma and anyonic fluids

We use alternative quantisation of the $D3/D5$ system to explore properties of a strongly coupled charged plasma and strongly coupled anyonic fluids. The $S$-transform of the $D3/D5$ system is used as a model for charged matter interacting with a U(1) gauge field in the large coupling regime, and we compute the dispersion relationship of the propagating electromagnetic modes as the density and temperature are changed. A more general $SL(2,\mathbb{Z})$ transformation gives a strongly interacting anyonic fluid, and we study its transport properties as we change the statistics of the anyons and the background magnetic field.

The Gaussian entropy of fermionic systems

We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in terms of these correlators. In a simple case when a set of N thermalised environmental fermionic oscillators interacts bi-linearly with the system fermion we can study its time dependent entropy, which also represents a quantitative measure for decoherence and classicalization. We then consider a relativistic fermionic quantum field theory and take a mass mixing term as a simple model for the Yukawa interaction. It turns out that even in this Gaussian approximation, the fermionic system decoheres quite effectively, such that in a large coupling and high temperature regime the system field approaches the temperature of the environmental fields.

Collective modes of a spin-orbit-coupled Bose-Einstein condensate: A hydrodynamic approach

We studied the collective modes of a Bose-Einstein condensate (BEC) with spin-orbit coupling. We developed the hydrodynamic equations for spin-orbit coupled BECs and used them to study collective modes in the plane-wave phase and large Rabi coupling regime for both a uniform BEC and a BEC in a harmonic trap. In the homogeneous situation, we obtained energy spectra of elementary excitations and found that the spin-orbit coupling can increase the effective mass of the atoms, which will suppress the sound velocity. The spin-orbit coupling can also change the spin mixing, which will modify the interaction energy, and may lead to an enhancement of sound velocity. The competition between these two effects gives the behavior of sound velocity. In a harmonic trap, we found that the dipole mode and the breathing mode are coupled together in the plane-wave phase, and these two modes have a $\ensuremath{\pi}/2$ phase difference, because the spin-orbit coupling and the interaction are not invariant under spin rotation. However, in the large Rabi coupling regime, the dipole mode and the breathing mode are decoupled due to the symmetry restriction.

Order parameter expansion and finite-size scaling study of coherent dynamics induced by quenched noise in the active rotator model

We use a recently developed order parameter expansion method to study the transition to synchronous firing occurring in a system of coupled active rotators under the exclusive presence of quenched noise. The method predicts correctly the existence of a transition from a rest state to a regime of synchronous firing and another transition out of it as the intensity of the quenched noise increases and leads to analytical expressions for the critical noise intensities in the large coupling regime. It also predicts the order of the transitions for different probability distribution functions of the quenched variables. Using numerical simulations and finite-size scaling theory to estimate the critical exponents of the transitions, we found values which are consistent with those reported in other scalar systems in the exclusive presence of additive static disorder.