Quartic Perturbation Research Articles

On the number of limit cycles coming from a uniform isochronous center with continuous and discontinuous quartic perturbations

Abstract In this paper, we study the number of limit cycles bifurcated from the periodic orbits of a cubic uniform isochronous center with continuous and discontinuous quartic polynomial perturbations. Using the averaging theory of first order for continuous and discontinuous differential systems and comparing the obtained results, we show that the discontinuous systems have at least 6 more limit cycles than the continuous ones. This study needs some computations that have been verified using Maple.

On relative bounds for interacting Fermion operators

We consider a system of interacting fermions whose Hamiltonian is unitarily transformed so that the interaction is a quartic perturbation of the Hartree–Fock effective Hamiltonian. It is shown under natural model assumptions that the interaction does not admit a relative bound with respect to the effective Hamiltonian that is uniform in the system’s size. This bound is exemplified on the Hubbard model with nearest neighbor interaction on a discrete d -dimensional torus of length L around its Hartree–Fock ground state and derive relative bounds of the effective interaction with respect to the effective kinetic energy. It is shown that there are no relative bounds uniform in L .

Cubic–quartic optical soliton perturbation with Fokas–Lenells equation having maximum intensity

Objective:This paper reviews cubic–quartic Fokas–Lenells equation with perturbation terms having power-law of nonlinear refractive index for the first time. Methods:Six integration algorithms granted success with this retrieval. Results:Mathematical formulations yield bright and singular solitons with the model along with their corresponding existence criterion. Conclusion:The novelty of this paper is the extension of Kerr law to power-law and that too for cubic–quartic solitons that have emerged from the model. It has been verified if the power law nonlinearity parameter collapses to unity, all results of the paper reduce to the ones for Kerr law which are visible all over.

Cubic–quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas–Lenells equation

The objective of this study is to investigate miscellaneous wave structures for perturbed Fokas–Lenells equation (FLE) with cubic-quartic dispersion in polarization-preserving fibers. Based on the improved projective Riccati equations method, various types of soliton solutions such as bright soliton, combo dark–bright soliton, singular soliton and combo singular soliton are constructed. Additionally, a set of periodic singular waves are also retrieved. The dynamical behaviors of some obtained solutions are depicted to provide a key to understanding the physics of the model. The modulation instability of the FLE is reported by employing the linear stability analysis which shows that all solutions are stable.

Cubic–quartic optical soliton perturbation with complex Ginzburg–Landau equation by the enhanced Kudryashov’s method

This paper implements the enhanced Kudryashov’s method to address cubic–quartic complex Ginzburg–Landau equation for locating its solitons. This is considered when chromatic dispersion is discarded because of its low count. Sis forms of self-phase modulation structures are studied and they are Kerr law, parabolic law, polynomial law, quadratic–cubic law, anti-cubic law and parabolic-nonlocal law. Thus, bright and singular solitons are recovered for this model. The existence criteria for such solitons have been indicated, as well.

Cubic–quartic optical soliton perturbation and conservation laws with Lakshmanan–Porsezian–Daniel model: Undetermined coefficients

This work recovers cubic–quartic soliton solutions to the Lakshmanan–Porsezian–Daniel model by the method of undetermined coefficients. Both polarization-preserving fibers and birefringent fibers are studied. The conservation laws for polarization-preserving fibers are also retrieved and enumerated. The existence criteria for the displayed solitons are also presented.

Cubic–quartic optical soliton perturbation with Fokas–Lenells equation by sine–Gordon equation approach

This paper recovers cubic–quartic optical solitons for perturbed Fokas–Lenells equation in polarization-preserving fibers and birefringent fibers. The perturbation terms appear with maximum permissible intensity. Singular and dark solitons, together with a few combo solitons, emerge from the sine–Gordon equation integration scheme.

Massive photon propagator in the presence of axionic fluctuations

The theory of massive photons in the presence of axions is studied as the effective theory describing the electromagnetic response of semimetals when a particular quartic fermionic pairing perturbation triggers the formation of charged chiral condensates, giving rise to an axionic superconductor. We investigate corrections to the Yukawa-like potential mediated by massive photons due to axion excitations up to one-loop order and compute the modifications of the London penetration length.

Cubic–quartic optical soliton perturbation Biswas–Milovic equation with Kudryashov’s law of refractive index using two integration methods

In this paper, we introduce the cubic–quartic perturbation with Biswas–Milovic equation including Kudryashov’s law of refractive index. Two mathematical approaches, namely, the modified Kudryashov’s approach and the addendum to Kudryashov’s approach are used to obtain optical soliton solutions to this equation. Dark soliton, bright soliton and singular soliton solutions have been existed. The comparative analysis of the two proposed approaches shows that the first approach gives the dark and singular solitons while the second approach gives the bright and singular solitons.

Cubic–quartic optical soliton perturbation with Kudryashov’s law of refractive index having quadrupled–power law and dual form of generalized nonlocal nonlinearity by sine-Gordon equation approach

This paper recovers cubic–quartic optical solitons for Kudryashov’s law having dual form of generalized nonlocal nonlinearity. Hamiltonian type perturbation terms are included and these appear with maximum intensity. Bright, dark and singular solitons have emerged with the implementation of sine-Gordon equation method to the model.

Cubic–quartic optical soliton perturbation with Lakshmanan–Porsezian–Daniel model

This paper studies cubic–quartic Lakshmanan–Porsezian–Daniel model with three integration algorithms. A spectrum of single as well as straddled soliton solutions emerge along with their existence criteria that naturally fall out from the schemes. These pave way to further future investigations to the governing model along with its extensions and generalizations.

Cubic–quartic optical soliton perturbation in polarization-preserving fibers with Fokas–Lenells equation

This research article yields solitons for Fokas–Lennel’s equation. A couple of integration approaches recover bright and singular soliton solutions together with their existence criteria.

Cubic–quartic optical soliton perturbation with Lakshmanan–Porsezian–Daniel model by sine-Gordon equation approach

This paper recovers cubic–quartic optical solitons for perturbed Lakshmanan–Porsezian–Daniel model. This is for both with and without polarization. The sine-Gordon equation approach is the scheme adopted to retrieve the soliton solutions. A full spectrum of soliton solutions have emerged.

Cubic–quartic optical soliton perturbation and conservation laws with generalized Kudryashov’s form of refractive index

This paper obtains cubic–quartic optical solitons of generalized Kudryashov’s law of refractive index. The included perturbation terms are with maximum intensity. The retrieved soliton solutions are with the aid of F-expansion, exp-expansion and Riccati equation methods. Finally, the conservation laws of the model are also recovered and listed.

Towards spacetime entanglement entropy for interacting theories

Entanglement entropy of quantum fields in gravitational settings is a topic of growing importance. This entropy of entanglement is conventionally computed relative to Cauchy hypersurfaces where it is possible via a partial tracing to associate a reduced density matrix to the spacelike region of interest. In recent years Sorkin has proposed an alternative, manifestly covariant, formulation of entropy in terms of the spacetime two-point correlation function. This formulation, developed for a Gaussian scalar field theory, is explicitly spacetime in nature and evades some of the possible non-covariance issues faced by the conventional formulation. In this paper we take the first steps towards extending Sorkin’s entropy to non-Gaussian theories where Wick’s theorem no longer holds and one would expect higher correlators to contribute. We consider quartic perturbations away from the Gaussian case and find that to first order in perturbation theory, the entropy formula derived by Sorkin continues to hold but with the two-point correlators replaced by their perturbation-corrected counterparts. We then show that our results continue to hold for arbitrary perturbations (of both bosonic and fermionic theories). This is a non-trivial and, to our knowledge, novel result. Furthermore we also derive closed-form formulas of the entanglement entropy for arbitrary perturbations at first and second order. Our work also suggests avenues for further extensions to generic interacting theories.

Dynamics within a tunable harmonic plus quartic waveguide

We present an analytical solution to the dynamics of a noninteracting cloud of thermal atoms in a cigar-shaped harmonic trap with a quartic perturbation along the axial direction. We calculate the first and second moments of position, which are sufficient to characterize the trap. The dynamics of the thermal cloud differ notably from those of a single particle, with an offset to the oscillation frequency that persists even as the oscillation amplitude approaches zero. We also present some numerical results that describe the effects of time-of-flight on the behavior of the cloud in order to better understand the results of a hypothetical experimental realization of this system.

Cubic–quartic optical soliton perturbation and conservation laws with Kudryashov's law of refractive index

This paper secures cubic–quartic optical solitons of Kudryashov's equation with Hamiltonian perturbations that appear with maximum intensity. Bright, dark, singular and combo singular soliton solutions are recovered with F–expansion scheme. The conserved quantities are obtained by implementing multiplier approach.

Non-integrability, stability and periodic solutions for a quartic galactic potential in a rotating reference frame

This work aims to study the influence of the rotation of the galaxy which it is modelled as a bi-symmetrical potential consists of a two-dimensional harmonic oscillator with quartic perturbing terms on some dynamics aspects for the problem of the motion of stars. We prove analytically the non-integrability of the motion (i.e., the motion is chaotic) when the parameters meet certain conditions. Poincare surface of section is introduced as a numerical method that is employed to confirm the obtained analytical results. We present the equilibrium points and examine their stability. We also clarify the force resulting from the rotating frame serves as a stabilizer for the maximum equilibrium points. We illustrate graphically the size of stability zones depends on the value of the angular velocity for the frame. Based on the Lyapunov theorem, the periodic solutions are constructed near the equilibrium point. Additionally, we prove the existence of one or two families of periodic solutions according to the equilibrium point is either saddle or stable, respectively. The permitted zones of possible motion are delimited and they are graphically explained for different values of the parameters.

Non-Gaussian disorder average in the Sachdev-Ye-Kitaev model

We study the effect of non-Gaussian average over the random couplings in a complex version of the celebrated Sachdev-Ye-Kitaev (SYK) model. Using a Polchinski-like equation and random tensor Gaussian universality, we show that the effect of this non-Gaussian averaging leads to a modification of the variance of the Gaussian distribution of couplings at leading order in N. We then derive the form of the effective action to all orders. An explicit computation of the modification of the variance in the case of a quartic perturbation is performed for both the complex SYK model mentioned above and the SYK generalization proposed in D. Gross and V. Rosenhaus, JHEP 1702 (2017) 093.

The quantum geometric tensor from generating functions

We introduce a new method to compute the Quantum Geometric Tensor, this procedure allows us to compute the Quantum Information Metric and the Berry curvature perturbatively for a theory with an arbitrary interaction Hamiltonian. The calculation uses the generating function method, and it is illustrated with the harmonic oscillator with a linear and a quartic perturbation.