Plane Wave Background Research Articles

Hagedorn behavior of the superstring propating in a cosmological time dependent background

In this work the Liouville-von Neumann (LvN) quantization of the type IIB superstring is carried on in a time dependent plane wave background with a constant self-dual Ramond-Ramond 5-form and a linear dilaton in the lightlike direction. Such an endeavor allows us to define an invariant density matrix and study important issues in real time string thermodynamics. In particular, a transcendental equation that determines the Hagedorn temperature as a function of the thermalization time is derived. It is shown that the Hagedorn temperature increases as the string approaches the singularity. Published by the American Physical Society 2024

All-multiplicity amplitudes in impulsive PP-waves from the worldline formalism

We use the worldline formalism to derive Bern-Kosower type Master Formulae for the tree-level scattering of a charged particle and an arbitrary number of photons on impulsive PP-waves, where the coupling of the PP-wave to matter is treated fully non-perturbatively. We show that, in a certain kinematic regime characterised by a semi-classical positive energy condition, both off-shell currents and scattering amplitudes exhibit two novel factorisation structures. First, they may be written as currents in vacuum but with a single additional photon, averaged over the momentum of that photon. This converts the all-orders interaction with the PP-wave into a single effective interaction. Second, the currents and amplitudes may be written as a weighted average of the corresponding quantities in an impulsive plane wave background, with the average taken over all possible field strengths of the plane wave. This generalises a known single-photon result to arbitrary multiplicity.

Rogue waves in a reverse space nonlocal nonlinear Schrödinger equation

Rogue waves in a reverse space nonlocal nonlinear Schrödinger (NLS) equation with real and parity-symmetric nonlinearity-induced potential are considered. This equation has clear physical meanings since it can be derived from the Manakov system with a special reduction. The N-fold Darboux transformation and its generalized form for the nonlocal NLS equation are constructed. As an application, the multiparametric Nth-order rogue wave solution in terms of Schur polynomials for the nonlocal NLS equation with focusing case is derived by the limit technique. The significant differences of rogue wave dynamics between the nonlocal NLS equation and its usual (local) counterpart are illustrated through two types of specific rogue wave solutions. Unlike the eye-shaped (Peregrine type) rogue waves, the rogue wave doublets which involve an eye-shaped rogue wave and a dark/four-petaled rogue wave merging or separating with each other, and the rogue wave sextets that are characterized by the superpositions of three eye-shaped rogue waves and three dark/four-petaled rogue waves with fundamental, triangular and quadrilateral patterns are shown. Moreover, some wave characteristics including the difference between the light intensity and the plane-wave background, and the pulse energy of the rogue wave doublets are discussed.

Elliptic-rogue waves and modulational instability in nonlinear soliton equations.

We present elliptic-rogue wave solutions for integrable nonlinear soliton equationsin rational form by elliptic functions. Unlike solutions generated on the plane wave background, these solutions depict rogue waves emerging on elliptic function backgrounds. By refining the modified squared wave function method in tandem with the Darboux-Bäcklund transformation, we establish a quantitative correspondence between elliptic-rogue waves and the modulational instability. This connection reveals that the modulational instability of elliptic function solutions triggers rational-form solutions displaying elliptic-rogue waves, whereas the modulational stability of elliptic function solutions results in the rational-form solutions exhibiting the elliptic solitons or elliptic breathers. Moreover, this approach enables the derivation of higher-order elliptic-rogue waves, offering a versatile framework for constructing elliptic-rogue waves and exploring modulational stability in other integrable equations.

Novel signatures of radiation reaction in electron–laser sidescattering

In this article we investigate novel signatures of radiation reaction via the angular deflection of an electron beam colliding at 90 degrees with an intense laser pulse. Due to the radiation reaction effect, the electrons can be deflected towards the beam axis for plane wave backgrounds, which is not possible in the absence of radiation reaction effects. The magnitude and size of the deflection angle can be controlled by tailoring the laser pulse shapes. The effect is first derived analytically using the Landau–Lifshitz equation, which allows to determine the important scaling behavior with laser intensity and particle energy. We then move on to full scale 3D Monte Carlo simulations to verify the effect is observable with present day laser technology. We investigate the opportunities for an indirect observation of laser depletion in such side scattering scenarios.

Soliton molecules and breather positon solutions for the coupled modified nonlinear Schrödinger equation

The coupled modified nonlinear Schrödinger equation, which can be regarded as a combination of nonlinear Schrödinger and derivative nonlinear Schrödinger equations, is investigated by Darboux transformation (DT) method. Based on the vector modified derivative nonlinear Schrödinger equation spectral problem, the related Lax pair and DT in compact determinant form are all successfully constructed to ensure integrability of the coupled modified nonlinear Schrödinger equation. According to DT method and the limiting technique, two main types of solutions that soliton molecules (SMs) and breather positon (B-P) solutions are systematically discussed. Beginning form zero plane wave backgrounds, the general M−SM-(N−M)-soliton solutions (0≤M≤N), including M SMs and N−M solitons, are subtly derived by the received DT. In particular, two degenerate cases can be reduced from the above general solutions, i.e., N-SM solutions (M=N) and N-soliton solutions (M=0). From the nonzero plane wave backgrounds, the higher-order B-P solutions are constructed via both DT and the limiting technique. It is interestingly shown that the central region of B-P solutions exhibit the patterns of rogue waves, and thus they are suggested to explain the generating mechanism of rogue waves. Finally, the corresponding dynamics of these received solutions are discussed in detail.

Four-wave mixing induced general localized waves for a coupled generalized nonlinear Schrödinger system

In this paper, we investigate the general localized waves on the nonvanishing background for a coupled generalized nonlinear Schrödinger system with four wave mixing (FWM) effect. Using a uniform Darboux transformation, we construct a unified analytical solution formula which can be used not only to generate some reported localized waves, but also to yield some new results. Based on whether the relative wave vector of the two seed continuous-waves is zero, we respectively obtained various localized waves on the plane wave and periodic backgrounds, including bright/dark solitons, breathers, and rogue waves. Especially, we assort these localized waves and provide detailed parameter conditions for generating them, and find that the FWM term b plays a decisive role in generating the periodic background for those localized waves. In addition, interaction dynamics of the hybrid localized waves on both the plane wave and periodic backgrounds composed of the bright/dark soliton, breather and rogue wave are analyzed. We expect that these results will shed light on the understanding of localized waves on the periodic background owing to the interference of multiple continuous-wave fields.

Quantum radiation reaction spectrum of electrons in plane waves

In previous works we derived equations for the average momentum of high-energy electrons experiencing quantum radiation reaction in strong electromagnetic plane-wave background fields. In this paper we derive similar equations for the momentum spectrum. We formulate the equations in terms of the cumulative function and study the relation between the equations for the spectrum and the equations for the moments, analyze the structure of the low-energy expansions, and finally explain how our formulation is essentially in terms of a “Green’s function” which allows us to study the dynamics without choosing a specific initial wave packet (or particle-bunch distribution). Published by the American Physical Society 2024

Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equation

In this paper, by using the Darboux transformation (DT) method and the Taylor expansion method, a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of the Kundu-DNLS equation is constructed when n is even. Breathers and rogue waves can be obtained from this determinant, respectively. Further to this, the hybrid rogue waves and breathers solutions on the different periodic backgrounds are given explicitly, including the single-periodic background, the double-periodic background and the plane wave background by selecting different parameters. In addition, the form of the obtained solutions is summarized.

Breathers for the sixth-order nonlinear Schrödinger equation on the plane wave and periodic wave background

In this paper, we study the breathers in the framework of the sixth-order nonlinear Schrödinger equation by using the Darboux transformation. The primary objective of this research is twofold. First, we consider the nonlinear superposition of breathers on the plane wave background. Based on the concept that rogue waves are formed from colliding Akhmediev breathers, we obtain rogue wave sequences and a first-order Akhmediev breather with a central second-order rogue wave peak. Second, we consider the formation of breathers on the periodic wave background. The difficulty of solving the Lax pair is overcome, and we successfully construct the breathers on the cn- and dn-periodic wave background.

Fully polarized Compton scattering in plane waves and its polarization transfer

Fully polarized Compton scattering from a beam of spin-polarized electrons is investigated in plane-wave backgrounds in a broad intensity region from the perturbative to the nonperturbative regimes. In the perturbative regime, polarized linear Compton scattering is considered for investigating polarization transfer from a single laser photon to a scattered photon, and in the high-intensity region, the polarized locally monochromatic approximation and locally constant field approximation are established and are employed to study polarization transfer from an incoming electron to a scattered photon. The numerical results suggest an appreciable improvement of about 10% in the scattering probability in the intermediate-intensity region if the electron’s longitudinal spin is parallel to the laser rotation. The longitudinal spin of the incoming electron can be transferred to the scattered photon with an efficiency that increases with laser intensity and collisional energy. For collision between an optical laser with frequency ∼1 eV and a 10 GeV electron, this polarization transfer efficiency can increase from about 20% in the perturbative regime to about 50% in the nonperturbative regime for scattered photons with relatively high energy.

Rogue waves solutions on the elliptic background of an extended (3 + 1)‐dimensional nonlinear Schrödinger equation

We construct rogue wave solutions of an extended (3 + 1)‐dimensional nonlinear Schrödinger equation on the Jacobian elliptic function background. The modulational stability of the plane wave background is analyzed. We derive the periodic wave solutions and non‐periodic wave solutions of the Lax spectral problem. Making use of the non‐periodic solutions, we construct rogue waves on the cnoidal background via one‐ and two‐fold Darboux transformation. By using one‐fold Darboux transformation, rogue waves on the dnoidal background are also proposed.

Master formulas for N -photon tree level amplitudes in plane wave backgrounds

The presence of strong electromagnetic fields adds huge complexity to QED Feynman diagrams, such that new methods are required to calculate higher-loop and higher-multiplicity scattering amplitudes. Here we use the worldline formalism to present “master formulas” for all tree level amplitudes of two massive particles and an arbitrary number of photons, in a plane wave background, in both scalar and spinor QED. The plane wave is treated without approximation throughout, meaning in particular that our formulas are valid in the strong-field regime of current theoretical and experimental interest. We check our results against literature expressions obtainable at low multiplicity via direct Feynman diagram calculations. Published by the American Physical Society 2024

Supersymmetric solutions of type-II supergravity from λ-deformations and zoom-in limits

We construct the embedding of the λ-model on SL(2, ℝ) × SU(2) × SU(2) in type-II supergravity. In the absence of deformation, the ten-dimensional background corresponds to the near-horizon limit of the NS1-NS5-NS5 brane intersection. We show that when the deformation is turned on, supersymmetry breaks by half, and the solution preserves 8 supercharges. The Penrose limits along two null geodesics of the deformed geometry are also considered. It turns out that none of the associated plane-wave backgrounds exhibit supernumerary supercharges.

Various types of discrete exact localized wave solutions and dynamical analysis for the discrete complex modified Korteweg-de Vries equation

Under consideration is the second-order integrable discretization of complex modified Korteweg-de Vries (mKdV) equation which is regarded as the discrete counterpart of the mKdV equation having an essential role in describing the propagation behavior of water waves and acoustic waves in nonlinear media. First of all, based on the known linear spectral problem, the discrete generalized (n,N−n)-fold Darboux transformation is constructed to derive various types of discrete exact localized wave solutions, including soliton and semi-rational soliton solutions on vanishing background, breather, rogue wave and hybrid interaction solutions on plane wave background, and rational soliton solution on constant background, and the relevant evolution structures are studied graphically. Secondly, the asymptotic analysis is used to discuss the elastic interaction for two-soliton solutions and limit states for rational soliton solutions. Finally, the numerical simulation is utilized to investigate the dynamical behavior and propagation stability of some exact solutions. The findings presented in this paper may contribute to explaining physical phenomena described by the mKdV equation.

Wave scattering event shapes at high energies

We study the space and properties of global and local observables for radiation emitted in the scattering of a massive scalar field in gauge and gravitational plane-wave backgrounds, in both the quantum and classical theory. We first compute the radiated momentum and angular momentum flow, demonstrating that they are good local observables determined by the amplitude and phase of the waveform. We then focus on the corresponding global observables, which in the gravitational case requires dealing with the collinear divergence of the gravitational Compton cross-section. We show using the KLN theorem that we can obtain an infrared-finite cross-section only by summing over forward scattering diagrams; this suggests dressing the initial state in the direction collinear to the plane wave in order to be able to compute observables integrated over the celestial sphere. Finally, we explore the high-energy behaviour of our observables. We find that classical global observables generically exhibit a power-law mass divergence in electrodynamics and a logarithmic mass divergence in gravity, even when radiation reaction is included. We then show explicitly how this is consistently resolved in the full quantum theory.

Rogue waves on the periodic wave background in the Kadomtsev–Petviashvili I equation

Rogue waves arising on the background of two families of periodic standing waves in the Kadomtsev–Petviashvili I (KPI) equation are investigated. By the nonlinearization of spectral problem and Darboux transformation approach, the rogue wave solutions of the KPI equation on the Jacobian elliptic functions dn and cn background are derived. Darboux transformation is also used to introduce trigonometric function periodic background for the higher-order rogue wave in the KPI equation. On the plane wave background, some rogue waves, breathers and hybrid waves in the KPI equation are obtained as a byproduct in this paper. Moreover, the results represented in this paper enrich the dynamics of (2+1) dimensional nonlinear wave equations.

Master formulas for photon amplitudes in a combined constant and plane-wave background field

The worldline formalism has previously been used for deriving compact master formulas for the QED N - photon amplitudes in vacuum, in a constant field and in a plane-wave field. Here we carry this program one step further by deriving master formulas for the scalar and spinor QED one-loop N-photon amplitudes in the background of the “parallel” special case of a combined constant and plane-wave field.

The worldline formalism in strong-field QED

The worldline formalism provides an alternative to Feynman diagrams that has been found particularly useful for external-field calculations in quantum electrodynamics. Here I summarize its present range of applications, which includes Schwinger pair creation, photon splitting in constant fields and plane-wave backgrounds, as well as non-linear Compton scattering in constant fields.

An envelope system with third order dispersion: ‘Unconventional’ modulation instability and Floquet analysis

Modulation instability of plane waves of the Hirota equation, an ‘integrable’ system with third order dispersion, arises from the interplay of dispersive and nonlinear effects. The conventional analysis cannot account for finite amplitude disturbances and suffers from a scenario of indefinite growth. In an attempt to remove these constraints, we consider, as an illustrative example, the exact doubly periodic solutions expressed via the Jacobi elliptic functions. Wavy profiles at the minima of the intensity are interpreted as finite amplitude disturbances on a plane wave background. The profiles are amplified and will saturate at the maxima of the intensity. Such periodic states and breathers can be generated from finite amplitude disturbances with wavenumbers falling outside the linear instability band. This growth phase thus qualifies as ‘unconventional’ or ‘extraordinary’ modulation instability. Floquet analysis is performed to investigate the stability of the periodic patterns.