<Emphasis Type="Italic">q</Emphasis>-Breathers in discrete nonlinear Schrödinger arrays with weak disorder

Nonlinearity and disorder are key players in vibrational lattice dynamics, responsible for localization and derealization phenomena. q-Breathers—periodic orbits in nonlinear lattices, exponentially localized in the reciprocal linear mode space—is a fundamental class of nonlinear oscillatory modes, currently found in disorder-free systems. In this paper we generalize the concept of q-breathers to the case of weak disorder, taking the Discrete Nonlinear Schrödinger chain as an example. We show that g-breathers retain exponential localization near the central mode, provided that disorder is sufficiently small. We analyze statistical properties of the instability threshold and uncover its sensitive dependence on a particular realization. Remarkably, the threshold can be intentionally increased or decreased by specifically arranged inhomogeneities. This effect allows us to formulate an approach to controlling the energy flow between the modes. The relevance to other model arrays and experiments with miniature mechanical lattices, light and matter waves propagation in optical potentials is discussed.     

Horizontal rolls in convective flow above a partially heated surface

Considering the nonlinearity arising from the interaction between electrons and lattice vibrations, an effective electronic model with a self-interaction cubic term is employed to study the interplay between electron-electron and electron-phonon interactions. Based on numerical solutions of the time-dependent nonlinear Schroedinger equation for an initially localized two-electron singlet state, we show that the magnitude of the electron-phonon coupling χ necessary to promote the self-trapping of the electronic wave packet decreases as a function of the electron-electron interaction U. We show that such dependence is directly linked to the narrowing of the band of bounded two-electron states as U increases. We obtain the transition line in the χ × U parameter space separating the phases of self-trapped and delocalized electronic wave packets. The present results indicates that nonlinear contributions plays a relevant role in the electronic wave packet dynamics, particularly in the regime of strongly correlated electrons.     

Leading-order 2πγ exchange NN interaction: Central potentials proportional to g<Subscript>A</Subscript><Superscript>0</Superscript> and g<Subscript>A</Subscript><Superscript>2</Superscript>

We calculate at two-loop order in chiral perturbation theory the electromagnetic corrections to the leading-order 2π exchange NN interaction proportional to g _A ⁰ and g _A ². The resulting 2πγ exchange potential contains isospin-breaking components which reach up to about -2% of the corresponding isovector 2π exchange potential. With a value of only -17keV at r = m _π ^-1 = 1.4fm the charge-independence breaking central potential obtained here is negligibly small in comparison to the one generated by the isoscalar c₃ contact vertex. Our calculation confirms that the largest long-range isospin-violating NN potentials arise from the 2πγ exchange diagrams involving the large low-energy constants c ₄ ≃ - c ₃ ≃ 3.3GeV^-1 representing the important Δ(1232) dynamics.     

Exact self-consistent plane-symmetric solutions of the spinor-field equation with a nonlinear term that depends on theS 2−P 2 invariant

Exact plane-symmetric solutions of the spinor-field equation with zero mass parameter and nonlinear term that depends arbitrarily on the S²−P² invariant are derived with consideration of an intrinsic gravitational field. The existence of regular solutions with localized energy density among the solutions obtained is investigated. Equations with powerlaw and polynomial nonlinearity types are examined in detail. For the power-law nonlinearity, when the nonlinear term entering into the Lagrangian has the form L_N=γIⁿ, where γ is the nonlinearity parameter and n=const, it is shown that the initial system of Einstein and spinor-field equations has regular solutions with localized energy density only under the conditions λ=−Λ² < 0, n > 1. In this case, the examined field configuration posesses a negative energy. In the case of polynomial nonlinearity, regular solutions with localized energy density T ₀ ⁰ (x), positive energy (upon integration over y and z between finite limits), and an everywhere regular metric that transforms into a two-dimensional space-time metric at spatial infinity are obtained. It is shown that the initial nonlinear spinor-field equations in two-dimensional space-time have no solutions with localized energy density. Thus, it is established that the intrinsic gravitational field plays a regularizing role in the frmation of regular localized solutions to the examined nonlinear spinor-field equations. Russian University of People's Friendship. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 12–19, November, 1999.     

Raman scattering by hot polaritons in NaClO3

Summary By nonlinear mixing of IR and visible radiation,i.e. coherent Raman scattering by polaritons driven by a CO₂ laser, it has been possible to get high-resolution spectra for theF-modes of a NaClO₃ crystal in the region (907÷957) cm⁻¹, where several isotopic modes are present. The obtained independent measurement of the refractive index and absorbance allows an accurate determination of the polariton dispersion curve and its width inq-space. The experimental data confirm the existence of a localized isotopic mode at 931 cm⁻¹ and a strongly damped isotopic mode near 960 cm⁻¹. Finally, an accurate measurement of the dispersion of the second-order nonlinear polarizability in the same energy region has been obtained for the first time. This work was supported by the Italian Consiglio Nazionale delle Ricerche and Ministero della Pubblica Istruzione.     

Nonlinear optical characterization of LaEr(MoO<Subscript>4</Subscript>)<Subscript>3</Subscript> thin films using the <Emphasis Type="BoldItalic">Z</Emphasis> -scan technique

The nonlinear optical properties of thin films of LaEr(MoO₄)₃ were studied using a ∼30 ps Nd:YAG laser at 532 nm with a repetition rate of 250 Hz. Closed aperture Z-scan measurement revealed a negative nonlinearity in the LaEr(MoO₄)₃. The nonlinear refractive index γ=1.38×10^-10 cm²/W and nonlinear absorption coefficient β=16.8×10^-6 cm/W were calculated from the Z-scan data. The fluorescent upconversion spectra were recorded with 980 nm excitation. An optical switching mechanism based on nonlinear absorption is also presented experimentally. PACS 81.15.Fg; 77.84.Bw; 33.50.Dq; 42.70.Mp     

Size and formation of a long wavelength mode packet in the FPU oscillator chain at low energy

The formation of a mode packet in the Fermi-Pasta-Ulam (FPU) oscillator chain, starting from a low frequency mode or modes, at low energy, is reexamined. Both the chain with cubic nonlinearity (FPU-α) and quartic nonlinearity (FPU-β) are examined for fixed boundary conditions. Some of the basic equations are reformulated to bring out the important scalings, which are compared with existing numerical data. It is shown, that for a single linear mode initial condition or for a small set of modes with random phases the resulting size of the mode packet scales as n_ef=?^x where n_ef is the fraction of occupied modes, ? is the energy density, and x=1/4,1/2 for the α, β chains, respectively. For other initial conditions, the results can depend on the initial number of modes and their phases. Some of the scaling relations are shown to have counterparts in exact nonlinear periodic solutions on the chains (q-breathers) and the similarities and differences to the results arising from the chaotic dynamics are pointed out.     

Solitons pinned to hot spots

We generalize a recently proposed model based on the cubic complex Ginzburg-Landau (CGL) equation, which gives rise to stable dissipative solitons supported by localized gain applied at a “hot spot” (HS), in the presence of the linear loss in the bulk. We introduce a model with the Kerr nonlinearity concentrated at the HS, together with the local gain and, possibly, with the local nonlinear loss. The model, which may be implemented in laser cavities based on planar waveguides, gives rise to exact solutions for pinned dissipative solitons. In the case when the HS does not include the localized nonlinear loss, numerical tests demonstrate that these solitons are stable/unstable if the localized nonlinearity is self-defocusing/focusing. Another new setting considered in this work is a pair of two symmetric HSs. We find exact asymmetric solutions for it, although they are unstable. Numerical simulations demonstrate that stable modes supported by the HS pair tend to be symmetric. An unexpected conclusion is that the interaction between breathers pinned to two broad HSs, which are the only stable modes in isolation in that case, transforms them into a static symmetric mode.     

Electron yield per ion charge-state correction for an ion collector with unsuppressed secondary electron emission

The electron yield per ion charge-state γ/q was measured for emission of electrons from clean polycrystalline gold induced due to impact of Ta ^q+ (11≤q≤41) ions with kinetic energy per chargeE _i/q from 15 keV/q to 150 keV/q. The dependence of γ on angle of incidence was analyzed with use of relation γ(ϑ)=γ₀ cos^−f ϑ. The fitting of experimental data gives a range of γ₀/q from 1 to 1.75 for Ta¹³⁺ and from 1.5 to 1.73 for Ta³⁹⁺. The dependence of γ₀/q onq andE _i is discussed with respect to measurement of ion currents emitted from laser-produced plasmas with an ion collector with unsuppressed secondary electron emission. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, U.S. Department of Energy, and by grant A1010819 from the Grant Agency of the Academy of Sciences of the Czech Republic.     

Quadrupole interactions in MoCl5 intercalated in graphite

The time-differential perturbed angular correlation technique was used to investigate quadrupole interactions following the decay of⁹⁹Mo as a probe in the intercalation compound graphite-molybdenum pentachloride. Analysis of the 740-(44) 141 keV γ-γ correlation in⁹⁹Tc reveals the presence of two sites with static electric field gradient interactions, one of which corresponds to a moderately damped (δ∼16%), high-frequency interaction (v _q∼630 MHz), the other to a heavily damped (δ∼28%), low-frequency (v _q∼283 MHz) component.     

High-order vibrational relaxation: a nonperturbative theory

A nonperturbative theory of the multiphonon relaxation of a localized vibrational mode, caused by a high-order anharmonic interaction with the nearest atoms of the crystal lattice, is proposed. It relates the rate of the process to the positive frequency part of the time-dependent non-stationary displacement correlation function of atoms. The nonlinear integral equation for this function is derived and solved numerically. We have found that the rate exhibits a critical behavior: it sharply increases near a specific (critical) value(s) of the interaction; the corresponding dependence is characterized by the critical index k - 1, where k is the number of the created phonons. Received 2 May 2002 Published online 31 July 2002     

Matter wave interferometry for measuring a molecular transition dipole moment

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ ₁) is less than that of the LOL (V ₀) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ ₁ > V ₀, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ ₁ < V ₀. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.     

Dynamic Critical Behavior of the Chayes–Machta Algorithm for the Random-Cluster Model,I. Two Dimensions

We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes–Machta dynamics for the Fortuin–Kasteleyn random-cluster model, which generalizes the Swendsen–Wang dynamics for the q-state Potts ferromagnet to non-integer q≥1. We consider spatial dimension d=2 and 1.25≤q≤4 in steps of 0.25, on lattices up to 1024², and obtain estimates for the dynamic critical exponent z _CM. We present evidence that when 1≤q≲1.95 the Ossola–Sokal conjecture z _CM≥β/ν is violated, though we also present plausible fits compatible with this conjecture. We show that the Li–Sokal bound z _CM≥α/ν is close to being sharp over the entire range 1≤q≤4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.     

Isospin violations in largeP T pion inclusive processes in perturbative quantum chromodynamics

We investigate the asymmetries arising due to electromagnetic interactions in largeP _T pion inclusive processes. The hardqcd processes that contribute to such asymmetries areq+g→q+γ,q+q→g+γ etc. which are suspected to be substantial, as indicated by theqcd predictions for a significant and increasingγ/π ^o ratio at largeP _T. We calculate the expected isospin related asymmetries and propose tests that might detect them. Our estimates indicate that the effects are much smaller than may be naively expected. We also observe a remarkable scaling of asymmetries in the variableP _T/(s)^1/2.     

Nonlinear Dynamics of Circularly Polarized Laser Pulse Propagating in a Magnetized Plasma with q ‐Nonextensive Velocity Distributions

The nonlinear dynamics of a circularly polarized laser pulse propagating in magnetized plasma contains hot nonextensive q ‐distributed electrons and ions is studied theoretically. A nonlinear equation which describes the dynamics of the slowly varying amplitude electromagnetic wave is obtained using the relativistic two‐fluids model. Some nonlinear phenomena include modulational instability, self‐focusing, soliton formation, and longitudinal and transversal evolutions of laser pulse in nonextensive plasma medium are investigated. Results show that the nonextensivity of particles can substantially change the nonlinearity of medium. The external magnetic field enhances the modulation instability growth rate of right‐hand polarization wave but for the left‐hand polarization the growth rate decreases. The spot size of the laser pulse is strongly affected by the plasma nonextensivity. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Low mass Higgs signals at the LHC in the Next-to-Minimal Supersymmetric Standard Model

In the NMSSM, because of introducing a complex singlet superfield, the lightest CP-odd Higgs boson, a ₁, can be a singlet-like state with a tiny doublet component in large regions of parameter space. In this paper, we examine the discovery potential of a ₁ produced in association with a bottom–antibottom pair at the LHC through τ ⁺ τ ⁻ and γγ decay modes. It is shown that an a ₁ with mass ≤M _Z can be extracted from the SM backgrounds by using the τ ⁺ τ ⁻ decay channel, a possibility precluded to the MSSM. In contrast, the γγ decay mode is overwhelmed by backgrounds despite the fact that the branching ratio of this mode can reach unity when a ₁ is a pure singlet.     

The process p¯↦γπwithin the handbag approach

We analyse the exclusive channel pˉ↦γπ⁰, assuming handbag dominance. The soft parts are parametrized in terms of CGLN amplitudes for the qˉ↦γπ⁰ transition and form factors for the pˉ↦qˉ ones; the latter represent moments of Generalized Distribution Amplitudes. We present a combined fit to Fermilab data from E760 taking simultaneously into account information from other exclusive reactions, especially from pˉ↦γγ data. Overall a nicely consistent picture emerges, such that one can hope, that our theoretical analysis will be reliable also for the kinematics of GSI/FAIR, which, hopefully, will provide much more precise and complete data. Consequently, data from this facility should improve our knowledge both on the proton-antiproton distribution amplitudes and the pion production mechanism.     

Two-photon decays of pseudotensor mesons <Emphasis Type="Italic">π</Emphasis><Subscript>2</Subscript>(1670), <Emphasis Type="Italic">π</Emphasis><Subscript>2</Subscript>(2250), and <Emphasis Type="Italic">π</Emphasis><Subscript>2</Subscript>(2510)

In terms of relativistic and gauge-invariant spectral-integral technique, we calculate amplitude for the π ₂ → γγ decay as a three-step transition π ₂ → q $ \bar q $ \bar q (2⁻⁺) → γ + q $ \bar q $ \bar q (1⁻⁻) → γγ. Using wave functions of the q $ \bar q $ \bar q components of photon (hep-ph/0406320) and those of pseudotensor mesons π ₂(1670), π ₂(2000), π ₂(2250), and π ₂(2510) (hep-ph/0511109), we obtain the following values for partial widths: Γ _{π2(1670)→γγ} = 0.072 ± 0.007 keV, Γ _{π2(2000)→γγ} = 0.037 ± 0.004 keV, Γ _{π2(2250)→γγ} = 0.027 ± 0.003 keV, and Γ _{π2(2510)→γγ} = 0.022 ± 0.002 keV. In the calculations, we use the momentum operator expansion, and, in this connection, discuss the problem of nilpotent operators inherent in the considered amplitude. It should be emphasized that measurement of two-photon decays of the π ₂ states can give valuable information about the long-range quark-antiquark forces which, as one may guess, are related to the quark confinement.