Induced photon emission from quark jets in ultrarelativistic heavy-ion collisions

We study the induced photon bremsstrahlung from a fast quark produced in AA-collisions due to multiple scattering in quark-gluon plasma. For RHIC and LHC conditions the induced photon spectrum is sharply peaked at photon energy close to the initial quark energy. In this region the contribution of the induced radiation to the photon fragmentation function exceeds the ordinary vacuum radiation. Contrary to previous analyses our results show that at RHIC and LHC energies the final-state interaction effects in quark-gluon plasma do not suppress the direct photon production, and even may enhance it at p_{T} about 5-15 GeV.Comment: 11 pages, 4 figure

Variation of jet quenching from RHIC to LHC and thermal suppression of QCD coupling constant

We perform a joint jet tomographic analysis of the data on the nuclear modification factor $R_{AA}$ from PHENIX at RHIC and ALICE at LHC. The computations are performed accounting for radiative and collisional parton energy loss with running coupling constant. Our results show that the observed slow variation of $R_{AA}$ from RHIC to LHC indicates that the QCD coupling constant is suppressed in the quark-gluon plasma produced at LHC.Comment: 9 pages, 2 figure

Jet quenching with running coupling including radiative and collisional energy losses

We calculate the nuclear modification factor for RHIC and LHC conditions accounting for the radiative and collisional parton energy loss with the running coupling constant.We find that the RHIC data can be explained both in the scenario with the chemically equilibrium quark-gluon plasma and purely gluonic plasma with slightly different thermal suppression of the coupling constant. The role of the parton energy gain due to gluon absorption is also investigated. Our results show that the energy gain gives negligible effect.Comment: 11 pages, 3 figure

Commutator identities on associative algebras and integrability of nonlinear pde's

It is shown that commutator identities on associative algebras generate solutions of linearized integrable equations. Next, a special kind of the dressing procedure is suggested that in a special class of integral operators enables to associate to such commutator identity both nonlinear equation and its Lax pair. Thus problem of construction of new integrable pde's reduces to construction of commutator identities on associative algebras.Comment: 12 page

Stable multiple-charged localized optical vortices in cubic-quintic nonlinear media

The stability of two-dimensional bright vortex solitons in a media with focusing cubic and defocusing quintic nonlinearities is investigated analytically and numerically. It is proved that above some critical beam powers not only one- and two-charged but also multiple-charged stable vortex solitons do exist. A vortex soliton occurs robust with respect to symmetry-breaking modulational instability in the self-defocusing regime provided that its radial profile becomes flattened, so that a self-trapped wave beam gets a pronounced surface. It is demonstrated that the dynamics of a slightly perturbed stable vortex soliton resembles an oscillation of a liquid stream having a surface tension. Using the idea of sustaining effective surface tension for spatial vortex soliton in a media with competing nonlinearities the explanation of a suppression of the modulational instability is proposed.Comment: 4 pages, 3 figures. Submitted to Journal of Optics A. The proceedings of the workshop NATO ARW, Kiev 2003 Singular Optics 200

Collapse in the nonlocal nonlinear Schr\"odinger equation

We discuss spatial dynamics and collapse scenarios of localized waves governed by the nonlinear Schr\"{o}dinger equation with nonlocal nonlinearity. Firstly, we prove that for arbitrary nonsingular attractive nonlocal nonlinear interaction in arbitrary dimension collapse does not occur. Then we study in detail the effect of singular nonlocal kernels in arbitrary dimension using both, Lyapunoff's method and virial identities. We find that for for a one-dimensional case, i.e. for $n=1$, collapse cannot happen for nonlocal nonlinearity. On the other hand, for spatial dimension $n\geq2$ and singular kernel $\sim 1/r^\alpha$, no collapse takes place if $\alpha<2$, whereas collapse is possible if $\alpha\ge2$. Self-similar solutions allow us to find an expression for the critical distance (or time) at which collapse should occur in the particular case of $\sim 1/r^2$ kernels. Moreover, different evolution scenarios for the three dimensional physically relevant case of Bose Einstein condensate are studied numerically for both, the ground state and a higher order toroidal state with and without an additional local repulsive nonlinear interaction. In particular, we show that presence of an additional local repulsive term can prevent collapse in those cases

Vector solitons in nonlinear isotropic chiral metamaterials

Starting from the Maxwell equations, we used the reductive perturbation method to derive a system of two coupled nonlinear Schr\"{o}dinger (NLS) equations for the two Beltrami components of the electromagnetic field propagating along a fixed direction in an isotropic nonlinear chiral metamaterial. With single-resonance Lorentz models for the permittivity and permeability and a Condon model for the chirality parameter, in certain spectral regimes, one of the two Beltrami components exhibits a negative real refractive index when nonlinearity is ignored and the chirality parameter is sufficiently large.We found that, inside such a spectral regime, there may exist a subregime wherein the system of the NLS equations can be approximated by the Manakov system. Bright-bright, dark-dark, and dark-bright vector solitons can be formed in that spectral subregime.Comment: 14 pages, 2 figure

The Development of Equilibrium After Preheating

We present a fully nonlinear study of the development of equilibrium after preheating. Preheating is the exponentially rapid transfer of energy from the nearly homogeneous inflaton field to fluctuations of other fields and/or the inflaton itself. This rapid transfer leaves these fields in a highly nonthermal state with energy concentrated in infrared modes. We have performed lattice simulations of the evolution of interacting scalar fields during and after preheating for a variety of inflationary models. We have formulated a set of generic rules that govern the thermalization process in all of these models. Notably, we see that once one of the fields is amplified through parametric resonance or other mechanisms it rapidly excites other coupled fields to exponentially large occupation numbers. These fields quickly acquire nearly thermal spectra in the infrared, which gradually propagates into higher momenta. Prior to the formation of total equilibrium, the excited fields group into subsets with almost identical characteristics (e.g. group effective temperature). The way fields form into these groups and the properties of the groups depend on the couplings between them. We also studied the onset of chaos after preheating by calculating the Lyapunov exponent of the scalar fields.Comment: 15 pages, 23 figure

The Boltzmann equation for colourless plasmons in hot QCD plasma. Semiclassical approximation

Within the framework of the semiclassical approximation, we derive the Boltzmann equation describing the dynamics of colorless plasmons in a hot QCD plasma. The probability of the plasmon-plasmon scattering at the leading order in the coupling constant is obtained. This probability is gauge-independent at least in the class of the covariant and temporal gauges. It is noted that the structure of the scattering kernel possesses important qualitative difference from the corresponding one in the Abelian plasma, in spite of the fact that we focused our study on the colorless soft excitations. It is shown that four-plasmon decay is suppressed by the power of $g$ relative to the process of nonlinear scattering of plasmons by thermal particles at the soft momentum scale. It is stated that the former process becomes important in going to the ultrasoft region of the momentum scale.Comment: 41, LaTeX, minor changes, identical to published versio

Dispersionful analogues of Benney's equations and NN-wave systems

We recall Krichever's construction of additional flows to Benney's hierarchy, attached to poles at finite distance of the Lax operator. Then we construct a ``dispersionful'' analogue of this hierarchy, in which the role of poles at finite distance is played by Miura fields. We connect this hierarchy with $N$-wave systems, and prove several facts about the latter (Lax representation, Chern-Simons-type Lagrangian, connection with Liouville equation, $\tau$-functions).Comment: 12 pages, latex, no figure