Stability of mode-locked kinks in the ac driven and damped sine-Gordon lattice

Kink dynamics in the underdamped and strongly discrete sine-Gordon lattice that is driven by the oscillating force is studied. The investigation is focused mostly on the properties of the mode-locked states in the {\it overband} case, when the driving frequency lies above the linear band. With the help of Floquet theory it is demonstrated that the destabilizing of the mode-locked state happens either through the Hopf bifurcation or through the tangential bifurcation. It is also observed that in the overband case the standing mode-locked kink state maintains its stability for the bias amplitudes that are by the order of magnitude larger than the amplitudes in the low-frequency case.Comment: To appear in Springer Series on Wave Phenomena, special volume devoted to the LENCOS'12 conference; 6 figure

The Small-x Behaviour of the Singlet Polarized Structure Function g_2 in the Double Logarithmic Approximation

The small-x behavior of the singlet contributions to the polarized structure function g_2(x,Q^2) is calculated in the double-logarithmic approximation of perturbative QCD. The dominant contribution is due to the gluons which, in contrast to the unpolarized case, mix with the fermions also in the small-x domain. We find a power-like growth in 1/x in the odd-signature parts of the amplitude with the same power as in the singlet function g_1(x,Q^2) at x<< 1.Comment: 20 pages, latex, 3 ps figure

The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics

The present work establishes the mean-field limit of a N-particle system towards a regularized variant of the relativistic Vlasov-Maxwell system, following the work of Braun-Hepp [Comm. in Math. Phys. 56 (1977), 101-113] and Dobrushin [Func. Anal. Appl. 13 (1979), 115-123] for the Vlasov-Poisson system. The main ingredients in the analysis of this system are (a) a kinetic formulation of the Maxwell equations in terms of a distribution of electromagnetic potential in the momentum variable, (b) a regularization procedure for which an analogue of the total energy - i.e. the kinetic energy of the particles plus the energy of the electromagnetic field - is conserved and (c) an analogue of Dobrushin's stability estimate for the Monge-Kantorovich-Rubinstein distance between two solutions of the regularized Vlasov-Poisson dynamics adapted to retarded potentials.Comment: 34 page

Charmonium from Statistical Hadronization of Heavy Quarks -- a Probe for Deconfinement in the Quark-Gluon Plasma

We review the statistical hadronization picture for charmonium production in ultra-relativistic nuclear collisions. Our starting point is a brief reminder of the status of the thermal model description of hadron production at high energy. Within this framework an excellent account is achieved of all data for hadrons built of (u,d,s) valence quarks using temperature, baryo-chemical potential and volume as thermal parameters. The large charm quark mass brings in a new (non-thermal) scale which is explicitely taken into account by fixing the total number of charm quarks produced in the collision. Emphasis is placed on the description of the physical basis for the resulting statistical hadronization model. We discuss the evidence for statistical hadronization of charmonia by analysis of recent data from the SPS and RHIC accelerators. Furthermore we discuss an extension of this model towards lower beam energies and develop arguments about the prospects to observe medium modifications of open and hidden charm hadrons. With the imminent start of the LHC accelerator at CERN, exciting prospects for charmonium production studies at the very high energy frontier come into reach. We present arguments that, at such energies, charmonium production becomes a fingerprint of deconfinement: even if no charmonia survive in the quark-gluon plasma, statistical hadronization at the QCD phase boundary of the many tens of charm quarks expected in a single central Pb-Pb collision could lead to an enhanced, rather than suppressed production probability when compared to results for nucleon-nucleon reactions scaled by the number of hard collisions in the Pb-Pb system.Comment: review article, 27 pages, Landoldt review volume "Relativistic Heavy Ion Physics", Reinhard Stock, edito

Review of Speculative "Disaster Scenarios" at RHIC

We discuss speculative disaster scenarios inspired by hypothetical new fundamental processes that might occur in high energy relativistic heavy ion collisions. We estimate the parameters relevant to black hole production; we find that they are absurdly small. We show that other accelerator and (especially) cosmic ray environments have already provided far more auspicious opportunities for transition to a new vacuum state, so that existing observations provide stringent bounds. We discuss in most detail the possibility of producing a dangerous strangelet. We argue that four separate requirements are necessary for this to occur: existence of large stable strangelets, metastability of intermediate size strangelets, negative charge for strangelets along the stability line, and production of intermediate size strangelets in the heavy ion environment. We discuss both theoretical and experimental reasons why each of these appears unlikely; in particular, we know of no plausible suggestion for why the third or especially the fourth might be true. Given minimal physical assumptions the continued existence of the Moon, in the form we know it, despite billions of years of cosmic ray exposure, provides powerful empirical evidence against the possibility of dangerous strangelet production.Comment: 28 pages, REVTeX; minor revisions for publication (Reviews of Modern Physics, ca. Oct. 2000); email to [email protected]

D∗DπD^*D\pi and B∗BπB^*B\pi couplings in QCD

We calculate the $D^*D\pi$ and $B^*B\pi$ couplings using QCD sum rules on the light-cone. In this approach, the large-distance dynamics is incorporated in a set of pion wave functions. We take into account two-particle and three-particle wave functions of twist 2, 3 and 4. The resulting values of the coupling constants are $g_{D^*D\pi}= 12.5\pm 1$ and $g_{B^*B\pi}= 29\pm 3$. From this we predict the partial width \Gamma (D^{*+} \ra D^0 \pi^+ )=32 \pm 5~ keV . We also discuss the soft-pion limit of the sum rules which is equivalent to the external axial field approach employed in earlier calculations. Furthermore, using $g_{B^*B\pi}$ and $g_{D^*D\pi}$ the pole dominance model for the B \ra \pi and D\ra \pi semileptonic form factors is compared with the direct calculation of these form factors in the same framework of light-cone sum rules.Comment: 27 pages (LATEX) +3 figures enclosed as .uu file MPI-PhT/94-62 , CEBAF-TH-94-22, LMU 15/9

Progress in the determination of the J/ψ−πJ/\psi-\pi cross section

Improving previous calculations, we compute the $J/\psi \pi\to {charmed mesons}$ cross section using QCD sum rules. Our sum rules for the $J/\psi \pi\to \bar{D} D^*$, $D \bar{D}^*$, ${\bar D}^* D^*$ and ${\bar D} D$ hadronic matrix elements are constructed by using vaccum-pion correlation functions, and we work up to twist-4 in the soft-pion limit. Our results suggest that, using meson exchange models is perfectly acceptable, provided that they include form factors and that they respect chiral symmetry. After doing a thermal average we get $\sim 0.3$ mb at T=150\MeV.Comment: 22 pages, RevTeX4 including 7 figures in ps file

Diffusion and Current of Brownian Particles in Tilted Piecewise Linear Potentials: Amplification and Coherence

Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their dependencies on temperature, tilting force, and the shape of the potential are analyzed. The necessary and sufficient conditions for the non-monotonic behavior of the diffusion coefficient as a function of temperature are determined. The diffusion coefficient and coherence level are found to be extremely sensitive to the asymmetry of the potential. It is established that at the values of the external force, for which the enhancement of diffusion is most rapid, the level of coherence has a wide plateau at low temperatures with the value of the Peclet factor 2. An interpretation of the amplification of diffusion in comparison with free thermal diffusion in terms of probability distribution is proposed.Comment: To appear in PR

Vlasov scaling for stochastic dynamics of continuous systems

We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of the realization of the proposed approach in particular models are presented.Comment: 23 page

Colored Spin Systems, BKP Evolution and finite N_c effects

Even within the framework of the leading logarithmic approximation the eigenvalues of the BKP kernel for states of more than three reggeized gluons are unknown in general, contrary to the planar limit case where the problem becomes integrable. We consider a 4-gluon kernel for a finite number of colors and define some simple toy models for the configuration space dynamics, which are directly solvable with group theoretical methods. Then we study the dependence of the spectrum of these models with respect to the number of colors and make comparisons with the large limit case.Comment: 17 pages, 4 figures, references update, to appear on EPJ