Non-Perturbative Isotropic Multi-Particle Production in Yang--Mills Theory

We use singular Euclidean solutions to find multi-particle production cross sections in field theories. We investigate a family of time-dependent O(3) symmetrical solutions of the Yang--Mills equations, which govern the isotropic high-energy gauge boson production. At low energies our approach reproduces the instanton-induced cross sections. For higher energies we get new results. In particular, we show that the cross section for isotropic multiparticle production remains exponentially small in the running gauge coupling constant. The result applies both to the baryon number violation in the electro-weak theory and to the QCD jet production. We find that the isotropic multi-gluon production cross section falls off approximately as a ninth power of energy but possibly might be observableComment: RUB preprint 52/93, 39p. Two figures (out of four) included at the end as uudecoded poscript file. Two other figures can be sent upon request: E-mail to [email protected]

Parametric Excitation of a 1D Gas in Integrable and Nonintegrable Cases

We study the response of a highly excited 1D gas with pointlike interactions to a periodic modulation of the coupling constant. We calculate the corresponding dynamic structure factors and show that their low-frequency behavior differs dramatically for integrable and nonintegrable models. Nonintegrable systems are sensitive to excitations with frequencies as low as the mean level spacing, whereas much higher frequencies are required to excite an integrable system. This effect can be used as a probe of integrability for mesoscopic 1D systems and can be observed experimentally by measuring the heating rate of a parametrically excited gas.Comment: Published version, 4 pages, 2 figure

Ultradilute low-dimensional liquids

We calculate the energy of one- and two-dimensional weakly interacting Bose-Bose mixtures analytically in the Bogoliubov approximation and by using the diffusion Monte Carlo technique. We show that in the case of attractive inter- and repulsive intraspecies interactions the energy per particle has a minimum at a finite density corresponding to a liquid state. We derive the Gross-Pitaevskii equation to describe droplets of such liquids and solve it analytically in the one-dimensional case.Comment: published version + supplemental materia

Elastic Multi-Body Interactions on a Lattice

We show that by coupling two hyperfine states of an atom in an optical lattice one can independently control two-, three-, and four-body on-site interactions in a non-perturbative manner. In particular, under typical conditions of current experiments one can have a purely three- or four-body interacting gas of $^{39}$K atoms characterized by on-site interaction shifts of several 100Hz.Comment: 6 pages, 3 figure

Nonlinearity of vacuum reggeons and exclusive diffractive production of vector mesons at HERA

The processes of exclusive photo- and electroproduction of vector mesons $\rho^0$(770), $\phi$(1020) and $J/\psi$(3096) at collision energies $30 GeV<W<300 GeV$ and transferred momenta squared $0<-t<2 GeV^2$ are considered in the framework of a phenomenological Regge-eikonal scheme with nonlinear Regge trajectories in which their QCD asymptotic behavior is taken into account explicitly. By comparison of available experimental data from ZEUS and H1 Collaborations with the model predictions it is demonstrated that corresponding angular distributions and integrated cross-sections in the above-mentioned kinematical range can be quantitatively described with use of two $C$-even vacuum Regge trajectories. These are the "soft" pomeron dominating the high energy reactions without a hard scale and the "hard" pomeron giving an essential contribution to photo- and electroproduction of heavy vector mesons and deeply virtual electroproduction of light vector mesons.Comment: 25 pages, 12 figure

Propagation of a Dark Soliton in a Disordered Bose-Einstein Condensate

We consider the propagation of a dark soliton in a quasi 1D Bose-Einstein condensate in presence of a random potential. This configuration involves nonlinear effects and disorder, and we argue that, contrarily to the study of stationary transmission coefficients through a nonlinear disordered slab, it is a well defined problem. It is found that a dark soliton decays algebraically, over a characteristic length which is independent of its initial velocity, and much larger than both the healing length and the 1D scattering length of the system. We also determine the characteristic decay time.Comment: 4 pages, 2 figure