Factorisation, Parton Entanglement and the Drell-Yan Process

We discuss the angular distribution of the lepton pair in the Drell-Yan process, hadron+hadron -> \gamma^* X -> l^+ l^- X. This process gives information on the spin-density matrix \rho^{(q,\bar{q})} of the annihilating quark-antiquark pair in q+\bar{q} -> l^+ l^-. There is strong experimental evidence that even for unpolarised initial hadrons \rho^{(q,\bar{q})} is nontrivial, and therefore the quark-antiquark system is polarised. We discuss the possibilities of a general \rho^{(q,\bar{q})} -which could be entangled- and a factorising \rho^{(q,\bar{q})}. We argue that instantons may lead to a nontrivial \rho^{(q,\bar{q})} of the type indicated by experiments.Comment: 14 pages, 2 figures, comments and references added; to appear in EPJ

Compatibility of phenomenological dipole cross sections with the Balitsky-Kovchegov equation

Phenomenological models of the dipole cross section that enters in the description of for instance deep inelastic scattering at very high energies have had considerable success in describing the available small-x data in both the saturation region and the so-called extended geometric scaling (EGS) region. We investigate to what extent such models are compatible with the numerical solutions of the Balitsky-Kovchegov (BK) equation which is expected to describe the nonlinear evolution in x of the dipole cross section in these momentum regions. We find that in the EGS region the BK equation yields results that are qualitatively different from those of phenomenological studies. In particular, geometric scaling around the saturation scale is only obtained at asymptotic rapidities. We find that in this limit, the anomalous dimension \gamma(r,x) of phenomenological models approaches a limiting function that is universal for a large range of initial conditions. At the saturation scale, this function equals approximately 0.44, in contrast to the value 0.628 commonly used in the models. We further investigate the dependence of these results on the starting distribution, the small-r limit of the anomalous dimension for fixed rapidities and the x-dependence of the saturation scale.Comment: 14 pages, 8 figures. Extensive revisions, several new results, plots, references and conclusions added; to appear in Phys.Rev.

High-Level Expression of Various Apolipoprotein (a) Isoforms by "Transferrinfection". The Role of Kringle IV Sequences in the Extracellular Association with Low-Density Lipoprotein

Characterization of the assembly of lipoprotein(a) [Lp(a)] is of fundamental importance to understanding the biosynthesis and metabolism of this atherogenic lipoprotein. Since no established cell lines exist that express Lp(a) or apolipoprotein(a) [apo(a)], a "transferrinfection" system for apo(a) was developed utilizing adenovirus receptor- and transferrin receptor-mediated DNA uptake into cells. Using this method, different apo(a) cDNA constructions of variable length, due to the presence of 3, 5, 7, 9, 15, or 18 internal kringle IV sequences, were expressed in cos-7 cells or CHO cells. All constructions contained kringle IV-36, which includes the only unpaired cysteine residue (Cys-4057) in apo(a). r-Apo(a) was synthesized as a precursor and secreted as mature apolipoprotein into the medium. When medium containing r-apo(a) with 9, 15, or 18 kringle IV repeats was mixed with normal human plasma LDL, stable complexes formed that had a bouyant density typical of Lp(a). Association was substantially decreased if Cys-4057 on r-apo(a) was replaced by Arg by site-directed mutagenesis or if Cys-4057 was chemically modified. Lack of association was also observed with r-apo(a) containing only 3, 5, or 7 kringle IV repeats without "unique kringle IV sequences", although Cys-4057 was present in all of these constructions. Synthesis and secretion of r-apo(a) was not dependent on its sialic acid content. r-Apo(a) was expressed even more efficiently in sialylation-defective CHO cells than in wild-type CHO cells. In transfected CHO cells defective in the addition of N-acetylglucosamine, apo(a) secretion was found to be decreased by 50%. Extracellular association with LDL was not affected by the carbohydrate moiety of r-apo(a), indicating a protein-protein interaction between r-apo(a) and apoB. These results show that, besides kringle IV-36, other kringle IV sequences are necessary for the extracellular association of r-apo(a) with LDL. Changes in the carbohydrate moiety of apo(a), however, do not affect complex formation

Semiclassical Description of Tunneling in Mixed Systems: The Case of the Annular Billiard

We study quantum-mechanical tunneling between symmetry-related pairs of regular phase space regions that are separated by a chaotic layer. We consider the annular billiard, and use scattering theory to relate the splitting of quasi-degenerate states quantized on the two regular regions to specific paths connecting them. The tunneling amplitudes involved are given a semiclassical interpretation by extending the billiard boundaries to complex space and generalizing specular reflection to complex rays. We give analytical expressions for the splittings, and show that the dominant contributions come from {\em chaos-assisted}\/ paths that tunnel into and out of the chaotic layer.Comment: 4 pages, uuencoded postscript file, replaces a corrupted versio

Quantum effects after decoherence in a quenched phase transition

We study a quantum mechanical toy model that mimics some features of a quenched phase transition. Both by virtue of a time-dependent Hamiltonian or by changing the temperature of the bath we are able to show that even after classicalization has been reached, the system may display quantum behaviour again. We explain this behaviour in terms of simple non-linear analysis and estimate relevant time scales that match the results of numerical simulations of the master-equation. This opens new possibilities both in the study of quantum effects in non-equilibrium phase transitions and in general time-dependent problems where quantum effects may be relevant even after decoherence has been completed.Comment: 7 pages, 7 figures, revtex, important revisions made. To be published in Phys. Rev.

Spectral Statistics in Chaotic Systems with Two Identical Connected Cells

Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells introduces an additional classical time scale that is manifest also in the spectral form factor. If the two cells are related by a spatial symmetry, the spectrum shows doublets, reflected in the form factor as a positive peak around the Heisenberg time. We combine a semiclassical analysis with an independent random-matrix approach to the doublet splittings to obtain the form factor on all time (energy) scales. Its only free parameter is the characteristic time of exchange between the cells in units of the Heisenberg time.Comment: 37 pages, 15 figures, changed content, additional autho

Bose-Einstein condensates in a double well: mean-field chaos and multi-particle entanglement

A recent publication [Phys. Rev. Lett. 100, 140408 (2008)] shows that there is a relation between mean-field chaos and multi-particle entanglement for BECs in a periodically shaken double well. 'Schrodinger-cat' like mesoscopic superpositions in phase-space occur for conditions for which the system displays mean-field chaos. In the present manuscript, more general highly-entangled states are investigated. Mean-field chaos accelerates the emergence of multi-particle entanglement; the boundaries of stable regions are particularly suited for entanglement generation.Comment: 5 Pages, 5 jpg-figures, to be published in the proceedings of the LPHYS0

Effect of dissipation and measurement on a tunneling system

We consider a parametrically driven Kerr medium in which the pumping may be sinusoidally varied. It has been previously found that this system exhibits coherent tunneling between two fixed points which can be either enhanced or suppressed by altering the driving frequency and strength. We numerically investigate the dynamics when damping is included. This is done both by solving a master equation and using the quantum-trajectory method. In the latter case it is also possible to model the result of a continuous heterodyne measurement of the cavity output. The dissipation destroys the coherences which give rise to the tunneling, causing the sinusoidal oscillation of the mean to give way to a stochastic jumping between the fixed points, manifested as a random telegraph signal. In the quantum-trajectory picture we show that the coherences responsible for tunneling are an exponentially decreasing function of the signal-to-noise ratio for heterodyne measurements. However, evidence of both the bare tunneling rate and the driving modified tunneling rate are still apparent in the random telegraph signal

Dynamical Tunneling in Mixed Systems

We study quantum-mechanical tunneling in mixed dynamical systems between symmetry-related phase space tori separated by a chaotic layer. Considering e.g. the annular billiard we decompose tunneling-related energy splittings and shifts into sums over paths in phase space. We show that tunneling transport is dominated by chaos-assisted paths that tunnel into and out of the chaotic layer via the ``beach'' regions sandwiched between the regular islands and the chaotic sea. Level splittings are shown to fluctuate on two scales as functions of energy or an external parameter: they display a dense sequence of peaks due to resonances with states supported by the chaotic sea, overlaid on top of slow modulations arising from resonances with states supported by the ``beaches''. We obtain analytic expressions which enable us to assess the relative importance of tunneling amplitudes into the chaotic sea vs. its internal transport properties. Finally, we average over the statistics of the chaotic region, and derive the asymptotic tail of the splitting distribution function under rather general assumptions concerning the fluctuation properties of chaotic states.Comment: 28 pages, Latex, 16 EPS figure