Advective collisions

Small particles advected in a fluid can collide (and therefore aggregate) due to the stretching or shearing of fluid elements. This effect is usually discussed in terms of a theory due to Saffman and Turner [J. Fluid Mech., 1, 16-30, (1956)]. We show that in complex or random flows the Saffman-Turner theory for the collision rate describes only an initial transient (which we evaluate exactly). We obtain precise expressions for the steady-state collision rate for flows with small Kubo number, including the influence of fractal clustering on the collision rate for compressible flows. For incompressible turbulent flows, where the Kubo number is of order unity, the Saffman-Turner theory is an upper bound.Comment: 4 pages, 1 figur

Weighted integral formulas on manifolds

We present a method of finding weighted Koppelman formulas for $(p,q)$-forms on $n$-dimensional complex manifolds $X$ which admit a vector bundle of rank $n$ over $X \times X$, such that the diagonal of $X \times X$ has a defining section. We apply the method to \Pn and find weighted Koppelman formulas for $(p,q)$-forms with values in a line bundle over \Pn. As an application, we look at the cohomology groups of $(p,q)$-forms over \Pn with values in various line bundles, and find explicit solutions to the \dbar-equation in some of the trivial groups. We also look at cohomology groups of $(0,q)$-forms over \Pn \times \Pm with values in various line bundles. Finally, we apply our method to developing weighted Koppelman formulas on Stein manifolds.Comment: 25 page

Event-by-event fluctuations of the charged particle ratio from non-equilibrium transport theory

The event by event fluctuations of the ratio of positively to negatively charged hadrons are predicted within the UrQMD model. Corrections for finite acceptance and finite net charge are derived. These corrections are relevant to compare experimental data and transport model results to previous predictions. The calculated fluctuations at RHIC and SPS energies are shown to be compatible with a hadron gas. Thus, deviating by a factor of 3 from the predictions for a thermalized quark-gluon plasma.Comment: This paper clarifies the previous predictions of Jeon and Koch (hep-ph/0003168) and addresses issues raised in hep-ph/0006023. 2 Figures, 10pp, uses RevTe

The dynamics of dissipative multi-fluid neutron star cores

We present a Newtonian multi-fluid formalism for superfluid neutron star cores, focussing on the additional dissipative terms that arise when one takes into account the individual dynamical degrees of freedom associated with the coupled "fluids". The problem is of direct astrophysical interest as the nature of the dissipative terms can have significant impact on the damping of the various oscillation modes of the star and the associated gravitational-wave signatures. A particularly interesting application concerns the gravitational-wave driven instability of f- and r-modes. We apply the developed formalism to two specific three-fluid systems: (i) a hyperon core in which both Lambda and Sigma^- hyperons are present, and (ii) a core of deconfined quarks in the colour-flavour-locked phase in which a population of neutral K^0 kaons is present. The formalism is, however, general and can be applied to other problems in neutron-star dynamics (such as the effect of thermal excitations close to the superfluid transition temperature) as well as laboratory multi-fluid systems.Comment: RevTex, no figure

The Feynman-Wilson gas and the Lund model

We derive a partition function for the Lund fragmentation model and compare it with that of a classical gas. For a fixed rapidity ``volume'' this partition function corresponds to a multiplicity distribution which is very close to a binomial distribution. We compare our results with the multiplicity distributions obtained from the JETSET Monte Carlo for several scenarios. Firstly, for the fragmentation vertices of the Lund string. Secondly, for the final state particles both with and without decays.Comment: Latex, 21+1 pages, 11 figure

A Relativistic Mean Field Model for Entrainment in General Relativistic Superfluid Neutron Stars

General relativistic superfluid neutron stars have a significantly more intricate dynamics than their ordinary fluid counterparts. Superfluidity allows different superfluid (and superconducting) species of particles to have independent fluid flows, a consequence of which is that the fluid equations of motion contain as many fluid element velocities as superfluid species. Whenever the particles of one superfluid interact with those of another, the momentum of each superfluid will be a linear combination of both superfluid velocities. This leads to the so-called entrainment effect whereby the motion of one superfluid will induce a momentum in the other superfluid. We have constructed a fully relativistic model for entrainment between superfluid neutrons and superconducting protons using a relativistic $\sigma - \omega$ mean field model for the nucleons and their interactions. In this context there are two notions of ``relativistic'': relativistic motion of the individual nucleons with respect to a local region of the star (i.e. a fluid element containing, say, an Avogadro's number of particles), and the motion of fluid elements with respect to the rest of the star. While it is the case that the fluid elements will typically maintain average speeds at a fraction of that of light, the supranuclear densities in the core of a neutron star can make the nucleons themselves have quite high average speeds within each fluid element. The formalism is applied to the problem of slowly-rotating superfluid neutron star configurations, a distinguishing characteristic being that the neutrons can rotate at a rate different from that of the protons.Comment: 16 pages, 5 figures, submitted to PR

Revival of quantum correlations without system-environment back-action

Revivals of quantum correlations have often been explained in terms of back-action on quantum systems by their quantum environment(s). Here we consider a system of two independently evolving qubits, each locally interacting with a classical random external field. The environments of the qubits are also independent, and there is no back-action on the qubits. Nevertheless, entanglement, quantum discord and classical correlations between the two qubits may revive in this model. We explain the revivals in terms of correlations in a classical-quantum state of the environments and the qubits. Although classical states cannot store entanglement on their own, they can play a role in storing and reviving entanglement. It is important to know how the absence of back-action, or modelling an environment as classical, affects the kind of system time evolutions one is able to describe. We find a class of global time evolutions where back-action is absent and for which there is no loss of generality in modelling the environment as classical. Finally, we show that the revivals can be connected with the increase of a parameter used to quantify non-Markovianity of the single-qubit dynamics.Comment: 8 pages, 4 figures; this version to appear in Phys. Rev.

Relativistic Two-stream Instability

We study the (local) propagation of plane waves in a relativistic, non-dissipative, two-fluid system, allowing for a relative velocity in the "background" configuration. The main aim is to analyze relativistic two-stream instability. This instability requires a relative flow -- either across an interface or when two or more fluids interpenetrate -- and can be triggered, for example, when one-dimensional plane-waves appear to be left-moving with respect to one fluid, but right-moving with respect to another. The dispersion relation of the two-fluid system is studied for different two-fluid equations of state: (i) the "free" (where there is no direct coupling between the fluid densities), (ii) coupled, and (iii) entrained (where the fluid momenta are linear combinations of the velocities) cases are considered in a frame-independent fashion (eg. no restriction to the rest-frame of either fluid). As a by-product of our analysis we determine the necessary conditions for a two-fluid system to be causal and absolutely stable and establish a new constraint on the entrainment.Comment: 15 pages, 2 eps-figure

Non-adiabatic holonomic quantum computation

We develop a non-adiabatic generalization of holonomic quantum computation in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit gates can be implemented by utilizing optical transitions in a generic three-level $\Lambda$ configuration. Our scheme opens up for universal holonomic quantum computation on qubits characterized by short coherence times.Comment: Some changes, journal reference adde