Indirect Evidence for L\'evy Walks in Squeeze Film Damping

Molecular flow gas damping of mechanical motion in confined geometries, and its associated noise, is important in a variety of fields, including precision measurement, gravitational wave detection, and MEMS devices. We used two torsion balance instruments to measure the strength and distance-dependence of `squeeze film' damping. Measured quality factors derived from free decay of oscillation are consistent with gas particle superdiffusion in L\'evy walks and inconsistent with those expected from traditional Gaussian random walk particle motion. The distance-dependence of squeeze film damping observed in our experiments is in agreement with a parameter-free Monte Carlo simulation. The squeeze film damping of the motion of a plate suspended a distance d away from a parallel surface scales with a fractional power between 1/d and 1/d^2.Comment: 5 pages 5 figures accepted for PRD; typo in equation 3 and figure 1 fixe

Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP

We perform a detailed study of lepton mixing patterns arising from a scenario with three Majorana neutrinos in which a discrete flavor group Gf=Delta (3 n^2) or Gf=Delta(6 n^2) and a CP symmetry are broken to residual symmetries Ge=Z3 and Gnu=Z2 x CP in the charged lepton and neutrino sectors, respectively. While we consider all possible Z3 and Z2 generating elements, we focus on a certain set of CP transformations. The resulting lepton mixing depends on group theoretical indices and one continuous parameter. In order to study the mixing patterns comprehensively for all admitted Ge and Gnu, it is sufficient to discuss only three types of combinations. One of them requires as flavor group Delta (6 n^2). Two types of combinations lead to mixing patterns with a trimaximal column, while the third one allows for a much richer structure. For the first type of combinations the Dirac as well as one Majorana phase are trivial, whereas the other two ones predict in general all CP phases to be non-trivial and also non-maximal. Already for small values of the index n of the group, n <= 11, experimental data on lepton mixing can be accommodated well for particular choices of the parameters of the theory. We also comment on the relation of the used CP transformations to the automorphisms of Delta (3 n^2) and Delta (6 n^2).Comment: 60 pages, 12 tables and 10 figures. v2: typos corrected, references updated, some minor improvement of the text, matches version accepted for publication in Nuclear Physics

Avoided crossings in mesoscopic systems: electron propagation on a non-uniform magnetic cylinder

We consider an electron constrained to move on a surface with revolution symmetry in the presence of a constant magnetic field $B$ parallel to the surface axis. Depending on $B$ and the surface geometry the transverse part of the spectrum typically exhibits many crossings which change to avoided crossings if a weak symmetry breaking interaction is introduced. We study the effect of such perturbations on the quantum propagation. This problem admits a natural reformulation to which tools from molecular dynamics can be applied. In turn, this leads to the study of a perturbation theory for the time dependent Born-Oppenheimer approximation

Fast Equilibration of Hadrons in an Expanding Fireball

Due to long chemical equilibration times within standard hadronic reactions during the hadron gas phase in relativistic heavy ion collisions it has been suggested that the hadrons are "born" into equilibrium after the quark gluon plasma phase. Here we develop a dynamical scheme in which possible Hagedorn states contribute to fast chemical equilibration times of baryon anti-baryon pairs (as well as kaon anti-kaon pairs) inside a hadron gas and just below the critical temperature. Within this scheme, we use master equations and derive various analytical estimates for the chemical equilibration times. Applying a Bjorken picture to the expanding fireball, the kaons and baryons as well as the bath of pions and Hagedorn resonances can indeed quickly chemically equilibrate for both an initial overpopulation or underpopulation of Hagedorn resonances. Moreover, a comparison of our results to $(B+\bar{B})/\pi^{+}$ and $K/\pi^{+}$ ratios at RHIC, indeed, shows a close match.Comment: 4 pages, 5 figure

High Sensitivity Torsion Balance Tests for LISA Proof Mass Modeling

We have built a highly sensitive torsion balance to investigate small forces between closely spaced gold coated surfaces. Such forces will occur between the LISA proof mass and its housing. These forces are not well understood and experimental investigations are imperative. We describe our torsion balance and present the noise of the system. A significant contribution to the LISA noise budget at low frequencies is the fluctuation in the surface potential difference between the proof mass and its housing. We present first results of these measurements with our apparatus.Comment: 6th International LISA Symposiu

Charge Management for Gravitational Wave Observatories using UV LEDs

Accumulation of electrical charge on the end mirrors of gravitational wave observatories, such as the space-based LISA mission and ground-based LIGO detectors, can become a source of noise limiting the sensitivity of such detectors through electronic couplings to nearby surfaces. Torsion balances provide an ideal means for testing gravitational wave technologies due to their high sensitivity to small forces. Our torsion pendulum apparatus consists of a movable Au-coated Cu plate brought near a Au-coated Si plate pendulum suspended from a non-conducting quartz fiber. A UV LED located near the pendulum photoejects electrons from the surface, and a UV LED driven electron gun directs photoelectrons towards the pendulum surface. We have demonstrated both charging and discharging of the pendulum with equivalent charging rates of $\sim$$10^5 e/\mathrm{s}$, as well as spectral measurements of the pendulum charge resulting in a white noise level equivalent to $3\times10^5 e/\sqrt{Hz}$.Comment: 5 pages, submitted to PR

Chemical equilibration due to heavy Hagedorn states

A scenario of heavy resonances, called massive Hagedorn states, is proposed which exhibits a fast ($t\approx 1$ fm/c) chemical equilibration of (strange) baryons and anti-baryons at the QCD critical temperature $T_c$. For relativistic heavy ion collisions this scenario predicts that hadronization is followed by a brief expansion phase during which the equilibration rate is higher than the expansion rate, so that baryons and antibaryons reach chemical equilibrium before chemical freeze-out occurs.Comment: 9 pages, 2 figures. Invited talk given at 8th International Conference on Strangeness in Quark Matter (SQM2004), Cape Town, South Africa, 15-20 September 200

An extension of the Statistical Bootstrap Model to include Strangeness. Implications on Particle Ratios

The Statistical Bootstrap Model (SBM) is extended to describe hadronic systems which carry the quantum number of strangeness. The study is conducted in the three-dimensional space of temperature, up-down and strange chemical potentials, wherein the existence of a ``critical'' surface is established, which sets the limits of the hadronic phase of matter. A second surface, defined by the null expectation value of strangeness number is also determined. The approach of the latter surface to the critical one becomes the focal point of the present considerations. Two different versions of the extended SBM are examined, corresponding to the values 2 and 4 for the exponent, which determines the asymptotic fall-off of the mass spectrum. It is found that the version with the value 4 has decisive physical advantages. This model is subsequently adopted to discuss (strange) particle ratios pertaining to multiparticle production processes, for which a thermal equilibrium mode of description applies.Comment: 29 pages, 38 figures, all the figures are joined in one file. accepted for publication in Phys. Rev.

Gell-Mann and Low formula for degenerate unperturbed states

The Gell-Mann and Low switching allows to transform eigenstates of an unperturbed Hamiltonian $H_0$ into eigenstates of the modified Hamiltonian $H_0 + V$. This switching can be performed when the initial eigenstate is not degenerate, under some gap conditions with the remainder of the spectrum. We show here how to extend this approach to the case when the ground state of the unperturbed Hamiltonian is degenerate. More precisely, we prove that the switching procedure can still be performed when the initial states are eigenstates of the finite rank self-adjoint operator \cP_0 V \cP_0, where \cP_0 is the projection onto a degenerate eigenspace of $H_0$