Average persistence in random walks

We study the first passage time properties of an integrated Brownian curve both in homogeneous and disordered environments. In a disordered medium we relate the scaling properties of this center of mass persistence of a random walker to the average persistence, the latter being the probability P_pr(t) that the expectation value of the walker's position after time t has not returned to the initial value. The average persistence is then connected to the statistics of extreme events of homogeneous random walks which can be computed exactly for moderate system sizes. As a result we obtain a logarithmic dependence P_pr(t)~{ln(t)}^theta' with a new exponent theta'=0.191+/-0.002. We note on a complete correspondence between the average persistence of random walks and the magnetization autocorrelation function of the transverse-field Ising chain, in the homogeneous and disordered case.Comment: 6 pages LaTeX, 3 postscript figures include

Survival of a Diffusing Particle in a Transverse Shear Flow: A First-Passage Problem with Continuously Varying Persistence Exponent

We consider a particle diffusing in the y-direction, dy/dt=\eta(t), subject to a transverse shear flow in the x-direction, dx/dt=f(y), where x \ge 0 and x=0 is an absorbing boundary. We treat the class of models defined by f(y) = \pm v_{\pm}(\pm y)^\alpha where the upper (lower) sign refers to y>0 (y<0). We show that the particle survives with probability Q(t) \sim t^{-\theta} with \theta = 1/4, independent of \alpha, if v_{+}=v_{-}. If v_{+} \ne v_{-}, however, we show that \theta depends on both \alpha and the ratio v_{+}/v_{-}, and we determine this dependence.Comment: 4 page

Surface Critical Behavior of Binary Alloys and Antiferromagnets: Dependence of the Universality Class on Surface Orientation

The surface critical behavior of semi-infinite (a) binary alloys with a continuous order-disorder transition and (b) Ising antiferromagnets in the presence of a magnetic field is considered. In contrast to ferromagnets, the surface universality class of these systems depends on the orientation of the surface with respect to the crystal axes. There is ordinary and extraordinary surface critical behavior for orientations that preserve and break the two-sublattice symmetry, respectively. This is confirmed by transfer-matrix calculations for the two-dimensional antiferromagnet and other evidence.Comment: Final version that appeared in PRL, some minor stylistic changes and one corrected formula; 4 pp., twocolumn, REVTeX, 3 eps fig

The Reaction πN→ππN\pi N \to \pi \pi N at Threshold

We consider the chiral expansion for the reaction $\pi N \to \pi \pi N$ in heavy baryon chiral perturbation theory. To order $M_\pi$ we derive novel low--energy theorems that compare favorably with recent determinations of the total cross sections for $\pi^+ p \to \pi^+ \pi^+ n$ and $\pi^- p \to \pi^0 \pi^0 n$.Comment: 7 pp, LateX (uses epsf.sty), 3 figures appended as ps files (split off as ppnf1.ps,ppnf2.ps,ppnf3.ps), CRN 94/1

Conformal off-diagonal boundary density profiles on a semi-infinite strip

The off-diagonal profile phi(v) associated with a local operator (order parameter or energy density) close to the boundary of a semi-infinite strip with width L is obtained at criticality using conformal methods. It involves the surface exponent x_phi^s and displays a simple universal behaviour which crosses over from surface finite-size scaling when v/L is held constant to corner finite-size scaling when v/L -> 0.Comment: 5 pages, 1 figure, IOP macros and eps

Collisional and thermal ionization of sodium Rydberg atoms I. Experiment for nS and nD atoms with n=8-20

Collisional and thermal ionization of sodium nS and nD Rydberg atoms with n=8-20 has been studied. The experiments were performed using a two-step pulsed laser excitation in an effusive atomic beam at atom density of about 2 10^{10} cm^{-3}. Molecular and atomic ions from associative, Penning, and thermal ionization processes were detected. It has been found that the atomic ions were created mainly due to photoionization of Rydberg atoms by photons of blackbody radiation at the ambient temperature of 300K. Blackbody ionization rates and effective lifetimes of Rydberg states of interest were determined. The molecular ions were found to be from associative ionization in Na(nL)+Na(3S) collisions. Rate constants of associative ionization have been measured using an original method based on relative measurements of Na_{2}^{+} and Na^{+} ion signals.Comment: 23 pages, 10 figure