Corrected confidence intervals for secondary parameters following sequential tests

Corrected confidence intervals are developed for the mean of the second component of a bivariate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a pivotal quantity, and then using very weak expansions to determine the correction terms. The asymptotic sampling distribution of the renormalised pivotal quantity is established in both the case where the covariance matrix is known and when it is unknown. The resulting approximations have a simple form and the results of a simulation study of two well-known sequential tests show that they are very accurate. The practical usefulness of the approach is illustrated by a real example of bivariate data. Detailed proofs of the main results are provided.Comment: Published at http://dx.doi.org/10.1214/074921706000000617 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Pairing versus phase coherence of doped holes in distinct quantum spin backgrounds

We examine the pairing structure of holes injected into two \emph{distinct} spin backgrounds: a short-range antiferromagnetic phase versus a symmetry protected topological phase. Based on density matrix renormalization group (DMRG) simulation, we find that although there is a strong binding between two holes in both phases, \emph{phase fluctuations} can significantly influence the pair-pair correlation depending on the spin-spin correlation in the background. Here the phase fluctuation is identified as an intrinsic string operator nonlocally controlled by the spins. We show that while the pairing amplitude is generally large, the coherent Cooper pairing can be substantially weakened by the phase fluctuation in the symmetry-protected topological phase, in contrast to the short-range antiferromagnetic phase. It provides an example of a non-BCS mechanism for pairing, in which the paring phase coherence is determined by the underlying spin state self-consistently, bearing an interesting resemblance to the pseudogap physics in the cuprate.Comment: 9 pages, 6 figure

Leading Twist Amplitudes for Exclusive Neutrino Interactions in the Deeply Virtual Limit

Neutrino scattering on nucleons in the regime of deeply virtual kinematics is studied both in the charged and the neutral electroweak sectors using a formalism developed by Blumlein, Robaschik, Geyer and Collaborators for the analysis of the Virtual Compton amplitude in the generalized Bjorken region. We discuss the structure of the leading twist amplitudes of the process.Comment: 14 pages, 1 fig revised final version to appear in Phys. Rev.

Spin-charge separation: From one hole to finite doping

In the presence of nonlocal phase shift effects, a quasiparticle can remain topologically stable even in a spin-charge separation state due to the confinement effect introduced by the phase shifts at finite doping. True deconfinement only happens in the zero-doping limit where a bare hole can lose its integrity and decay into holon and spinon elementary excitations. The Fermi surface structure is completely different in these two cases, from a large band-structure-like one to four Fermi points in one-hole case, and we argue that the so-called underdoped regime actually corresponds to a situation in between.Comment: 4 pages, 2 figures, presented in M2S-HTSC-VI conference (2000