Conditional probabilities in quantum theory, and the tunneling time controversy

It is argued that there is a sensible way to define conditional probabilities in quantum mechanics, assuming only Bayes's theorem and standard quantum theory. These probabilities are equivalent to the ``weak measurement'' predictions due to Aharonov {\it et al.}, and hence describe the outcomes of real measurements made on subensembles. In particular, this approach is used to address the question of the history of a particle which has tunnelled across a barrier. A {\it gedankenexperiment} is presented to demonstrate the physically testable implications of the results of these calculations, along with graphs of the time-evolution of the conditional probability distribution for a tunneling particle and for one undergoing allowed transmission. Numerical results are also presented for the effects of loss in a bandgap medium on transmission and on reflection, as a function of the position of the lossy region; such loss should provide a feasible, though indirect, test of the present conclusions. It is argued that the effects of loss on the pulse {\it delay time} are related to the imaginary value of the momentum of a tunneling particle, and it is suggested that this might help explain a small discrepancy in an earlier experiment.Comment: 11 pages, latex, 4 postscript figures separate (one w/ 3 parts

Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A. Groisman and V. Steinberg, \sl Nature $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of width of the region available for flow to radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high molecular weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. Those include: (i)randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales; (ii) significant increase in the rates of momentum and mass transfer (compared to those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms, and parameter dependence of the elastic turbulence are compared with those of the conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure

Sub-femtosecond determination of transmission delay times for a dielectric mirror (photonic bandgap) as a function of angle of incidence

Using a two-photon interference technique, we measure the delay for single-photon wavepackets to be transmitted through a multilayer dielectric mirror, which functions as a ``photonic bandgap'' medium. By varying the angle of incidence, we are able to confirm the behavior predicted by the group delay (stationary phase approximation), including a variation of the delay time from superluminal to subluminal as the band edge is tuned towards to the wavelength of our photons. The agreement with theory is better than 0.5 femtoseconds (less than one quarter of an optical period) except at large angles of incidence. The source of the remaining discrepancy is not yet fully understood.Comment: 5 pages and 5 figure

Particle production and equilibrium properties within a new hadron transport approach for heavy-ion collisions

The microscopic description of heavy-ion reactions at low beam energies is achieved within hadronic transport approaches. In this article a new approach SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) is introduced and applied to study the production of non-strange particles in heavy-ion reactions at $E_{\rm kin}=0.4-2A$ GeV. First, the model is described including details about the collision criterion, the initial conditions and the resonance formation and decays. To validate the approach, equilibrium properties such as detailed balance are presented and the results are compared to experimental data for elementary cross sections. Finally results for pion and proton production in C+C and Au+Au collisions is confronted with HADES and FOPI data. Predictions for particle production in $\pi+A$ collisions are made.Comment: 30 pages, 30 figures, replaced with published version; only minor change

Clustering by genetic ancestry using genome-wide SNP data

<p>Abstract</p> <p>Background</p> <p>Population stratification can cause spurious associations in a genome-wide association study (GWAS), and occurs when differences in allele frequencies of single nucleotide polymorphisms (SNPs) are due to ancestral differences between cases and controls rather than the trait of interest. Principal components analysis (PCA) is the established approach to detect population substructure using genome-wide data and to adjust the genetic association for stratification by including the top principal components in the analysis. An alternative solution is genetic matching of cases and controls that requires, however, well defined population strata for appropriate selection of cases and controls.</p> <p>Results</p> <p>We developed a novel algorithm to cluster individuals into groups with similar ancestral backgrounds based on the principal components computed by PCA. We demonstrate the effectiveness of our algorithm in real and simulated data, and show that matching cases and controls using the clusters assigned by the algorithm substantially reduces population stratification bias. Through simulation we show that the power of our method is higher than adjustment for PCs in certain situations.</p> <p>Conclusions</p> <p>In addition to reducing population stratification bias and improving power, matching creates a clean dataset free of population stratification which can then be used to build prediction models without including variables to adjust for ancestry. The cluster assignments also allow for the estimation of genetic heterogeneity by examining cluster specific effects.</p

Worm Structure in Modified Swift-Hohenberg Equation for Electroconvection

A theoretical model for studying pattern formation in electroconvection is proposed in the form of a modified Swift-Hohenberg equation. A localized state is found in two dimension, in agreement with the experimentally observed ``worm" state. The corresponding one dimensional model is also studied, and a novel stationary localized state due to nonadiabatic effect is found. The existence of the 1D localized state is shown to be responsible for the formation of the two dimensional ``worm" state in our model

Church-Rosser Systems, Codes with Bounded Synchronization Delay and Local Rees Extensions

What is the common link, if there is any, between Church-Rosser systems, prefix codes with bounded synchronization delay, and local Rees extensions? The first obvious answer is that each of these notions relates to topics of interest for WORDS: Church-Rosser systems are certain rewriting systems over words, codes are given by sets of words which form a basis of a free submonoid in the free monoid of all words (over a given alphabet) and local Rees extensions provide structural insight into regular languages over words. So, it seems to be a legitimate title for an extended abstract presented at the conference WORDS 2017. However, this work is more ambitious, it outlines some less obvious but much more interesting link between these topics. This link is based on a structure theory of finite monoids with varieties of groups and the concept of local divisors playing a prominent role. Parts of this work appeared in a similar form in conference proceedings where proofs and further material can be found.Comment: Extended abstract of an invited talk given at WORDS 201

Universality relations in non-solvable quantum spin chains

We prove the exact relations between the critical exponents and the susceptibility, implied by the Haldane Luttinger liquid conjecture, for a generic lattice fermionic model or a quantum spin chain with short range weak interaction. The validity of such relations was only checked in some special solvable models, but there was up to now no proof of their validity in non-solvable models