Three-point density correlation functions in the fractional quantum Hall regime

In this paper we consider the three-particle density correlation function for a fractional quantum Hall liquid. The study of this object is motivated by recent experimental studies of fractional quantum Hall systems using inelastic light scattering and phonon absorption techniques. Symmetry properties of the correlation function are noted. An exact sum-rule is derived which this quantity must obey. This sum-rule is used to assess the convolution approximation that has been used to estimate the matrix elements for such experiments. PACS Numbers: 73.40.Hm, 73.20.Mf, 72.10.DiComment: 12 pages + 1 (PS) figur

On the feasibility of studying vortex noise in 2D superconductors with cold atoms

We investigate the feasibility of using ultracold neutral atoms trapped near a thin superconductor to study vortex noise close to the Kosterlitz-Thouless-Berezinskii transition temperature. Alkali atoms such as rubidium probe the magnetic field produced by the vortices. We show that the relaxation time $T_1$ of the Zeeman sublevel populations can be conveniently adjusted to provide long observation times. We also show that the transverse relaxation times $T_2$ for Zeeman coherences are ideal for studying the vortex noise. We briefly consider the motion of atom clouds held close to the surface as a method for monitoring the vortex motion.Comment: 4 pages, 1 figur

Accurate statistics of a flexible polymer chain in shear flow

We present exact and analytically accurate results for the problem of a flexible polymer chain in shear flow. Under such a flow the polymer tumbles, and the probability distribution of the tumbling times $\tau$ of the polymer decays exponentially as $\sim \exp(-\alpha \tau/\tau_0)$ (where $\tau_0$ is the longest relaxation time). We show that for a Rouse chain, this nontrivial constant $\alpha$ can be calculated in the limit of large Weissenberg number (high shear rate) and is in excellent agreement with our simulation result of $\alpha \simeq 0.324$. We also derive exactly the distribution functions for the length and the orientational angles of the end-to-end vector of the polymer.Comment: 4 pages, 2 figures. Minor changes. Texts differ slightly from the PRL published versio

Classical diffusion of N interacting particles in one dimension: General results and asymptotic laws

I consider the coupled one-dimensional diffusion of a cluster of N classical particles with contact repulsion. General expressions are given for the probability distributions, allowing to obtain the transport coefficients. In the limit of large N, and within a gaussian approximation, the diffusion constant is found to behave as N^{-1} for the central particle and as (\ln N)^{-1} for the edge ones. Absolute correlations between the edge particles increase as (\ln N)^{2}. The asymptotic one-body distribution is obtained and discussed in relation of the statistics of extreme events.Comment: 6 pages, 2 eps figure

Dephasing by a nonstationary classical intermittent noise

We consider a new phenomenological model for a $1/f^{\mu}$ classical intermittent noise and study its effects on the dephasing of a two-level system. Within this model, the evolution of the relative phase between the $|\pm>$ states is described as a continuous time random walk (CTRW). Using renewal theory, we find exact expressions for the dephasing factor and identify the physically relevant various regimes in terms of the coupling to the noise. In particular, we point out the consequences of the non-stationarity and pronounced non-Gaussian features of this noise, including some new anomalous and aging dephasing scenarii.Comment: Submitted to Phys. Rev.

Dressed-State Approach to Population Trapping in the Jaynes-Cummings Model

The phenomenon of atomic population trapping in the Jaynes-Cummings Model is analysed from a dressed-state point of view. A general condition for the occurrence of partial or total trapping from an arbitrary, pure initial atom-field state is obtained in the form of a bound to the variation of the atomic inversion. More generally, it is found that in the presence of initial atomic or atom-field coherence the population dynamics is governed not by the field's initial photon distribution, but by a `weighted dressedness' distribution characterising the joint atom-field state. In particular, individual revivals in the inversion can be analytically described to good approximation in terms of that distribution, even in the limit of large population trapping. This result is obtained through a generalisation of the Poisson Summation Formula method for analytical description of revivals developed by Fleischhauer and Schleich [Phys. Rev. A {\bf 47}, 4258 (1993)].Comment: 24 pages, 5 figures, to appear in J. Mod. Op

Broad-tailed force distributions and velocity ordering in a heterogeneous membrane model for collective cell migration

Correlated velocity patterns and associated large length-scale transmission of traction forces have been observed in collective live cell migration as a response to a "wound". We argue that a simple physical model of a force-driven heterogeneous elastic membrane sliding over a viscous substrate can qualitatively explain a few experimentally observed facts: (i) the growth of velocity ordering which spreads from the wound boundary to the interior, (ii) the exponential tails of the traction force distributions, and (iii) the swirling pattern of velocities in the interior of the tissue.Comment: 7 pages and 5 figure

Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators

Ground state energies and wave functions of quartic and pure quartic oscillators are calculated by first casting the Schr\"{o}dinger equation into a nonlinear Riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method (QLM). In the QLM the nonlinear differential equation is solved by approximating the nonlinear terms by a sequence of linear expressions. The QLM is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter. Our explicit analytic results are then compared with exact numerical and also with WKB solutions and it is found that our ground state wave functions, using a range of small to large coupling constants, yield a precision of between 0.1 and 1 percent and are more accurate than WKB solutions by two to three orders of magnitude. In addition, our QLM wave functions are devoid of unphysical turning point singularities and thus allow one to make analytical estimates of how variation of the oscillator parameters affects physical systems that can be described by the quartic and pure quartic oscillators.Comment: 8 pages, 12 figures, 1 tabl

Hamiltonian solutions of the 3-body problem in (2+1)-gravity

We present a full study of the 3-body problem in gravity in flat (2+1)-dimensional space-time, and in the nonrelativistic limit of small velocities. We provide an explicit form of the ADM Hamiltonian in a regular coordinate system and we set up all the ingredients for canonical quantization. We emphasize the role of a U(2) symmetry under which the Hamiltonian is invariant and which should generalize to a U(N-1) symmetry for N bodies. This symmetry seems to stem from a braid group structure in the operations of looping of particles around each other, and guarantees the single-valuedness of the Hamiltonian. Its role for the construction of single-valued energy eigenfunctions is also discussed.Comment: 25 pages, no figure. v2: some calculation details removed to make the paper more concise (see v1 for the longer version), minor correction in a formula in the section on quantization, references added; results and conclusions unchange

Upper bounds on success probabilities in linear optics

We develop an abstract way of defining linear-optics networks designed to perform quantum information tasks such as quantum gates. We will be mainly concerned with the nonlinear sign shift gate, but it will become obvious that all other gates can be treated in a similar manner. The abstract scheme is extremely well suited for analytical as well as numerical investigations since it reduces the number of parameters for a general setting. With that we show numerically and partially analytically for a wide class of states that the success probability of generating a nonlinear sign shift gate does not exceed 1/4 which to our knowledge is the strongest bound to date.Comment: 8 pages, typeset using RevTex4, 5 EPS figure