Special cases of orthogonal polynomials on the semicircle and applications in numerical analysis

Orthogonal polynomials on the semicircle was introduced by Gautschi and Milovanovic in ´ [Rend. Sem. Mat. Univ. Politec. Torino, Special Issue (July 1985), 179−185] and [J. Approx. Theory 46 (1986), 230 − 250]. In this paper we give an account of this kind of orthogonality, weighted generalizations mainly oriented to Chebyshev weights of the first and second kind, as well as the corresponding applications in numerical analysis. Moreover, we also present a number of new results including those for Laurent polynomials orthogonal to a semicircle and applications to quasi-singular integrals.Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles. Sciences mathématiques. 44, 152 (2019)

Stochastic Time Response and Ultimate Noise Performance of Adsorption-Based Microfluidic Biosensors

In order to improve the interpretation of measurement results and to achieve the optimal performance of microfluidic biosensors, advanced mathematical models of their time response and noise are needed. The random nature of adsorption–desorption and mass transfer (MT) processes that generate the sensor response makes the sensor output signal inherently stochastic and necessitates the use of a stochastic approach in sensor response analysis. We present a stochastic model of the sensor time response, which takes into account the coupling of adsorption–desorption and MT processes. It is used for the analysis of response kinetics and ultimate noise performance of protein biosensors. We show that slow MT not only decelerates the response kinetics, but also increases the noise and decreases the sensor’s maximal achievable signal-to-noise ratio, thus degrading the ultimate sensor performance, including the minimal detectable/quantifiable analyte concentration. The results illustrate the significance of the presented model for the correct interpretation of measurement data, for the estimation of sensors’ noise performance metrics important for reliable analyte detection/quantification, as well as for sensor optimization in terms of the lower detection/quantification limit. They are also incentives for the further investigation of the MT influence in nanoscale sensors, as a possible cause of false-negative results in analyte detection experiments.This article belongs to the Special Issue Microfluidics for Biosensing

Linearizability conditions for a cubic system

Abstract We obtain the necessary and sufficient conditions for linearizability of an eight-parameter family of two-dimensional system of differential equations in the form of linear canonical saddle perturbed by polynomials with four quadratic and four cubic terms

Composite bosons in bilayer nu = 1 system: An application of the Murthy-Shankar formalism

We calculate the dispersion of the out-of-phase mode characteristic for the bilayer nu = 1 quantum Hall system applying the version of Chern-Simons theory of Murthy and Shankar that cures the unwanted bare electron mass dependence in the low-energy description of quantum Hall systems. The obtained value for the mode when d, distance between the layers, is zero is in a good agreement with the existing pseudospin picture of the system. For d nonzero but small we find that the mode is linearly dispersing and its velocity to a good approximation depends linearly on d. This is in agreement with the Hartree-Fock calculations of the pseudospin picture that predicts a linear dependance on d, and contrary to the naive Hartree predictions with dependence on the square-root of d. We set up a formalism that enables one to consider fluctuations around the found stationary point values. In addition we address the case of imbalanced layers in the Murthy-Shankar formalism.Comment: 10 pages, 1 figur

Mean field theory of the Mott-Anderson transition

We present a theory for disordered interacting electrons that can describe both the Mott and the Anderson transition in the respective limits of zero disorder and zero interaction. We use it to investigate the T=0 Mott-Anderson transition at a fixed electron density, as a the disorder strength is increased. Surprisingly, we find two critical values of disorder W_{nfl} and W_c. For W > W_{nfl}, the system enters a ``Griffiths'' phase, displaying metallic non-Fermi liquid behavior. At even stronger disorder, W=W_c > W_{nfl} the system undergoes a metal insulator transition, characterized by the linear vanishing of both the typical density of states and the typical quasiparticle weight.Comment: 4 pages, 2 figures, REVTEX, eps

Spin-singlet hierarchy in the fractional quantum Hall effect

We show that the so-called permanent quantum Hall states are formed by the integer quantum Hall effects on the Haldane-Rezayi quantum Hall state. Novel conformal field theory description along with this picture is deduced. The odd denominator plateaux observed around $\nu=5/2$ are the permanent states if the $\nu=5/2$ plateau is the Haldane-Rezayi state. We point out that there is no such hierarchy on other candidate states for $\nu=5/2$. We propose experiments to test our prediction.Comment: RevTex,4 pages, v2:typo,one reference adde

Fractional quantum Hall state at \nu=1/4 in a wide quantum well

We investigate, with the help of Monte-Carlo and exact-diagonalization calculations in the spherical geometry, several compressible and incompressible candidate wave functions for the recently observed quantum Hall state at the filling factor $\nu=1/4$ in a wide quantum well. The quantum well is modeled as a two-component system by retaining its two lowest subbands. We make a direct connection with the phenomenological effective-bilayer model, which is commonly used in the description of a wide quantum well, and we compare our findings with the established results at $\nu=1/2$ in the lowest Landau level. At $\nu=1/4$, the overlap calculations for the Halperin (5,5,3) and (7,7,1) states, the generalized Haldane-Rezayi state and the Moore-Read Pfaffian, suggest that the incompressible state is likely to be realized in the interplay between the Halperin (5,5,3) state and the Moore-Read Pfaffian. Our numerics shows the latter to be very susceptible to changes in the interaction coefficients, thus indicating that the observed state is of multicomponent nature.Comment: 14 pages, 8 figures; minor changes, accepted for publication in Phys. Rev.

Edge Theories for Polarized Quantum Hall States

Starting from recently proposed bosonic mean field theories for fully and partially polarized quantum Hall states, we construct corresponding effective low energy theories for the edge modes. The requirements of gauge symmetry and invariance under global O(3) spin rotations, broken only by a Zeeman coupling, imply boundary conditions that allow for edge spin waves. In the generic case, these modes are chiral, and the spin stiffness differs from that in the bulk. For the case of a fully polarized $\nu=1$ state, our results agree with previous Hartree-Fock calculations.Comment: 15 pages (number of pages has been reduced by typesetting in RevTeX); 2 references adde

Quasi-Particle Tunneling in Anti-Pfaffian Quantum Hall State

We study tunneling phenomena at the edge of the anti-Pfaffian quantum Hall state at the filling factor $\nu=5/2$. The edge current in a single point-contact is considered. We focus on nonlinear behavior of two-terminal conductance with the increase in negative split-gate voltage. Expecting the appearance of the intermediate conductance plateau we calculate the value of its conductance by using the renormalization group (RG) analysis. Further, we show that non-perturbative quasi-particle tunneling is effectively described as perturbative electron tunneling by the instanton method. The two-terminals conductance is written as a function of the gate voltage. The obtained results enable us to distinguish the anti-Pfaffian state from the Pfaffian state experimentally.Comment: 5 pages, 4 figure

Bulk and edge correlations in the compressible half-filled quantum Hall state

We study bulk and edge correlations in the compressible half-filled state, using a modified version of the plasma analogy. The corresponding plasma has anomalously weak screening properties, and as a consequence we find that the correlations along the edge do not decay algebraically as in the Laughlin (incompressible) case, while the bulk correlations decay in the same way. The results suggest that due to the strong coupling between charged modes on the edge and the neutral Fermions in the bulk, reflected by the weak screening in the plasma analogue, the (attractive) correlation hole is not well defined on the edge. Hence, the system there can be modeled as a free Fermi gas of {\em electrons} (with an appropriate boundary condition). We finally comment on a possible scenario, in which the Laughlin-like dynamical edge correlations may nevertheless be realized.Comment: package now includes the file epsfig.sty, needed to incorporate properly the 8 magnificent figure