Painlev\'e V and time dependent Jacobi polynomials

In this paper we study the simplest deformation on a sequence of orthogonal polynomials, namely, replacing the original (or reference) weight $w_0(x)$ defined on an interval by $w_0(x)e^{-tx}.$ It is a well-known fact that under such a deformation the recurrence coefficients denoted as $\alpha_n$ and $\beta_n$ evolve in $t$ according to the Toda equations, giving rise to the time dependent orthogonal polynomials, using Sogo's terminology. The resulting "time-dependent" Jacobi polynomials satisfy a linear second order ode. We will show that the coefficients of this ode are intimately related to a particular Painlev\'e V. In addition, we show that the coefficient of $z^{n-1}$ of the monic orthogonal polynomials associated with the "time-dependent" Jacobi weight, satisfies, up to a translation in $t,$ the Jimbo-Miwa $\sigma$-form of the same $P_{V};$ while a recurrence coefficient $\alpha_n(t),$ is up to a translation in $t$ and a linear fractional transformation $P_{V}(\alpha^2/2,-\beta^2/2, 2n+1+\alpha+\beta,-1/2).$ These results are found from combining a pair of non-linear difference equations and a pair of Toda equations. This will in turn allow us to show that a certain Fredholm determinant related to a class of Toeplitz plus Hankel operators has a connection to a Painlev\'e equation

On the variable capacity property of CC/DS-CDMA systems

A complete complementary code based direct sequence code division multiple access (CC/DS-CDMA) system has been proposed recently as a potential candidate for beyond third generation (B3G) wireless communications. This paper addresses the issues that design of efficient code assignment schemes should be based on a flexible physical layer support, which is extremely important for emerging cross-layer designs in future wireless applications. The study in this paper considers a CC/DS-CDMA system with multiple time slots, three traffic classes and two dynamic code-flock assignment schemes, namely random assignment (RA) and compact assignment (CA). Simulation results show that the CC/DS-CDMA system has variable capacity property (VCP), which is sensitively affected by different code-flock assignment schemes. In general, CA can offer lower blocking probability, whereas RA can offer a larger mean system capacity and higher throughput when offered traffic is heavy

Fast quantum information transfer with superconducting flux qubits coupled to a cavity

We present a way to realize quantum information transfer with superconducting flux qubits coupled to a cavity. Because only resonant qubit-cavity interaction and resonant qubit-pulse interaction are applied, the information transfer can be performed much faster, when compared with the previous proposals. This proposal does not require adjustment of the qubit level spacings during the operation. Moreover, neither uniformity in the device parameters nor exact placement of qubits in the cavity is needed by this proposal.Comment: 6 pages, 3 figure