Boundary value problems for doubly perturbed first order ordinary differential systems

The aim of this paper is to present new results on existence theory for perturbed BVPs for first order ordinary differential systems. A nonlinear alternative for the sum of a contraction and a compact mapping is used

The boundary states and correlation functions of the tricritical Ising model from the Coulomb-gas formalism

We consider the minimal conformal model describing the tricritical Ising model on the disk and on the upper half plane. Using the coulomb-gas formalism we determine its consistents boundary states as well as its 1-point and 2-point correlation functions.Comment: 20 pages, no figure. Version 2:A paragraph for the calculation of the 2-point correlators was added. Some typos and garammatical errors were corrected.Version 3: Equations 24 are modified. Version 4 : new introduction and minor correction

Comments on the height reducing property II

A complex number αα is said to satisfy the height reducing property if there is a finite set F⊂ZF⊂Z such that Z[α]=F[α]Z[α]=F[α], where ZZ is the ring of the rational integers. It is easy to see that αα is an algebraic number when it satisfies the height reducing property. We prove the relation Card(F)≥max{2,|Mα(0)|}Card(F)≥max{2,|Mα(0)|}, where MαMα is the minimal polynomial of αα over the field of the rational numbers, and discuss the related optimal cases, for some classes of algebraic numbers αα. In addition, we show that there is an algorithm to determine the minimal height polynomial of a given algebraic number, provided it has no conjugate of modulus one

Wick's theorem for q-deformed boson operators

In this paper combinatorial aspects of normal ordering arbitrary words in the creation and annihilation operators of the q-deformed boson are discussed. In particular, it is shown how by introducing appropriate q-weights for the associated ``Feynman diagrams'' the normally ordered form of a general expression in the creation and annihilation operators can be written as a sum over all q-weighted Feynman diagrams, representing Wick's theorem in the present context.Comment: 9 page

Impact of quantum confinement on transport and the electrostatic driven performance of silicon nanowire transistors at the scaling limit

In this work we investigate the impact of quantum mechanical effects on the device performance of n-type silicon nanowire transistors (NWT) for possible future CMOS applications at the scaling limit. For the purpose of this paper, we created Si NWTs with two channel crystallographic orientations <110> and <100> and six different cross-section profiles. In the first part, we study the impact of quantum corrections on the gate capacitance and mobile charge in the channel. The mobile charge to gate capacitance ratio, which is an indicator of the intrinsic performance of the NWTs, is also investigated. The influence of the rotating of the NWTs cross-sectional geometry by 90o on charge distribution in the channel is also studied. We compare the correlation between the charge profile in the channel and cross-sectional dimension for circular transistor with four different cross-sections diameters: 5nm, 6nm, 7nm and 8nm. In the second part of this paper, we expand the computational study by including different gate lengths for some of the Si NWTs. As a result, we establish a correlation between the mobile charge distribution in the channel and the gate capacitance, drain-induced barrier lowering (DIBL) and the subthreshold slope (SS). All calculations are based on a quantum mechanical description of the mobile charge distribution in the channel. This description is based on the solution of the Schrödinger equation in NWT cross sections along the current path, which is mandatory for nanowires with such ultra-scale dimensions

Some recursive formulas for Selberg-type integrals

A set of recursive relations satisfied by Selberg-type integrals involving monomial symmetric polynomials are derived, generalizing previously known results. These formulas provide a well-defined algorithm for computing Selberg-Schur integrals whenever the Kostka numbers relating Schur functions and the corresponding monomial polynomials are explicitly known. We illustrate the usefulness of our results discussing some interesting examples.Comment: 11 pages. To appear in Jour. Phys.

Some families of density matrices for which separability is easily tested

We reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree condition") to test separability of density matrices of graphs. The condition is directly related to the PPT-criterion. We prove that the degree condition is necessary for separability and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest point graphs and perfect matchings. We observe that the degree condition appears to have value beyond density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. The paper isolates a number of problems and delineates further generalizations.Comment: 14 pages, 4 figure

Atoms-to-Circuits Simulation Investigation of CNT Interconnects for Next Generation CMOS Technology

In this study, we suggest a hierarchical model to investigate the electrical performance of carbon nanotube (CNT)- based interconnects. From the density functional theory, we have obtained important physical parameters, which are used in TCAD simulators to obtain the RC netlists. We then use these RC netlists for the circuit-level simulations to optimize interconnect design in VLSI. Also, we have compared various CNT-based interconnects such as single-walled CNTs, multi-walled CNTs, doped CNTs, and Cu-CNT composites in terms of conductivity, ring oscillator delay, and propagation time delay