Horia D. Cornean

A rigorous proof of the Landauer–Büttiker formula

Recently, Avron et al. in a series of papers shed new light on the question of quantum transport in mesoscopic samples coupled to particle reservoirs by semi-infinite leads. They rigorously treat the case, when the sample undergoes an adiabatic evolution thus generating a current through the leads, and prove the so-called BPT formula. Using a discrete model, we complement their work by giving a rigorous proof of the Landauer–Buttiker formula, which deals with the current generated by an adiabatic evolution on the leads. As is well known from physics, both of these formulas link the conductance coefficients for such systems to the S-matrix of the associated scattering problem. As an application, we discuss resonant transport through a quantum dot. The single charge tunneling processes are mediated by extended edge states, simultaneously localized near several leads.

Performance Evaluation of AODV, DSDV & DSR for Quasi Random Deployment of Sensor Nodes in Wireless Sensor Networks

Sensor deployment is one of the key topics addressed in Wireless Sensor Network (WSN). This paper proposes a new deployment technique of sensor nodes for WSN called as Quasi Random Deployment (QRD). The novel approach to deploy sensor nodes in QRD fashion is to improve the energy efficiency of the WSN in order to increase the network life time and coverage. The QRD produces highly uniform coordinates and it systematically fills the specified area. Along with Random Deployment (RD) pattern of wireless sensor node QRD is analysed in this study. The network is simulated using NS-2 simulator. The efficiency of this deployment is evaluated assuming three routing protocols used for the adhoc networks. They are AODV, DSDV, and DSR. The protocol assumed at transport layer is UDP. Application layer generates the CBR traffic. The performance of these three routing techniques is compared based on total energy consumption, coverage area. The simulation results show that the conventional routing protocols like DSR have a best performance for both RD and QRD of the sensor nodes when there is no mobility of the sensor nodes as compared to AODV and DSDV. Among AODV and DSDV, AODV performs better as compared to DSDV.

The Faraday effect revisited: Thermodynamic limit

Abstract This paper is the second in a series revisiting the (effect of) Faraday rotation. We formulate and prove the thermodynamic limit for the transverse electric conductivity of Bloch electrons, as well as for the Verdet constant. The main mathematical tool is a regularized magnetic and geometric perturbation theory combined with elliptic regularity and Agmon–Combes–Thomas uniform exponential decay estimates.

Locating the spectrum for magnetic Schrödinger and Dirac operators

ABSTRACT Some spectral properties of magnetic Schrödinger and Dirac operators perturbed by long range magnetic fields are investigated. If the intensity of the field is small enough, a better location of the perturbed spectrum is given. In particular, if the unperturbed spectrum is discrete, we show that the perturbed eigenvalues are given in terms of an absolutely convergent series with respect to a magnetic parameter, from which the usual asymptotic expansion can be derived.

Correlation and dimensional effects of trions in carbon nanotubes

We study the binding energies of singlet trions, i.e. charged excitons, in carbon nanotubes. The problem is modeled, through the effective-mass model, as a three-particle complex on the surface of a cylinder, which we investigate using both one- and two-dimensional expansions of the wave function. The effects of dimensionality and correlation are studied in detail. We find that the Hartree-Fock approximation significantly underestimates the trion binding energy. Combined with band structures calculated using a non-orthogonal nearest neighbour tight binding model, the results from the cylinder model are used to compute physical binding energies for a wide selection of carbon nanotubes. In addition, the dependence on dielectric screening is examined. Our findings indicate that trions are detectable at room temperature in carbon nanotubes with radius below 8{\AA}.

Towards a d-bar reconstruction method for three-dimensional EIT

Three-dimensional electrical impedance tomography (EIT) is considered. Both uniqueness proofs and theoretical reconstruction algorithms available for this problem rely on the use of exponentially growing solutions to the governing conductivity equation. The study of those solutions is continued here. It is shown that exponentially growing solutions exist for low complex frequencies without imposing any regularity assumption on the conductivity. Further, a reconstruction method for conductivities close to a constant is given. In this method the complex frequency is taken to zero instead of infinity. Since this approach involves only moderately oscillatory boundary data, it enables a new class of three-dimensional EIT algorithms, free from the usual high frequency instabilities.

Adiabatically switched-on electrical bias and the Landauer-Buttiker formula

Consider a three dimensional system which looks like a cross connected pipe system, i.e., a small sample coupled to a finite number of leads. We investigate the current running through this system, in the linear response regime, when we adiabatically turn on an electrical bias between leads. The main technical tool is the use of a finite volume regularization, which allows us to define the current coming out of a lead as the time derivative of its charge. We finally prove that in virtually all physically interesting situations, the conductivity tensor is given by a Landauer–Buttiker type formula.

ON THE INFIMUM OF THE ENERGY-MOMENTUM SPECTRUM OF A HOMOGENEOUS BOSE GAS

We consider second-quantized homogeneous Bose gas in a large cubic box with periodic boundary conditions at zero temperature. We discuss the energy-momentum spectrum of the Bose gas and its physical significance. We review various rigorous and heuristic results as well as open conjectures about its properties. Our main aim is to convince the readers, including those with mainly mathematical background, that this subject has many interesting problems for rigorous research. In particular, we investigate the upper bound on the infimum of the energy for a fixed total momentum k given by the expectation value of one-particle excitations over a squeezed states. This bound can be viewed as a rigorous version of the famous Bogoliubov method. We show that this approach seems to lead to a (nonphysical) energy gap. The variational problem involving squeezed states can serve as the preparatory step in a perturbative approach that should be useful in computing excitation spectrum. This version of a perturbative approa...

On the Construction of Composite Wannier Functions

We give a constructive proof for the existence of a Bloch basis of rank