SUSY transformation of the Green function and a trace formula

An integral relation is established between the Green functions corresponding to two Hamiltonians which are supersymmetric (SUSY) partners and in general may possess both discrete and continuous spectra. It is shown that when the continuous spectrum is present the trace of the difference of the Green functions for SUSY partners is a finite quantity which may or may not be equal to zero despite the divergence of the traces of each Green function. Our findings are illustrated by using the free particle example considered both on the whole real line and on a half line

Connection between the Green functions of the supersymmetric pair of Dirac Hamiltonians

The Sukumar theorem about the connection between the Green functions of the supersymmetric pair of the Schr\"odinger Hamiltonians is generalized to the case of the supersymmetric pair of the Dirac Hamiltonians.Comment: 12 pages,Latex, no figure

Second Order Darboux Displacements

The potentials for a one dimensional Schroedinger equation that are displaced along the x axis under second order Darboux transformations, called 2-SUSY invariant, are characterized in terms of a differential-difference equation. The solutions of the Schroedinger equation with such potentials are given analytically for any value of the energy. The method is illustrated by a two-soliton potential. It is proven that a particular case of the periodic Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the corresponding Schroedinger equation equation are found for any value of the energy. A simple analytic expression for a family of two-gap potentials is derived

PT-symmetric square well and the associated SUSY hierarchies

The PT-symmetric square well problem is considered in a SUSY framework. When the coupling strength $Z$ lies below the critical value $Z_0^{\rm (crit)}$ where PT symmetry becomes spontaneously broken, we find a hierarchy of SUSY partner potentials, depicting an unbroken SUSY situation and reducing to the family of $\sec^2$-like potentials in the $Z \to 0$ limit. For $Z$ above $Z_0^{\rm (crit)}$, there is a rich diversity of SUSY hierarchies, including some with PT-symmetry breaking and some with partial PT-symmetry restoration.Comment: LaTeX, 18 pages, no figure; broken PT-symmetry case added (Sec. 6

A New Modified MPPT Controller for Indirect Vector Controlled Induction Motor Drive with Variable Irradiance and Variable Temperature

Due to the increase in power demand and the earth natural resources are depleting day by day, renewable energy sources have become an important alternate and solar energy is mainly used. In order to track the radiations from the sun in an efficient manner the maximum power point tracking (MPPT) controller is used. But the existed MPPT controllers were developed based upon the ideal characteristics of constant irradiation and temperature. To overcome the above problem a practical data is considered for designing of MPPT controller which is based upon variable irradiance under various temperatures. The output obtained from the MPPT is given to the boost converter with an inverter to find the performance of an indirect vector controlled induction motor drive under different operating conditions. For inverter control, a SVM algorithm in which the calculation of switching times proportional to the instantaneous values of the reference phase voltage. It eliminates the calculation of sector and angle information. The torque ripple and the performance of induction motor drive with ideal and practical data MPPT controllers are compared under different operating conditions. An experimental validation is carried out and the comparison is made with the simulation results. Keywords: maximum power point tracking, variable irradiance, indirect vector controlled, total harmonic distortions, space vector modulation, induction motor drive and torque ripple

QoS Routing Protocols and Privacy in Wireless Sensor Networks

Full network level privacy has often been categorized into four sub-categories: Identity, Route, Location and Data privacy. Achieving full network level privacy is a challenging problem due to the conditions imposed by the sensor nodes (e.g., energy, memory and computation power), sensor networks (e.g., mobility and topology) and QoS issues (e.g., packet reach-ability and timeliness). This proposed paper consists of two algorithms IRL algorithm and data privacy mechanism that addresses this problem. The proposed system provides additional trustworthiness, less computation power, less storage space and more reliability. Also, we proved that our proposed solutions provide protection against various privacy disclosure attacks, such as eavesdropping and hop-by-hop trace back attacks

Toward a Spin- and Parity-Independent Nucleon-Nucleon Potential

A supersymmetric inversion method is applied to the singlet $^1S_0$ and $^1P_1$ neutron-proton elastic phase shifts. The resulting central potential has a one-pion-exchange (OPE) long-range behavior and a parity-independent short-range part; it fits inverted data well. Adding a regularized OPE tensor term also allows the reproduction of the triplet $^3P_0$, $^3P_1$ and $^3S_1$ phase shifts as well as of the deuteron binding energy. The potential is thus also spin-independent (except for the OPE part) and contains no spin-orbit term. These important simplifications of the neutron-proton interaction are shown to be possible only if the potential possesses Pauli forbidden bound states, as proposed in the Moscow nucleon-nucleon model.Comment: 9 pages, RevTeX, 5 ps figure

The Trigonometric Rosen-Morse Potential in the Supersymmetric Quantum Mechanics and its Exact Solutions

The analytic solutions of the one-dimensional Schroedinger equation for the trigonometric Rosen-Morse potential reported in the literature rely upon the Jacobi polynomials with complex indices and complex arguments. We first draw attention to the fact that the complex Jacobi polynomials have non-trivial orthogonality properties which make them uncomfortable for physics applications. Instead we here solve above equation in terms of real orthogonal polynomials. The new solutions are used in the construction of the quantum-mechanic superpotential.Comment: 16 pages 7 figures 1 tabl