Jacobi algorithm for symmetric eigenvalue problem and integrable gradient system of Lax form

Abstract

An intimate connection between matrix eigenvMue algorithms and integrable dynamical systems is studied. It is proved that an infinitesimal rotation of each step of the Jacobi algorithm for symmetric eigenwlue problem is an integrable gradient system of Lax form.

Effect of non-drifting hot phonons on high-field drift velocity in GaN/AlGaN

“…The choice of phase-matched mode in these assumptions is a natural one since it is the pivot about which electron-phonon interaction turns according to the necessity for conserving energy and crystal momentum. (6) The electrons are confined to the lowest subband in a deep double heterojunction triangular well. (7) Interface phonon spectrum is used in the calculations and the interaction between electrons and phonons confined to the same triangular well is considered.…”

“…Over the last decade, there has been growing interest in GaNbased structures owing to the large band gap and favourable material properties of GaN. They are ideal structures for high-power FETs operating at high temperatures [1][2][3][4][5], LEDs and lasers for applications in displays and high-density data storage, respectively [6]. In order to analyse and improve the design of functional devices based on these materials, a thorough understanding of electron transport, particularly at high fields, is necessary.…”

A new approach to numerical algorithms in terms of integrable systems

“…Note that ij (∞) = ji (∞) = 0 at the stable equilibrium L(∞) for the fixed i and j. It was shown in [29] that if ii (0) = jj (0), then the stable equilibrium L(∞) is uniquely given by the similarity transformation…”

“…A generalization of the double bracket equation was discussed in [29]. The resulting gradient system for an objec- …”