Asymptotic Analysis - Volume 17, issue 4

Authors: Ichinose, Takashi | Tamura, Hideo

Article Type: Research Article

Abstract: We study the error bound in the trace norm for the Trotter–Kato exponential product formula of Schrödinger semigroups with a certain class of singular potentials. The error bound heavily depends on the growth and smoothness properties of potentials. As an application, we can also obtain the error estimate in calculating an approximate value of partition function, which is one of the most important quantities in quantum statistical mechanics, by use of the exponential product formula.

Citation: Asymptotic Analysis, vol. 17, no. 4, pp. 239-266, 1998

Authors: Almog, Y.

Article Type: Research Article

Abstract: It is well known that, when the Ginzburg–Landau parameter \kappa=1/\sqrt{2} , the second‐order Ginzburg–Landau equations may be reduced to the first‐order Bogomolnyi equations. It is established in this critical case that, for any given set of vortex locations and orders, these equations possess a unique solution which tends to the purely superconducting state at infinity. In the present contribution we focus on cases in which normal state conditions at infinity are imposed. It is found that, for any given set of vortex locations and orders, an infinite number of solutions satisfying such conditions at infinity exist.

Citation: Asymptotic Analysis, vol. 17, no. 4, pp. 267-278, 1998

Authors: Génieys, S.

Article Type: Research Article

Abstract: This paper is concerned with the derivation of an energy‐transport model from the Boltzmann equation for a nondegenerate semiconductor with a parabolic band structure. Electron–electron collisions and elastic collisions (i.e., impurity scattering and the “elastic part” of phonon collisions) are retained as leading order terms. Then, a Hilbert expansion leads to an energy‐transport model, and a Chapman–Enskog expansion leads to the same energy‐transport model if the electric field vanishes. For the case of the Boltzmann equation linearized about a global equilibrium, the convergence of the Hilbert expansion is shown when the electric field vanishes.

Citation: Asymptotic Analysis, vol. 17, no. 4, pp. 279-308, 1998

Authors: Zhang, Changgui

Article Type: Research Article

Abstract: On décrit la croissance des coefficients des séries entières solutions formelles d’une équation holomorphe mélangeant opérateurs différentiels et opérateurs aux q ‐différences. Suivant une idée de Malgrange (Asympt. Anal. 2 (1989), 1–4), nous établissons une version généralisée du théorème de Maillet–Malgrange à l’aide du théorème des fonctions implicites. Abstract. The growth of the coefficients of a formal power series satisfying a holomorphic q ‐difference differential equation is described, where differential and q ‐difference operators are mixed. Following an idea of Malgrange (Asympt. Anal. 2 (1989), 1–4) and using implicit function theorem, a generalization of …the Maillet–Malgrange theorem is established. Show more

Citation: Asymptotic Analysis, vol. 17, no. 4, pp. 309-314, 1998