Estimates of the fundamental solution for magnetic Schrödinger operators and their applications

Edge currents and eigenvalue estimates for magnetic barrier Schrödinger operators

We study two-dimensional magnetic Schrödinger operators with a magnetic field that is equal to b > 0 for x > 0 and −b for x < 0. This magnetic Schrödinger operator exhibits a magnetic barrier at x = 0. The unperturbed system is invariant with respect to translations in the ydirection. As a result, the Schrödinger operator admits a direct integral decomposition. We analyze the band functions of ...

semi-analytical solution for static and forced vibration problems of laminated beams through smooth fundamental functions method

در این پایان نامه روش جدیدی مبتنی بر روش حل معادلات دیفرانسیل پارهای بر اساس روش توابع پایه برای حل مسایل ارتعاش اجباری واستاتیک تیرها و صفحات لایه ای ارایه شده است که می توان تفاوت این روش با روش های متداول توابع پایه را در استفاده از توابع هموار در ارضاء معادلات حاکم و شرایط مرزی دانست. در روش ارایه شده در این پایاننامه از معادله تعادل به عنوان معادله حاکم بر رفتار سیستم استفاده شده است که مو...

Ü Estimates for Time - Dependent Schrödinger Operators

It is well known that the local decay estimates (2) are useful in studying nonlinear Schrödinger equations (see [8, §XI.13], [11]). On the other hand little seems to be known when one replaces the free operator HQ by more general Hamiltonians (4) H = -A + V(x), even when the potential V is in C^°(R). Obviously, one has to assume that H has no bound states for an estimate like (2) to it M hold f...

Uniform Estimates of the Fundamental Solution for a Family of Hypoelliptic Operators

In this paper we are concerned with a family of elliptic operators represented as sum of square vector fields: L = ∑m i=1X 2 i + ∆, in Rn where ∆ is the Laplace operator, m < n, and the limit operator L = ∑m i=1X 2 i is hypoelliptic. It is well known that L admits a fundamental solution Γ . Here we establish some a priori estimates uniform in of it, using a modification of the lifting technique...

Locating the Spectrum for Magnetic Dirac and Schrödinger Operators