On Non - Linear Schrödinger Equation with Magnetic Field
نویسنده
چکیده
We study the non-linear Schödinger equation with time depending magnetic field without smallness assumption at infinity. We obtain some results on the Cauchy problem, WKB asymptotics and instability.
منابع مشابه
Strichartz Estimates for the Magnetic Schrödinger Equation
We prove global, scale invariant Strichartz estimates for the linear magnetic Schrödinger equation with small time dependent magnetic field. This is done by constructing an appropriate parametrix. As an application, we show a global regularity type result for Schrödinger maps in dimensions n ≥ 6.
متن کاملLinear Response Theory for Magnetic Schrödinger Operators in Disordered Media
We justify the linear response theory for an ergodic Schrödinger operator with magnetic field within the non-interacting particle approximation, and derive a Kubo formula for the electric conductivity tensor. To achieve that, we construct suitable normed spaces of measurable covariant operators where the Liouville equation can be solved uniquely. If the Fermi level falls into a region of locali...
متن کاملSignificant Error Propagation in the Finite Difference Solution of Non-Linear Magnetostatic Problems Utilizing Boundary Condition of the Third Kind
This paper poses two magnetostatic problems in cylindrical coordinates with different permeabilities for each region. In the first problem the boundary condition of the second kind is used while in the second one, the boundary condition of the third kind is utilized. These problems are solved using the finite element and finite difference methods. In second problem, the results of the finite di...
متن کاملMulti objective optimization of the vibration analysis of composite natural gas pipelines in nonlinear thermal and humidity environment under non-uniform magnetic field
The fluid-conveying pipe is a fundamental dynamical problem in the field of fluid– structure interactions. In recent years considerable attention has been given to the lateral vibrations of pipes containing by a moving fluid. In this paper, the vibration analysis of composite natural gas pipeline in the thermal and humidity environment is studied. The effect of the non-uniform magnetic field is...
متن کاملWhen the classical & quantum mechanical considerations hint to a single point; a microscopic particle in a one dimensional box with two infinite walls and a linear potential inside it
In this paper we have solved analytically the Schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. Based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007