Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schrödinger Operators in One Dimension
نویسندگان
چکیده
V. KOSTRYKIN AND R. SCHRADER ABSTRACT. In this article we prove an upper bound for the Lyapunov exponent (E) and a two-sided bound for the integrated density of states N(E) at an arbitrary energy E > 0 of random Schrödinger operators in one dimension. These Schrödinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both (E) and N(E) pE= decay at infinity at least like 1=pE. As an example we consider the random Kronig-Penney model.
منابع مشابه
Studying Transition Behavior of Neutron Point Kinetics Equations Using the Lyapunov Exponent Method
The neutron density is one of the most important dynamical parameters in a reactor. It is directly related to the control and stability of the reactor power. Any change in applied reactivity and some of dynamical parameters in the reactor causes a change in the neutron density. Lyapunov exponent method is a powerful tool for investigating the range of stability and the transient behavior of the...
متن کاملA survey of rigorous results on random Schrödinger operators for amorphous solids
Electronic properties of amorphous or non-crystalline disordered solids are often modelled by one-particle Schrödinger operators with random potentials, which are ergodic with respect to Euclidean translations. We give a short, reasonably self-contained survey of rigorous results on such operators, where we allow for the presence of a constant magnetic field. We first compile robust properties ...
متن کاملThe Integrated Density of States and its Absolute Continuity for Magnetic Schrödinger Operators with Unbounded Random Potentials
The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schrödinger operator with magnetic field and unbounded random potential. In case of a constant magnetic field and an ergodic random potential, we prove the existence of the integrated density of states as the infinite-volume limit of suitable...
متن کاملThe Absolute Continuity of the Integrated Density of States for Magnetic Schrödinger Operators with Certain Unbounded Random Potentials
The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schrödinger operator with magnetic field and a random potential which may be unbounded from above and below. In case that the magnetic field is constant and the random potential is ergodic and admits a so-called one-parameter decomposition, w...
متن کاملar X iv : m at h - ph / 0 01 10 32 v 1 1 8 N ov 2 00 0 Scattering Theory Approach to Random Schrödinger Operators in One Dimension
Methods from scattering theory are introduced to analyze random Schrödinger operators in one dimension by applying a volume cutoff to the potential. The key ingredient is the Lifshitz-Krein spectral shift function, which is related to the scattering phase by the theorem of Birman and Krein. The spectral shift density is defined as the " thermodynamic limit " of the spectral shift function per u...
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 2000