Dynamics of unitary operators

Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics

We consider pseudo-unitary quantum systems and discuss various properties of pseudounitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal blocks. Furthermore, we show that every pseudo-unitary matrix is the exponential of i = √ −1 times a pseudo-Hermitian matrix, and determine the structure of the L...

Generalized Unitary Operators

1. Let C be the complex field and T be the unit circle { \ £ C : | \ | = 1} . For a non-negative integer m or for m = oo, let OCT) be the space of all m-times continuously differentiable functions on T. (Here we consider T as a C°°-manifold in the natural way. Thus, any / £ C m ( r ) can be identified with an m-times continuously differentiable periodic function f (6) of a real variable 0 with ...

Unitary Operators Preserving Wavelets

We characterize a special class of unitary operators that preserve orthonormal wavelets. In the process we also prove that symmetric wavelet sets cover the real line.

Localization for Random Unitary Operators

We consider unitary analogs of 1−dimensional Anderson models on l2(Z) defined by the product Uω = DωS where S is a deterministic unitary and Dω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of Uω is pure point almost surely for all val...

Quadratic Forms in Unitary Operators