4 papers
A detailed proof of the von Neumann's Quantum Ergodic Theorem
Artur O. Lopes, Marcos Sebastiani
We present a simplified proof of the von Neumann's Quantum Ergodic Theorem. This important result was initially published in german by J. von Neumann in 1929. We are interested her…
Generic properties for random repeated quantum iterations
Artur O. Lopes, M. Sebastiani
We denote by the set of by complex matrices. Given a fixed density matrix and a fixed unitary operator $U : \mathbb{C}^n \otimes \ma…
On Bertelson-Gromov Dynamical Morse Entropy
Artur O. Lopes, Marcos Sebastiani
In this mainly expository paper we present a detailed proof of several results contained in a paper by M. Bertelson and M. Gromov on Dynamical Morse Entropy. This is an introductio…
Poncelet pairs and the Twist Map associated to the Poncelet Billiard
Artur O. Lopes, M. Sebastiani
We show that for a fixed curve and for a family of variables curves , the number of -Poncelet pairs is , where is the number of natural numbers $m…