Stochasticity of orbits in non linear dynamical systems with recurrent scattering

Doctoral Dissertation uoadl:1309108 386 Read counter

Τομέας Αστροφυσικής, Αστρονομίας και Μηχανικής
Library of the School of Science
Deposit date:
Δελής Νικόλαος
Dissertation committee:
Μουσάς Ξενοφώντας Καθηγητής ΕΚΠΑ (επιβλέπων), Ευθυμιόπουλος Χρήστος Ερευνητής Α' Ακαδημία Αθηνών, Φραντζεσκάκης Δημήτριος Καθηγητής ΕΚΠΑ
Original Title:
Μελέτη της στοχαστικότητας τροχιών μη γραμμικών δυναμικών συστημάτων - Συστήματα με επαναλαμβανόμενες σκεδάσεις
Translated title:
Stochasticity of orbits in non linear dynamical systems with recurrent scattering
In this PhD thesis we studied the effects of the phenomenon of scattering in
two different classes of dynamical systems. The first part refers to the
scattering of stars on a supermassive black hole in the center of an elliptical
or barred spiral galaxy. The presence of a supermassive black hole at the
center of a galaxy causes a series of phenomena that have been studied
extensively. In this research we investigated the relation between the black
hole’s mass parameter and the chaotic indices of the orbits scattered by the
black hole. Our main result is the dependence of the mean Lyapunov
characteristic number L of chaotic orbits on the parameter of the black hole’
s mass m with a power law of the form L mp, with p0.5. In the second part
we examined the effects of scattering of trajectories from quantum vortices.
Quantum vortices were studied in the framework of the orbital theory of de
Broglie-Bohm. Initially we examined how the scattering by quantum vortices
generates chaos in the quantum system of two harmonic oscillators and the
corre- sponding Hιnon-Heiles system. Furthermore we demonstrated that this kind
of scattering is related with the phenomenon of quantum relaxation. Finally,
we studied the role of quantum vortices in the case of the interaction of a
beam of charged particles with a thin metal target. In this case, scattering
by quantum vortices explains many of the observed phenomena, like the
appearance of a diffraction pattern. Also, it allows to make predictions
related to time measurements in quantum processes .
Scattering, Galaxies, Black Holes, Quantum Vortices, Chaos
Number of index pages:
Contains images:
Number of references:
Number of pages:
[8], 172
document.pdf (8 MB) Open in new window