Poster (Scientific congresses and symposiums)
Chaotic Bohmian trajectories for the hydrogen atom
Cesa, Alexandre; Struyve, Ward; Martin, John
2015Annual Scientific Meeting of the Belgian Physical Society 2015
 

Files


Full Text
posterfinal.pdf
Publisher postprint (9.04 MB)
Download

All documents in ORBi are protected by a user license.

Send to



Details



Keywords :
Bohmian mechanics; de Broglie-Bohm theory; chaos
Abstract :
[en] In Bohmian mechanics, a single-particle quantum system is described in part by its wave function and in part by the actual position of the particle. The trajectory of the latter can be computed using the guiding equation. This equation states that the velocity of the particle is proportional to the usual probability current associated with its wave function. In this work, we study the quantum trajectory of a single particle in a Coulomb potential whose eigenstates are the well known eigenstates of the hydrogen atom. More precisely, we focus on the relation between chaotic Bohmian trajectories and the motion of wave function nodes. At wave function nodes i.e., where the wave function vanishes, the velocity is not defined which generically induces vorticity. In order to probe chaos, we compute Poincaré map and we numerically evaluate Lyapounov exponents, which characterize the divergence of close trajectories as time increases. For the 2d Coulomb potential, although the superposition of two eigenstates with different energies can lead to an arbitrary high number of moving nodes of the wave function, the Bohmian trajectories display no trace of chaos. This absence of chaotic behaviour originates from the existence of a constant of motion. Therefore, the motion and the number of nodes do not constitute a sufficient condition for the emergence of chaos in Bohmian mechanics. For superpositions of more than two eigenstates, there is no constant of motion, there are moving nodes and we find that the Bohmian trajectories are chaotic.
Disciplines :
Physics
Author, co-author :
Cesa, Alexandre ;  Université de Liège > Département de physique > Optique quantique
Struyve, Ward ;  Université de Liège > Département de physique > Spectroscopie atomique et Physique des atomes froids
Martin, John  ;  Université de Liège > Département de physique > Optique quantique
Language :
English
Title :
Chaotic Bohmian trajectories for the hydrogen atom
Publication date :
13 May 2015
Number of pages :
A0
Event name :
Annual Scientific Meeting of the Belgian Physical Society 2015
Event organizer :
Belgian Physical Society
Event place :
Liège, Belgium
Event date :
13 mai 2015
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif
Funders :
CÉCI - Consortium des Équipements de Calcul Intensif [BE]
Available on ORBi :
since 18 May 2015

Statistics


Number of views
167 (14 by ULiège)
Number of downloads
132 (7 by ULiège)

Bibliography


Similar publications



Contact ORBi