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Finite-size effects in the dynamics of few bosons in a ring potential

Eriksson, G. LU ; Bengtsson, J. LU ; Karabulut, E. LU ; Kavoulakis, G. M. LU and Reimann, S. M. LU (2018) In Journal of Physics B: Atomic, Molecular and Optical Physics 51(3).
Abstract

We study the temporal evolution of a small number N of ultra-cold bosonic atoms confined in a ring potential. Assuming that initially the system is in a solitary-wave solution of the corresponding mean-field problem, we identify significant differences in the time evolution of the density distribution of the atoms when it instead is evaluated with the many-body Schrödinger equation. Three characteristic timescales are derived: the first is the period of rotation of the wave around the ring, the second is associated with a 'decay' of the density variation, and the third is associated with periodic 'collapses' and 'revivals' of the density variations, with a factor of separating each of them. The last two timescales tend to infinity in... (More)

We study the temporal evolution of a small number N of ultra-cold bosonic atoms confined in a ring potential. Assuming that initially the system is in a solitary-wave solution of the corresponding mean-field problem, we identify significant differences in the time evolution of the density distribution of the atoms when it instead is evaluated with the many-body Schrödinger equation. Three characteristic timescales are derived: the first is the period of rotation of the wave around the ring, the second is associated with a 'decay' of the density variation, and the third is associated with periodic 'collapses' and 'revivals' of the density variations, with a factor of separating each of them. The last two timescales tend to infinity in the appropriate limit of large N, in agreement with the mean-field approximation. These findings are based on the assumption of the initial state being a mean-field state. We confirm this behavior by comparison to the exact solutions for a few-body system stirred by an external potential. We find that the exact solutions of the driven system exhibit similar dynamical features.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
exact diagonalization, few-body systems, quantum rings, time evolution
in
Journal of Physics B: Atomic, Molecular and Optical Physics
volume
51
issue
3
publisher
IOP Publishing
external identifiers
  • scopus:85040718989
ISSN
0953-4075
DOI
10.1088/1361-6455/aaa05c
language
English
LU publication?
yes
id
53a78e6a-d432-4787-912a-563af0a9fa91
date added to LUP
2018-01-30 11:56:15
date last changed
2018-01-30 11:56:15
@article{53a78e6a-d432-4787-912a-563af0a9fa91,
  abstract     = {<p>We study the temporal evolution of a small number N of ultra-cold bosonic atoms confined in a ring potential. Assuming that initially the system is in a solitary-wave solution of the corresponding mean-field problem, we identify significant differences in the time evolution of the density distribution of the atoms when it instead is evaluated with the many-body Schrödinger equation. Three characteristic timescales are derived: the first is the period of rotation of the wave around the ring, the second is associated with a 'decay' of the density variation, and the third is associated with periodic 'collapses' and 'revivals' of the density variations, with a factor of separating each of them. The last two timescales tend to infinity in the appropriate limit of large N, in agreement with the mean-field approximation. These findings are based on the assumption of the initial state being a mean-field state. We confirm this behavior by comparison to the exact solutions for a few-body system stirred by an external potential. We find that the exact solutions of the driven system exhibit similar dynamical features.</p>},
  articleno    = {035504},
  author       = {Eriksson, G. and Bengtsson, J. and Karabulut, E. and Kavoulakis, G. M. and Reimann, S. M.},
  issn         = {0953-4075},
  keyword      = {exact diagonalization,few-body systems,quantum rings,time evolution},
  language     = {eng},
  month        = {01},
  number       = {3},
  publisher    = {IOP Publishing},
  series       = {Journal of Physics B: Atomic, Molecular and Optical Physics},
  title        = {Finite-size effects in the dynamics of few bosons in a ring potential},
  url          = {http://dx.doi.org/10.1088/1361-6455/aaa05c},
  volume       = {51},
  year         = {2018},
}