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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
; ; ; and
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
article number
035504
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
2023-09-21 20:55:25
@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>}},
  author       = {{Eriksson, G. and Bengtsson, J. and Karabulut, E. and Kavoulakis, G. M. and Reimann, S. M.}},
  issn         = {{0953-4075}},
  keywords     = {{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}},
  doi          = {{10.1088/1361-6455/aaa05c}},
  volume       = {{51}},
  year         = {{2018}},
}