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Lund University Lund University Publications2000-01-01T00:00+00:001dailyFinite-size effects in the dynamics of few bosons in a ring potential
https://lup.lub.lu.se/search/publication/53a78e6a-d432-4787-912a-563af0a9fa91
Eriksson, G.Bengtsson, J.Karabulut, E.Kavoulakis, G. M.Reimann, S. M.2018-01-16We 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.http://lup.lub.lu.se/record/53a78e6a-d432-4787-912a-563af0a9fa91http://dx.doi.org/10.1088/1361-6455/aaa05cscopus:85040718989engJournal of Physics B: Atomic, Molecular and Optical Physics; 51(3), no 035504 (2018)ISSN: 0953-4075Atom- och molekylfysik och optikexact diagonalizationfew-body systemsquantum ringstime evolutionFinite-size effects in the dynamics of few bosons in a ring potentialcontributiontojournal/articleinfo:eu-repo/semantics/articletextOn the renormalization of contact interactions for the configuration-interaction method in two-dimensions
https://lup.lub.lu.se/search/publication/31934167-5122-40d2-aee1-438962e908fb
Rontani, MassimoEriksson, G.Åberg, S.Reimann, S. M.2017-03-07The configuration interaction (CI) method for calculating the exact eigenstates of a quantum-mechanical few-body system is problematic when applied to particles interacting through contact forces. In dimensions higher than one the approach fails due to the pathology of the Dirac δ-potential, making it impossible to reach convergence by gradually increasing the size of the Hilbert space. However, this problem may be cured in a rather simple manner by renormalizing the strength of the contact potential when diagonalizing in a truncated Hilbert space. One hereby relies on the comparison of the CI results to the two-body ground-state energy obtained by the exact solution of the Schrödinger equation for a regularized contact interaction. We discuss here a scheme that provides cutoff-independent few-body physical observables. The method is applied to a few-body system of ultracold atoms confined by a two-dimensional harmonic oscillator.http://lup.lub.lu.se/record/31934167-5122-40d2-aee1-438962e908fbhttp://dx.doi.org/10.1088/1361-6455/aa606ascopus:85015049270wos:000396176200001engJournal of Physics B: Atomic, Molecular and Optical Physics; 50(6), no 065301 (2017)ISSN: 0953-4075Atom- och molekylfysik och optikconfiguration interaction methoddegenerate Bose gasesdegenerate Fermi gasesexact diagonalizationFermi pseudopotentialfew-body physicstwo-dimensional harmonic trapOn the renormalization of contact interactions for the configuration-interaction method in two-dimensionscontributiontojournal/articleinfo:eu-repo/semantics/articletext