Usporedba SKWB i WKB aproksimacija za konačnu pravokutnu jamu

Both the WKB and the supersymmetric WKB (SWKB) approximations have been applied to the finite square-well potential and compared with the corresponding exact results. Even though this potential is not shape-invariant, an analytic expression for the superpotential is possible and it is seen that the SWKB is better than the WKB for almost all states.Razmatraju se Wentzel-Kramers-Brillouin (WKB) i suprasimetrična WKB (SWKB) aproksimacija za pravokutnu jamu konačne dubine, te uspoređuju s rezultatima točnih računa. Iako promatrani potencijal nije invarijantan po obliku, moguće je analitičko rješenje za suprapotencijal te se nalazi da su rješenja SWKB točnija nego rješenja WKB

Usporedba SKWB i WKB aproksimacija za konačnu pravokutnu jamu

Both the WKB and the supersymmetric WKB (SWKB) approximations have been applied to the finite square-well potential and compared with the corresponding exact results. Even though this potential is not shape-invariant, an analytic expression for the superpotential is possible and it is seen that the SWKB is better than the WKB for almost all states.Razmatraju se Wentzel-Kramers-Brillouin (WKB) i suprasimetrična WKB (SWKB) aproksimacija za pravokutnu jamu konačne dubine, te uspoređuju s rezultatima točnih računa. Iako promatrani potencijal nije invarijantan po obliku, moguće je analitičko rješenje za suprapotencijal te se nalazi da su rješenja SWKB točnija nego rješenja WKB

Macroscopic quantum many-body tunneling of attractive Bose-Einstein condensate in anharmonic trap

We study the stability of attractive atomic Bose-Einstein condensate and the macroscopic quantum many-body tunneling (MQT) in the anharmonic trap. We utilize correlated two-body basis function which keeps all possible two-body correlations. The anharmonic parameter ($\lambda$) is slowly tuned from harmonic to anharmonic. For each choice of $\lambda$ the many-body equation is solved adiabatically. The use of the van der Waals interaction gives realistic picture which substantially differs from the mean-field results. For weak anharmonicity, we observe that the attractive condensate gains stability with larger number of bosons compared to that in the pure harmonic trap. The transition from resonances to bound states with weak anharmonicity also differs significantly from the earlier study of Moiseyev {\it et.al.}[J. Phys. B: At. Mol. Opt. Phys. {\bf{37}}, L193 (2004)]. We also study the tunneling of the metastable condensate very close to the critical number $N_{cr}$ of collapse and observe that near collapse the MQT is the dominant decay mechanism compared to the two-body and three-body loss rate. We also observe the power law behavior in MQT near the critical point. The results for pure harmonic trap are in agreement with mean-field results. However we fail to retrieve the power law behavior in anharmonic trap although MQT is still the dominant decay mechanism.Comment: Accepted in Eur. Phys. J. D (2013

Pair-correlation properties and momentum distribution of finite number of interacting trapped bosons in three dimension

We study the ground state pair-correlation properties of a weakly interacting trapped Bose gas in three dimension by using a correlated many-body method. Use of the van der Waals interaction potential and an external trapping potential shows realistic features. We also test the validity of shape-independent approximation in the calculation of correlation properties.Comment: Accepted for publication in The Journal of Chemical Physic

Stability of attractive bosonic cloud with van der Waals interaction

We investigate the structure and stability of Bose-Einstein condensate of $^{7}$Li atoms with realistic van der Waals interaction by using the potential harmonic expansion method. Besides the known low-density metastable solution with contact delta function interaction, we find a stable branch at a higher density which corresponds to the formation of an atomic cluster. Comparison with the results of non-local effective interaction is also presented. We analyze the effect of trap size on the transition between the two branches of solutions. We also compute the loss rate of a Bose condensate due to two- and three-body collisions.Comment: 9 pages, 5 figure