najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2015-6-2-213-215najo-921Research ArticlePAPERS, PRESENTED AT THE CONFERENCEPAPERS, PRESENTED AT THE CONFERENCEPerturbative hydrodynamic Gross-Pitaevskii treatment for Bose-Einstein condensate in infinite length ring with disorderAbdullaevD. B.

Institute of Applied Physics

Tashkent 100174

abdullaev_davron@mail.ruAbdullaevB.

Institute of Applied Physics

Tashkent 100174

bakhodir_abdullaev@yahoo.comMusakhanovM. M.

Tashkent 100174

yousufmm@list.ruNational University of UzbekistanUzbekistan20151408202562213215Copyright © Abdullaev D.B., Abdullaev B., Musakhanov M.M., 20252025Abdullaev D.B., Abdullaev B., Musakhanov M.M.Abdullaev D.B., Abdullaev B., Musakhanov M.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/921

For the derivation of the dilute Bose–Einstein condensate density and its phase, we have developed the perturbative approach for the solution of the stationary state couple Gross–Pitaevskii hydrodynamic equations. The external disorder potential is considered as a small parameter in this approach. We have derived expressions for the total density, condensate density, condensate density depletion and superfluid velocity of the Bose–Einstein condensate in an infinite length ring with disorder potential having a general form. For the delta correlated disorder, the explicit analytical forms of these quantities (except the superfluid velocity) have been obtained.

Bose–Einstein condensate in ringGross–Pitaevskii hydrodynamic equationsdisorder potentialcondensate densitycondensate density depletiondelta correlated disorderReferencesE. M. Lifshitz and L. P. Pitaevskii. Statistical Physics, Part 2: Theory of Condensed State, Course of Theoretical Physics, V. 9, Elsevier Ltd., Amsterdam 1980, 387 p.E. M. Lifshitz and L. P. Pitaevskii. Statistical Physics, Part 2: Theory of Condensed State, Course of Theoretical Physics, V. 9, Elsevier Ltd., Amsterdam 1980, 387 p.L. Pitaevskii and S. Stringari, Bose–Einstein Condensation, Oxford University Press, Oxford, 2003, 492 p.L. Pitaevskii and S. Stringari, Bose–Einstein Condensation, Oxford University Press, Oxford, 2003, 492 p.L. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari. Theory of Bose–Einstein condensation in trapped gases. Rev. Mod. Phys., 71, P. 463 –512 (1999).L. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari. Theory of Bose–Einstein condensation in trapped gases. Rev. Mod. Phys., 71, P. 463 –512 (1999).C. Krumnow and A. Pelster. Dipolar Bose–Einstein condensates with weak disorder. Phys. Rev. A, 84, P. 021608(R) (2011).C. Krumnow and A. Pelster. Dipolar Bose–Einstein condensates with weak disorder. Phys. Rev. A, 84, P. 021608(R) (2011).

The authors declare that there are no conflicts of interest present.