The ripplon modes of two segregated Bose-Einstein condensates (BECs) confined by one and two hard walls are respectively studied by means of the hydrodynamic approach within the Gross-Pitaevskii (GP) theory. For the system at rest we find that due to the spatial restriction the dispersion relations are of the form ω ∼ k 2 in low momentum limit for both cases, while for the system in motion parallel to the interface the dispersion relations for both cases are ω ∼ k at low momentum limit and, furthermore, the system becomes unstable. | Communications in Physics, Vol. 26, No. 1 (2016), pp. 11-18 DOI: RIPPLON MODES OF TWO SEGREGATED BOSE-EINSTEIN CONDENSATES IN CONFINED GEOMETRY TRAN HUU PHAT Vietnam Atomic Energy Commission, 59 Ly Thuong Kiet, Hanoi, Vietnam HOANG VAN QUYET† Department of Physics, Hanoi Pedagogical University No. 2, Hanoi, Vietnam † E-mail: hoangvanquyetsp2@ Received 20 February 2016 Accepted for publication 12 April 2016 Abstract. The ripplon modes of two segregated Bose-Einstein condensates (BECs) confined by one and two hard walls are respectively studied by means of the hydrodynamic approach within the Gross-Pitaevskii (GP) theory. For the system at rest we find that due to the spatial restriction the dispersion relations are of the form ω ∼ k2 in low momentum limit for both cases, while for the system in motion parallel to the interface the dispersion relations for both cases are ω ∼ k at low momentum limit and, furthermore, the system becomes unstable. Keywords: Bose-Einstein condensates, hydrodynamic approach, ripplon modes, Kelvin-Helmholtz instability, Bernoulli equation. Classification numbers: , , g. I. INTRODUCTION The phase separation in binary mixtures of Bose-Einstein condensates was theoretically predicted [1, 2] and observed later in experiments [3–8]. Since then many works have been devoted to explore the statics, the dynamics and the ripplon modes of two segregated BECs [9–25]. However, most of them concerned with the systems in infinite space, while all experimental realizations have been carried out in restricted regions of space with spatial structure being more and more complicated. In this respect, the present paper deals with the problem: how ripplon modes are influenced by the spatial restriction when a system of two segregated BECs is confined by one or two hard walls and the method we use to tackle the problem is the hydrodynamic approach. To c 2016 Vietnam Academy of Science and .
