The analytical expressions for the wave functions of two-component Bose-Einstein Condensates are derived by means of the Gross-Pitaevskii equations in linear approximation. Based on the Bernoulli equation the shape of the interface and the dispersion relations for both phonon and ripplonare studied. | JOURNAL OF SCIENCE OF HNUE DOI Mathematical and Physical Sci. 2015 Vol. 60 No. 7 pp. 88-93 This paper is available online at http THE INTERFACE PROPERTIES OF TWO-COMPONENT BOSE-EINSTEIN CONDENSATES Le Viet Hoa1 Nguyen Tuan Anh2 Le Huy Son3 and Nguyen Van Hop1 1 Faculty of Physics Hanoi National University of Education 2 Faculty of Energy Technology Electric Power University 3 Faculty of Physics Hanoi Metropolitan University Abstract. The analytical expressions for the wave functions of two-component Bose-Einstein Condensates are derived by means of the Gross-Pitaevskii equations in linear approximation. Based on the Bernoulli equation the shape of the interface and the dispersion relations for both phonon and ripplonare studied. It is shown that the numbers of Nambu-Goldstone modes in a system obey a modified counting rule which states that the number of type I plus twice the number of type II Nambu-Goldstone modes are greater than or equal to the generators of spontaneously broken symmetries. Here the type I type II consists of Nambu-Goldstone modes with linear fractional dispersion relation. Keywords Bose-Einstein Condensates shape of interface Nambu-Goldstone modes. 1. Introduction The theoretical studies of two immiscible Bose-Einstein Condensates BECs 1 2 and the experimental realizations of such systems 3-5 have allowed us to explore many interesting physical properties of BECs in which the superfluid dynamics of interface between two segregated BECs has attracted special attention. Following this trend in recent years one has focused on considerations of hydrodynamic instabilities at the interface of two BECs such as the Kelvin-Helmholtz instability the Rayleigh-Taylor instability and the Richtmayer-Meshkov instability 6 7 . Combining the hydrodynamic approach and the Bogoliubov- de Gennes method these considerations confirmed that the foregoing instabilities of fluid in classic hydrodynamics are also to take .
