ИСТИНА

Various methods can be applied for studying of ultracold atoms, and gauge theories give powerful methods. However, our attention is focused on development of an alternative method, which allows to represent the many-particle Schrodinger equation as a chain of equations having hydrodynamic form [1]. Developing method of quantum hydrodynamic for neutral ultracold Bose atoms, in simplest case when chain can be cut off giving the continuity and Euler equations, gives the Gross-Pitaevskii equation [1], in the case of Fermi atoms it gives us corresponding nonlinear Schrodinger equation [1]. Considering evolution of neutral polar molecules in the BEC state we show that the quantum hydrodynamics allows to derive corresponding generalization of the Gross-Pitaevskii equation suggested in Ref.s [2], [3], [4], which appears for fully polarized dipoles [5]. This equation has been actively used in last decade [6]. We present non-integral form of the Gross- Pitaevskii equation for polarized molecules. We present estimation of evolution of electric dipole directions and consequences of the evolution on properties of wave dispersion in polarized BEC. We also point out differences in evolution of dipole directions for magnetic and electric dipoles, which reveals in differences in dispersion of collective excitation. 1. P. A. Andreev, L. S. Kuz’menkov, Phys. Rev. A 78, 053624 (2008). 2. S. Yi and L. You, Phys. Rev. A 61, 041604(R) (2000). 3. K. Goral, K. Rzazewski, and T. Pfau, Phys. Rev. A 61, 051601(R) (2000). 4. L. Santos, G.V. Shlyapnikov, P. Zoller, and M. Lewenstein, Phys. Rev. Lett. 85, 1791 (2000). 5. P. A. Andreev and L. S. Kuz’menkov, arXiv: 1201.2440. 6. M. A. Baranov, M. Dalmonte, G. Pupillo, and P. Zoller, Chem. Rev., 112, 5012 (2012).