scholarly journals Critical Exponent η up to 1/n2for the Three-Dimensional System with Short-Range Interaction

1973 ◽  
Vol 49 (3) ◽  
pp. 1074-1075 ◽  
Author(s):  
Ryuzo Abe
Keyword(s):  
Critical Exponent ◽  
Short Range ◽  
Three Dimensional ◽  
Dimensional System ◽  
Short Range Interaction ◽  
Range Interaction ◽  
Three Dimensional System

scholarly journals NONINTEGRAL FORM OF THE GROSS–PITAEVSKII EQUATION FOR POLARIZED MOLECULES

2013 ◽  
Vol 27 (13) ◽  
pp. 1350096 ◽  
Author(s):  
PAVEL A. ANDREEV
Keyword(s):  
Dipole Moment ◽  
Electric Dipole Moment ◽  
Electric Dipole ◽  
Short Range ◽  
Linear Equations ◽  
Three Dimensional ◽  
Interaction Constant ◽  
Pitaevskii Equation ◽  
Short Range Interaction ◽  
Range Interaction

The Gross–Pitaevskii equation for polarized molecules is an integro-differential equation, consequently it is complicated for solving. We find a possibility to represent it as a nonintegral nonlinear Schrödinger equation, but this equation should be coupled with two linear equations describing the electric field. These two equations are the Maxwell equations. We recapture the dispersion of collective excitations in the three-dimensional electrically polarized BEC with no evolution of the electric dipole moment directions. We trace the contribution of the electric dipole moment. We explicitly consider the contribution of the electric dipole moment in the interaction constant for the short-range interaction. We show that the spectrum of dipolar BEC does not reveal instability at repulsive short-range interaction. Nonlinear excitations are also considered. We present dependence of the bright soliton characteristics on the electric dipole moment.

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