scholarly journals Short-range interaction in three-dimensional quantum mechanics

2010 ◽  
Vol 374 (45) ◽  
pp. 4585-4588
Author(s):  
Taksu Cheon
Keyword(s):  
Quantum Mechanics ◽  
Short Range ◽  
Three Dimensional ◽  
Short Range Interaction ◽  
Range Interaction

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.

Static critical behaviors in random-spin systems with short-range interaction

1978 ◽  
Vol 56 (1) ◽  
pp. 139-148 ◽  
Author(s):  
Yoshitake Yamazaki
Keyword(s):  
Short Range ◽  
Spin Systems ◽  
Three Dimensions ◽  
Index Formula ◽  
Spin Component ◽  
Renormalization Group Theory ◽  
Short Range Interaction ◽  
Range Interaction ◽  
The Stability ◽  
Component Models

Critical behaviors in quenched random-spin systems with N-spin component are studied in the limit M → 0 of the non-random MN-component models by means of the renormalization group theory. As the static critical phenomena the stability of the fixed points is investigated and the critical exponents η[~ O(ε3); ε ≡ 4 – d], γ, α, and crossover index [Formula: see text] and the equation of state [~ O(ε)] are obtained. Within the approximation up to the order ε2, even the random-spin systems with N = 2 or 3 are unstable in the three dimensions and the pure systems are stable there.

scholarly journals Short-Range Interaction Impact on Two-Dimensional Dipolar Scattering

2018 ◽  
Vol 173 ◽  
pp. 06008 ◽  
Author(s):  
Eugene A. Koval ◽  
Oksana A. Koval
Keyword(s):  
Cross Section ◽  
Short Range ◽  
Strong Dependence ◽  
Dipolar Interaction ◽  
Two Dimensional ◽  
Short Range Interaction ◽  
Range Interaction ◽  
Interaction Radius ◽  
Ultracold Polar Molecules ◽  
Spatial Dimensions

We report numerical investigation of the short range interaction influence on the two-dimensional quantum scattering of two dipoles. The model simulates two ultracold polar molecules collisions in two spatial dimensions. The used algorithm allows us to quantitatively analyse the scattering of two polarized dipoles with account for strongly anisotropic nature of dipolar interaction. The strong dependence of the scattering total cross section on the short range interaction radius was discovered for threshold collision energies. We also discuss differences of calculated scattering cross section dependencies for different polarisation axis tilt angles.

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