Analytical solutions to the spin-1 Bose–Einstein condensates

Spin evolution of spin-1 Bose-Einstein condensates

An analytical formula is obtained to describe the evolution of the average populations of spin components of spin-1 atomic gases. The formula is derived from the exact time-dependent solution of the Hamiltonian HS = cS 2 without using approximation. Therefore it goes beyond the mean field theory and provides a general, accurate, and complete description for the whole process of nondissipative e...

Entanglement Entropy of the Spin-1 Condensates at Zero Temperature

For spin-1 condensates, the spatial degrees of freedom can be considered as being frozen at temperature zero, while the spin-degrees of freedom remain free. Under this condition, the entanglement entropy has been derived exactly with an analytical form. The entanglement entropy is found to decrease monotonically with the increase of the magnetic polarization as expected. However, for the ground...

Analytical solutions for the fractional Fisher's equation

In this paper, we consider the inhomogeneous time-fractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables  method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified...

Stability of nonstationary states of spin-1 Bose-Einstein condensates

Equation Chapter 1 Section 1 Analytical Solutions for Radially Functionally Graded Annular Plates

A closed-form solution for deflections and stresses in an annular thin plate of radially functionally graded material under transverse uniform pressure loading is presented. The small displacement theory of elasticity is assumed in the present work. Young’s modulus of the material is taken in the form of a simple power law to vary in the radial direction with an arbitrary exponent showing heter...