Monday, January 12, 2009
What is Gross-Pitaevskii Equation?
A non-degenerate system can be explained by the Schrodinger equation, which is a linear second order differential equation: ( i hbar del/ del t ) psi = (- hbar^2/(2m) * laplacian^2) psi + V psi. But for a degenerate quantum gas like a Bose-Einstein Condensate(BEC), there is a non-linearity caused by the atom-atom interactions, which needs to be explained by a non-linear second order differential equation of the form: ( i hbar del/ del t ) psi = (- hbar^2/(2m) * laplacian^2) psi + V psi + NU|psi|^2 psi. This equation was first derived by Gross and Pitaevskii independently and is called the Gross-Pitaevskii equation. The last term in the equation is the nonlinear term introduced by the atom-atom interactions.