The Gross-Pitaevskii Equation and Bose-Einstein condensates

Understand

The Gross-Pitaevskii equation is discussed at the level of an advanced course on statistical physics.

• In the standard literature the Gross-Pitaevskii equation is usually obtained in the framework of the second quantisation formalism, which in many cases goes beyond the material covered in many advanced undergraduate courses.
• In this paper, we motivate the derivation of the Gross-Pitaevskii equation (GPE) in relationship to concepts from statistical physics, highlighting a number of applications from dynamics of a Bose-Einstein condensate to the excitations of the gas cloud.
• This paper may be helpful not only in encouraging the discussion of modern developments in a statistical mechanics course, but also can be of use in other contexts such as mathematical physics and modelling.