Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensates

The Gross-Pitaevskii Model of Spinor BEC

Bose–Einstein condensates: Analytical methods for the Gross–Pitaevskii equation

We present simple analytical methods for solving the Gross–Pitaevskii equation (GPE) for the Bose–Einstein condensation (BEC) in the dilute atomic alkali gases. Using a soliton variational Ansatz we consider the effects of repulsive and attractive effective nonlinear interactions on the BEC ground state. We perform a comparative analysis of the solutions obtained by the variational Ansatz, the ...

Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models

Motivated by recent experiments on trapped ultra-cold bosonic atoms in an optical lattice potential, we consider the non-equilibrium dynamic properties of such bosonic systems for a number of experimentally relevant situations. When the number of bosons per lattice site is large, there is a wide parameter regime where the effective boson interactions are strong, but the ground state remains a s...

The Gross-Pitaevskii Equation and Bose-Einstein condensates

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 equa...

Chaotic dynamics in spinor Bose–Einstein condensates

Concentrating on experimentally relevant cases we discuss nonlinear dynamics and deterministic chaos in F = 1 and F = 2 spinor Bose–Einstein condensates. A thorough numerical and analytical treatment of the equations of motion of symmetric F = 2 spin dynamics in the single-mode approximation elucidates the complex dynamics and uncovers regions of classical chaos in this important quantum gas sy...