Gutzwiller method for bosons
Nowadays ultracold quantum gases act as a playground for many types of many-body interacting system. A very high-interest issue for all of these systems is their dynamics; how the system evolve its property in time. For the case of strongly interacting systems, this is very complex problem to address. There are already well-established numerical methods to study the many-body systems at equilibrium. However along the experimental progress of dynamical process, systematic study of time-dependent many-body systems is unavoidable. Because of complexity, the practical choices are limited respect to equilibrium. For instance to describe the dynamic of a one-dimensional system, time-dependent Density Matrix Renormalization Group (t-DMRG) has been developed during the past few years.
A powerful applicable method to study the dynamic of cold-gases is time-dependent Gutzwiller mean-field approximation. In this framework, the total wave-function is assumed to be a product wave-function over the lattice sites
Each of the on-site wave-function is evolved in time according to the local Schrödinger equation
This gives very reliable results in 3D and also provides qualitatively good results in 2D. This method has been successfully implemented to describe two-dimensional dynamics of single-component Bose gas in optical lattices [1]. More recently it it was applied to investigate lattice-ramp induced dynamics in a Bose-Bose mixture [2] which was motivated by a new experiment carried out in Florence [3].
[1] M. Snoek and W. Hofstetter, Phys. Rev. A 76, 051603 (2007)
[2] J. Wernsdorfer, M. Snoek and W. Hofstetter. arXiv:0911.0697
[3] J. Catani et.al, Phys. Rev. A. 77, 011603(R) (2008)
