Imaginary time integration method using a quantum lattice gas approach
By modifying the collision operator in the quantum lattice gas (QLG) algorithm one can develop an imaginary time (IT) integration to determine the ground state solutions of the Schrodinger equation and its variants. These solutions are compared to those found by other methods (in particular the backward-Euler finite-difference scheme and the quantum lattice Boltzmann). In particular, the ground state of the quantum harmonic oscillator is considered as well as bright solitons in the one-dimensional (1D) non-linear Schrodinger equation. The dark solitons in an external potential are then determined. An advantage of the QLG IT algorithm is the avoidance of any real/complex matrix inversion and that its extension to arbitrary dimensions is straightforward.