Scaling dynamics of the ultracold Bose gas

The large-scale expansion dynamics of quantum gases is a central tool for ultracold gas experiments and poses significant challenge theory. In this work we provide an exact reformulation the Gross-Pitaevskii equation Bose in coordinate frame that adaptively scales with system size during evolution, enabling simulations long evolution times or similar manipulation. Our approach makes no hydrodynamic approximations, not restricted to scaling ansatz, harmonic potentials, energy eigenstates, can be generalized readily non-contact interactions via appropriate stress tensor fluid. As applications, simulate ideal gas, cigar-shaped condensate Thomas-Fermi regime, linear superposition counter propagating Gaussian wavepackets. We recover known regimes, identify regime aspect-ratio preserving free expansion; analysis equations shows exact, invariant, does exist nonlinear evolution. treatment enables exploration effects matter-wave over large scale-changing