P. Grochowski | Searcharxiv

arXiv2016

Spectra and Bifurcations

The concept of spectrum for a class of non-linear wave equations is studied. Instead of looking for stability, the key to the spectral structure is found in the instability phenomena (bifurcations). This aspect is best seen in the `classical model' of the non-linear wave mechanics. The solitons (macro-localizations) are a part of the non-linear spectral problem; their bifurcations reflect the dynamical symmetry breaking. The computer simulations suggest that the bifurcations of the asymptotic behaviour occur also for the general, non-stationary states. A~phenomenon of the soliton splitting is observed.

quant-ph↗

arXiv2015

Ground-state densities of repulsive two-component Fermi gases

We investigate separations of trapped balanced two-component atomic Fermi gases with repulsive contact interaction. Candidates for ground-state densities are obtained from the imaginary-time evolution of a nonlinear pseudo-Schr\"odinger equation in three dimensions, rather than from the cumbersome variational equations. With the underlying hydrodynamical approach, gradient corrections to the Thomas-Fermi approximation are conveniently included and are shown to be vital for reliable density profiles. We provide critical repulsion strengths that mark the onset of phase transitions in a harmonic trap. We present transitions from identical density profiles of the two fermion species towards isotropic and anisotropic separations for various confinements, including harmonic and double-well-type traps. Our proposed method is suited for arbitrary trap geometries and can be straightforwardly extended to study dynamics in the light of ongoing experiments on degenerate Fermi gases.

cond-mat.quant-gas↗