3 research outputs found
Adaptive propagation of quantum few-body systems with time-dependent Hamiltonians
In this study, a variety of methods are tested and compared for the numerical
solution of the Schr\"odinger equation for few-body systems with explicitely
time-dependent Hamiltonians, with the aim to find the optimal one. The
configuration interaction method, generally applied to find stationary
eigenstates accurately and without approximations to the wavefunction's
structure, may also be used for the time-evolution, which results in a large
linear system of ordinary differential equations. The large basis sizes
typically present when the configuration interaction method is used calls for
efficient methods for the time evolution. Apart from efficiency, adaptivity (in
the time domain) is the other main focus in this study, such that the time step
is adjusted automatically given some requested accuracy. A method is suggested
here, based on an exponential integrator approach, combined with different ways
to implement the adaptivity, which was found to be faster than a broad variety
of other methods that were also considered.Comment: 16 pages, 1 figure (4 panels
Ground-state properties of few dipolar bosons in a quasi-one-dimensional harmonic trap
We study the ground state of few bosons with repulsive dipole-dipole
interaction in a quasi-one-dimensional harmonic trap by means of the exact
diagonalization method. Up to three interaction regimes are found depending on
the strength of the dipolar interaction and the ratio of transverse to axial
oscillator lengths: a regime where the dipolar Bose gas resembles a system of
weakly delta-interacting bosons, a second regime where the bosons are
fermionized, and a third regime where the bosons form a Wigner crystal. In the
first two regimes, the dipole-dipole potential can be replaced by a delta
potential. In the crystalline state, the overlap between the localized wave
packets is strongly reduced and all the properties of the boson system equal
those of its fermionic counterpart. The transition from the Tonks-Girardeau gas
to the solidlike state is accompanied by a rapid increase of the interaction
energy and a considerable change of the momentum distribution, which we trace
back to the different short-range correlations in the two interaction regimes.Comment: This arXiv version contains at the end the Erratum to the published
versio
Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes
We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to construct an approximation for the exchange-correlation term of the Kohn-Sham approach. The resulting exchange-correlation potential is able to capture the features of the strongly correlated regime without breaking the spin or any other symmetry. In particular, it shows “bumps” (or barriers) that give rise to charge localization at low densities and that are a well-known key feature of the exact Kohn-Sham potential for strongly correlated systems. Here, we illustrate this approach for the study of both weakly and strongly correlated model quantum wires, comparing our results with those obtained with the configuration interaction method and with the usual Kohn-Sham local density approximation