arXiv subjects
Publications and source records attributed to Patrick Plötz.
The fidelity, defined as overlap of eigenstates of two slightly different Hamiltonians, is proposed as an efficient detector of avoided c rossings in the energy spectrum. This new application of fidelity is motivated for model systems, and its value for analyzing complex qua ntum spectra is underlined by applying it to a random matrix model and a tilted Bose-Hubbard system.
We show that and how ultra-cold atoms in an accelerated two-band lattice are a controlled realization of Landau--Zener--Stückelberg interferometry.
We show that the interband dynamics in a tilted two-band Bose-Hubbard model can be reduced to an analytically accessible spin model in the case of resonant interband oscillations. This allows us to predict the revival time of these oscillations which decay and revive due to inter-particle interactions. The presented mapping onto the spin model and the so achieved reduction of complexity has interesting perspectives for future studies of many-body systems.
We study Rabi oscillations between the bands of an arbitrary biased superlattice in a tight-binding model. We reduce the problem to an equation of Whittaker--Hill type and, in absence of any known solutions in closed form, discuss different approximations to describe the oscillations between the Bloch bands. We identify regimes of weak and strong inter-band coupling and compare predictions for these Rabi oscillations to numerical results.
We study the effect of a many-body interaction on inter-band oscillations in a two-band Bose-Hubbard model with external Stark force. Weak and strong inter-band oscillations are observed, where the latter arise from a resonant coupling of the bands. These oscillations collapse and revive due to a weak two-body interaction between the atoms. Effective models for oscillations in and out of resonance are introduced that provide predictions for the system's behaviour, particularly for the time-scales for the collapse and revival of the resonant inter-band oscillations.
We derive expressions for the charge and spin response function for the Tomonaga model with quadratic dispersion and arbitrary (but finite for zero momentum) interaction. For constant interaction these expressions are analytic and for other types of interaction only a simple matrix has to be diagonalised. We use a truncated expansion in particle-hole states with and without inclusion of correlations in the ground state yielding an exact result for pure intra-band interaction. We also discuss the possibility of power-laws in the dynamic structure factor for the spinful and spinless model.