Bose-Einstein condensation in a minimal inhomogeneous system

We study the effects of repulsive interaction and disorder on Bosons in a two-site Bose-Hubbard system, which provides a simple model of the dirty boson problem. By comparison with exact numerical results, we demonstrate how a straightforward application of the Bogoliubov approximation fails even to deliver a qualitatively correct picture: It wrongly predicts an increase of the condensate depletion due to disorder. We show that, in the presence of disorder, the noncommutative character of the condensate operator has to be retained for a correct description of the system.Comment: 6 pages, 4 figure

Bogoliubov theory on the disordered lattice

Quantum fluctuations of Bose-Einstein condensates trapped in disordered lattices are studied by inhomogeneous Bogoliubov theory. Weak-disorder perturbation theory is applied to compute the elastic scattering rate as well as the renormalized speed of sound in lattices of arbitrary dimensionality. Furthermore, analytical results for the condensate depletion are presented, which are in good agreement with numerical data.Comment: 10 pages, contributed to Lyon BEC 201

A grand-canonical approach to the disordered Bose gas

We study the problem of disordered interacting bosons within grand-canonical thermodynamics and Bogoliubov theory. We compute the fractions of condensed and non-condensed particles and corrections to the compressibility and the speed of sound due to interaction and disorder. There are two small parameters, the disorder strength compared to the chemical potential and the dilute-gas parameter.Comment: 9 pages, 3 figure

Anderson localization of Bogoliubov excitations on quasi-1D strips

Anderson localization of Bogoliubov excitations is studied for disordered lattice Bose gases in planar quasi-one-dimensional geometries. The inverse localization length is computed as function of energy by a numerical transfer-matrix scheme, for strips of different widths. These results are described accurately by analytical formulas based on a weak-disorder expansion of backscattering mean free paths.Comment: 4 pages, 2 figure

Machine Learning for Screening Large Organic Molecules

Organic semiconductors are promising materials for cheap, scalable and sustainable electronics, light-emitting diodes and photovoltaics. For organic photovoltaic cells, it is a challenge to find compounds with suitable properties in the vast chemical compound space. For example, the ionization energy should fit to the optical spectrum of sun light, and the energy levels must allow efficient charge transport. Here, a machine-learning model is developed for rapidly and accurately estimating the HOMO and LUMO energies of a given molecular structure. It is build upon the SchNet model (Sch\"utt et al. (2018)) and augmented with a `Set2Set' readout module (Vinyals et al. (2016)). The Set2Set module has more expressive power than sum and average aggregation and is more suitable for the complex quantities under consideration. Most previous models have been trained and evaluated on rather small molecules. Therefore, the second contribution is extending the scope of machine-learning methods by adding also larger molecules from other sources and establishing a consistent train/validation/test split. As a third contribution, we make a multitask ansatz to resolve the problem of different sources coming at different levels of theory. All three contributions in conjunction bring the accuracy of the model close to chemical accuracy.Comment: Presented at E-MRS Fall Meeting 2022, Symposium

Speed of sound in disordered Bose-Einstein condensates

Disorder modifies the sound-wave excitation spectrum of Bose-Einstein condensates. We consider the classical hydrodynamic limit, where the disorder correlation length is much longer than the condensate healing length. By perturbation theory, we compute the phonon lifetime and correction to the speed of sound. This correction is found to be negative in all dimensions, with universal asymptotics for smooth correlations. Considering in detail optical speckle potentials, we find a quite rich intermediate structure. This has consequences for the average density of states, particularly in one dimension, where we find a "boson dip" next to a sharp "boson peak" as function of frequency. In one dimension, our prediction is verified in detail by a numerical integration of the Gross-Pitaevskii equation.Comment: final, extended version with 2 new figure

Stability and decay of Bloch oscillations in presence of time-dependent nonlinearity

We consider Bloch oscillations of Bose-Einstein condensates in presence of a time-modulated s-wave scattering length. Generically, interaction leads to dephasing and decay of the wave packet. Based on a cyclic-time argument, we find---additionally to the linear Bloch oscillation and a rigid soliton solution---an infinite family of modulations that lead to a periodic time evolution of the wave packet. In order to quantitatively describe the dynamics of Bloch oscillations in presence of time-modulated interactions, we employ two complementary methods: collective-coordinates and the linear stability analysis of an extended wave packet. We provide instructive examples and address the question of robustness against external perturbations.Comment: 15 pages, 8 figures. Slightly amended final versio