51 research outputs found
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
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