20 research outputs found
Correlated Quantum Dynamics of a Single Atom Collisionally Coupled to an Ultracold Finite Bosonic Ensemble
We explore the correlated quantum dynamics of a single atom, regarded as an
open system, with a spatio-temporally localized coupling to a finite bosonic
environment. The single atom, initially prepared in a coherent state of low
energy, oscillates in a one-dimensional harmonic trap and thereby periodically
penetrates an interacting ensemble of bosons, held in a displaced trap.
We show that the inter-species energy transfer accelerates with increasing
and becomes less complete at the same time. System-environment
correlations prove to be significant except for times when the excess energy
distribution among the subsystems is highly imbalanced. These correlations
result in incoherent energy transfer processes, which accelerate the early
energy donation of the single atom and stochastically favour certain energy
transfer channels depending on the instantaneous direction of transfer.
Concerning the subsystem states, the energy transfer is mediated by
non-coherent states of the single atom and manifests itself in singlet and
doublet excitations in the finite bosonic environment. These comprehensive
insights into the non-equilibrium quantum dynamics of an open system are gained
by ab-initio simulations of the total system with the recently developed
Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons
Quantum breathing dynamics of ultracold bosons in 1D-harmonic traps: Unraveling the pathway from few- to many-body systems
Following a `bottom-up approach' in understanding many-particle effects and
dynamics we provide a systematic ab initio study of the dependence of the
breathing dynamics of ultracold bosons in a 1D harmonic trap on the number of
bosons ranging from few to many. To this end, we employ the Multi-Layer
Multi-Configuration Time-Dependent Hartree method for Bosons (ML-MCTDHB) which
has been developed very recently [S. Kr\"onke, L. Cao, O. Vendrell and P.
Schmelcher. {\it New J. Phys.} {\bf 15}, 063018 (2013)]. The beating behavior
for two bosons is found numerically and consequently explained by an analytical
approach. Drawing on this, we show how to compute the complete breathing mode
spectrum in this case. We examine how the two-mode breathing behavior of two
bosons evolves to the single-frequency behavior of the many-particle limit when
adding more particles. In the limit of many particles, we numerically study the
dependence of the breathing mode frequency on both the interaction strength as
well as on the particle number. We provide an estimate for the parameter region
in which Gross-Pitaevskii theory is well applicable
Modelling nonlinear dynamics of interacting tipping elements on complex networks: the PyCascades package
Tipping elements occur in various systems such as in socio-economics, ecology and the climate system. In many cases, the individual tipping elements are not independent of each other, but they interact across scales in time and space. To model systems of interacting tipping elements, we here introduce the PyCascades open source software package for studying interacting tipping elements (https://doi.org/10.5281/zenodo.4153102). PyCascades is an object-oriented and easily extendable package written in the programming language Python. It allows for investigating under which conditions potentially dangerous cascades can emerge between interacting dynamical systems, with a focus on tipping elements. With PyCascades it is possible to use different types of tipping elements such as double-fold and Hopf types and interactions between them. PyCascades can be applied to arbitrary complex network structures and has recently been extended to stochastic dynamical systems. This paper provides an overview of the functionality of PyCascades by introducing the basic concepts and the methodology behind it. In the end, three examples are discussed, showing three different applications of the software package. First, the moisture recycling network of the Amazon rainforest is investigated. Second, a model of interacting Earth system tipping elements is discussed. And third, the PyCascades modelling framework is applied to a global trade network