N. J. Mauser's research while affiliated with University of Vienna and other places

We present a detailed analysis of the relaxation dynamics in an extended bosonic Josephson junction. We show that stochastic classical field simulations using Gross-Pitaevskii equations in three spatial dimensions reproduce the main experimental findings of Pigneur et al. [Phys. Rev. Lett. 120, 173601 (2018)]. We give an analytic solution describing the short time evolution through multimode dephasing. For longer times, the observed relaxation to a phase-locked state is caused by nonlinear dynamics beyond the sine-Gordon model, induced by the longitudinal confinement potential and persisting even at zero temperature. Finally, we analyze different experimentally relevant trapping geometries to mitigate these effects. Our results provide the basis for future experimental implementations aiming to study nonlinear and quantum effects of the relaxation in extended bosonic Josephson junctions.

Bose-Einstein condensates (BECs) offer a fruitful, often uncharted ground for exploring physics of many-particle systems. In the present year of the MCTDHB project at the HLRS, we maintained and extended our investigations of BECs and interacting bosonic systems using the MultiConfigurational Time-Dependent Hartree for Bosons (MCTDHB) method and running the MCTDHB and MCTDH-X software packages on the Cray XC40 system Hazel Hen. The results we disseminate within this report comprise: (i) Entropies and correlations of ultracold bosons in a lattice; (ii) Crystallization of bosons with dipole-dipole interactions and its detection in single-shot images; (iii) Management of correlations in ultracold gases; (iv) Pulverizing a BEC; (v) Dynamical pulsation of ultracold droplet crystals by laser light; (vi) Two-component bosons interacting with photons in a cavity; (vii) Quantum dynamics of a bosonic Josephson junction and the impact of the range of the interaction; (viii) Trapped bosons in the infinite-particle limit and their exact many-body wavefunction and properties; (ix) Angular-momentum conservation in a BEC and Gross-Pitaevskii versus many-body dynamics; (x) Variance of an anisotropic BEC; and (xi) excitation spectrum of a weakly-interacting rotating BEC showing enhanced many-body effects. These are all basic and appealing, sometimes unexpected many-body results put forward with the generous allocation of computer time by the HLRS to the MCTDHB project. Finally, expected future developments and research tasks are prescribed, too.

Dipolar Bose–Einstein condensates have recently attracted much attention in the world of quantum many body experiments. While the theoretical principles behind these experiments are typically supported by numerical simulations, the application of optimal control algorithms could potentially open up entirely new possibilities. As a proof of concept, we demonstrate that the formation process of a single dipolar droplet state could be dramatically accelerated using advanced concepts of optimal control. More specifically, our optimization is based on a multilevel B-spline method reducing the number of required cost function evaluations and hence significantly reducing the numerical effort. Moreover, our strategy allows to consider box constraints on the control inputs in a concise and efficient way. To further improve the overall efficiency, we show how to evaluate the dipolar interaction potential in the generalized Gross–Pitaevskii equation without sacrificing the spectral convergence rate of the underlying time-splitting spectral method.

We develop a quantum model based on the correspondence between energy distribution between harmonic oscillators and the partition of an integer number. A proper choice of the interaction Hamiltonian acting within this manifold of states allows us to examine both the quantum typicality and the non-exponential relaxation in the same system. A quantitative agreement between the field-theoretical calculations and the exact diagonalization of the Hamiltonian is demonstrated.

The perfectly matched layers (PML) and exterior complex scaling (ECS) methods for absorbing boundary conditions are analyzed using spectral decomposition. Both methods are derived through analytical continuations from unitary to contractive transformations. We find that the methods are mathematically and numerically distinct: ECS is complex stretching that rotates the operator's spectrum into the complex plane, whereas PML is a complex gauge transform which shifts the spectrum. Consequently, the schemes differ in their time-stability. Numerical examples are given.

We numerically model the evolution of a pair of coherently split quasicondensates. A truly one-dimensional case is assumed, so that the loss of the (initially high) coherence between the two quasicondensates is due to dephasing only, but not due to the violation of integrability and subsequent thermalization (which are excluded from the present model). We confirm the subexponential time evolution of the coherence between two quasicondensates $\propto \exp [-(t/t_0)^{2/3}]$, experimentally observed by S. Hofferberth {\em et. al.}, Nature {\bf 449}, 324 (2007). The characteristic time $t_0$ is found to scale as the square of the ratio of the linear density of a quasicondensate to its temperature, and we analyze the full distribution function of the interference contrast and the decay of the phase correlation.

We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter, we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled, and compare with the Luttinger-liquid theory.

We study the behavior of solutions of the (mixed state) Dirac-Maxwell sys-tem in the simultaneous non-relativistic and semi-classical limits, i.e., as the speed of light c tends to infinity and the Planck constant ¯ h tends to zero. Under a constraint of the form 1 c exp 1 ¯ h M = o(1), where M is a sufficiently large integer, and with suitable conditions on the initial data, we prove that the scalar Wigner transform of the Dirac spinors converges weakly to a solution of the classical Vlasov-Poisson system. Our key technique is a blend of null form bilinear estimates with the machinery of the Wigner transform.

We study the relaxation of kinetic BGK models involving a high-field term in the transport operator. This leads to multidimensional scalar conservation laws with a flux which is perturbed with respect to classical relaxation. The proof of the relaxation limit makes appear modified Maxwellians. We consider "pseudo distribution functions" which can take also negative values and introduce appropriate admissible states. This is a first step towards adapting this kind of analysis to quantum kinetic BGK models.