Timo Hartmann

Dynamics of Bloch oscillations

We study the dynamics of Bloch oscillations in a one-dimensional periodic potential plus a (relatively weak) static force. The tight-binding and single-band approximations are analysed in detail, and also in a classicalized version. A number of numerically exact results obtained from wavepacket propagation are analysed and interpreted in terms of the tight-binding and single-band model, both in co-ordinate and momentum space.

Propagating wave correlations in complex systems

We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local mean of these correlation functions in terms of the underlying classical dynamics. By defining appropriate ensemble averages, we show that fluctuations about the mean can be characterised in terms of classical correlations. We give in particular an explicit expression relating fluctuations of diagonal contributions to those of the full wave correlation function. The methods have a wide range of applications both in quantum mechanics and for classical wave problems such as in vibro-acoustics and electromagnetism. We apply the methods here to simple quantum systems, so-called quantum maps, which model the behaviour of generic problems on PoincarA© sections. Although low-dimensional, these models exhibit a chaotic classical limit and share common characteristics with wave propagation in complex structures.

Weak localization with nonlinear bosonic matter waves

Abstract We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the nonlinear Gross–Pitaevskii equation, we develop a diagrammatic theory for the self-consistent stationary scattering state of the interacting condensate, which is combined with the semiclassical representation of the single-particle Green function in terms of chaotic classical trajectories within the billiard. This analytical approach predicts a universal dephasing of weak localization in the presence of a small interaction strength between the atoms, which is found to be in good agreement with the numerically computed reflection and transmission probabilities of the propagating condensate. The numerical simulation of this quasi-stationary scattering process indicates that this interaction-induced dephasing mechanism may give rise to a signature of weak antilocalization, which we attribute to the influence of non-universal short-path contributions.

Statistics of fluctuation in the response of cavities excited by noisy sources

Emissions from modern electronic circuitry are inherently complex and necessarily statistically characterized. The goal in this work is to characterise such emissions as they operate in a realistic environment. When the surrounding environment is electromagnetically large, or complex, the problem of simulating such emissions is further compounded by the intractability of full EM wave modeling: at high enough frequencies, approximate methods based on ray tracing may be the only feasible approach. In this paper, we present a statistical description of fluctuations in the high-frequency response of complex or ray-chaotic cavities to such stochastic sources. It is based on a method proposed in [1], which exploits information available as a byproduct of ray-tracing simulations to predict in addition to the averaged intensity that is typically obtained directly from ray tracing, higher moments which characterize fluctuations about the mean response. This paper extends that approach to provide full statistical distributions of the intensity when damping is moderate and under assumptions that multiple reflections in the surrounding environment are sufficiently randomizing.

Fluctuation of correlation within enclosures

Emission from complex EM sources may be characterised by measurements of two-point correlations functions, which contain directional as well as positional information for radiated power. When such sources radiate within enclosures, the average power arising from multiple reflection can be modelled by ray tracing techniques. In this paper we describe how a bootstrapping method may be employed which exploits information gained as part of such ray-tracing simulations to provide additional information regarding fluctuation about the mean.

Modelling of high-frequency structure-borne sound transmission on FEM grids using the Discrete Flow Mapping technique

Dynamical Energy Analysis (DEA) combined with the Discrete Flow Mapping technique (DFM) has recently been introduced as a mesh-based high frequency method modelling structure borne sound for complex built-up structures. This has proven to enhance vibro-acoustic simulations considerably by making it possible to work directly on existing finite element meshes circumventing time-consuming and costly re-modelling strategies. In addition, DFM provides detailed spatial information about the vibrational energy distribution within a complex structure in the mid-to-high frequency range. We will present here progress in the development of the DEA method towards handling complex FEM-meshes including Rigid Body Elements. In addition, structure borne transmission paths due to spot welds are considered. We will present applications for a car floor structure.

Discrete Flow Mapping in coupled two and three dimensional domains: a global interface problem

Discrete Flow Mapping (DFM) was recently introduced as a mesh-based high frequency method for modelling structure-borne sound in complex structures comprised of two-dimensional shell and plate subsystems. The method has now been extended to model three-dimensional meshed structures, giving a wider range of applicability and also naturally leading to the question of how to couple the two- and three-dimensional substructures. We consider this problem for the case of a three dimensional interior fluid domain, enclosed by a two dimensional shell/plate system. In Discrete Flow Mapping, the transport of vibrational energy between substructures is typically described via a local interface treatment where wave theory is employed to generate reflection/transmission and mode coupling coefficients. In our case the entire two-dimensional substructure forms a global interface whose radiating properties will depend on both the geometry and the frequency. In this paper we discuss how such a model may be formulated, including both structural radiation and the back-loading of the fluid pressure on the structure.

Intensity distribution of non-linear scattering states

We investigate the interplay between coherent effects characteristic of the propagation of linear waves, the non-linear effects due to interactions, and the quantum manifestations of classical chaos due to geometrical confinement, as they arise in the context of the transport of Bose-Einstein condensates. We specifically show that, extending standard methods for non-interacting systems, the body of the statistical distribution of intensities for scattering states solving the Gross-Pitaevskii equation is very well described by a local Gaussian ansatz with a position-dependent variance. We propose a semiclassical approach based on interfering classical paths to fix the single parameter describing the universal deviations from a global Gaussian distribution. Being tail effects, rare events like rogue waves characteristic of non-linear field equations do not affect our results.