Gregor Veble

Edge states for the turbulence transition in the asymptotic suction boundary layer

We study the transition to turbulence in the asymptotic suction boundary layer (ASBL) by direct numerical simulation. Tracking the motion of trajectories intermediate between laminar and turbulent ...

Expanded boundary integral method and chaotic time-reversal doublets in quantum billiards

We present the expanded boundary integral method for solving the planar Helmholtz problem, which combines the ideas of the boundary integral method and the scaling method and is applicable to arbitrary shapes. We apply the method to a chaotic billiard with unidirectional transport, where we demonstrate the existence of doublets of chaotic eigenstates, which are quasi-degenerate due to time-reversal symmetry, and a very particular level spacing distribution that attains a chaotic Shnirelman peak at short energy ranges and exhibits Gaussian Unitary Ensemble (GUE) like statistics for large energy ranges. We show that, as a consequence of such particular level statistics or algebraic tunnelling between disjoint chaotic components connected by time-reversal operation, the system exhibits quantum current reversals.

Dispersion interactions in stratified anisotropic and optically active media at all separations

We propose a method to calculate dispersion interactions in a system composed of a one dimensional layering of finite thickness anisotropic and optically active slabs. The result is expressed within the algebra of 4x4 matrices and is demonstrated to be equivalent to the known limits of isotropic, nonretarded and uniaxial dispersion interactions. The method is also capable of handling dielectric media with smoothly varying anisotropy axes.

The boundary element approach to Van der Waals interactions

Abstract.We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response of a general boundary shape. We achieve this by rewriting the interaction energy expression presented in Phys. Rev. B, 62 (2000) 6997 exclusively in terms of surface integrals of surface operators. We validate this approach in the Lifshitz case and give numerical results for the interaction of two spheres as well as the van der Waals self-interaction of a uniaxial ellipsoid. Our method is simple to implement and is particularly suitable for a full, non-perturbative numerical evaluation of non-retarded van der Waals interactions between objects of a completely general shape.

Ray-trace modeling of acoustic Green's function based on the semiclassical (eikonal) approximation

The Greens function (GF) for the scalar wave equation is numerically constructed by an advanced geometric ray-tracing method based on the eikonal approximation related to the semiclassical propagator. The underlying theory is first briefly introduced, and then it is applied to acoustics and implemented in a ray-tracing-type numerical simulation. The so constructed numerical method is systematically used to calculate the sound field in a rectangular (cuboid) room, yielding also the acoustic modes of the room. The simulated GF is rigorously compared to its analytic approximation. Good agreement is found, which proves the devised numerical approach potentially useful also for low frequency acoustic modeling, which is in practice not covered by geometrical methods.

Self-consistent inhomogeneous dielectric response profiles from a nonlocal continuous Lifshitz formulation of van der Waals interactions

We show that a nonlocal formulation of the Lifshitz theory of van der Waals interactions valid for continuous dielectric profiles can be used as a starting point to calculateself-consistent dielectric profiles. The general approach advocated here is very close to the formulation of electrostatic self-consistent charge density profiles obtained from the Poisson - Boltzmann theory. The calculated dielectric profiles obtained from minimization of the free energy containing a lattice gas entropy contribution on top of the Lifshitz interaction energy give quite surprising and interesting results. The ramifications of these results for the distribution of polarizable matter between two homogeneous dielectric slabs will be discussed in detail.

Comparison of density functional theory and field approaches to van der Waals interactions in plan parallel geometry

We establish a general equivalence between van der Waals interaction energies within the formalism of the nonlocal van der Waals functional of the density functional theory and within the formalism of the field approach based on the secular determinants of the electromagnetic field modes. We then compare the two methods explicitly in the case of a plan parallel geometry with a continuously varying dielectric response function and show that their respective numerical implementations are not equivalent. This allows us to discuss the merits of the two approaches and possible advantages of either method in a simple model calculation.