Condensate deformation and quantum depletion of Bose-Einstein condensates in external potentials

The one-body density matrix of weakly interacting, condensed bosons in external potentials is calculated using inhomogeneous Bogoliubov theory. We determine the condensate deformation caused by weak external potentials on the mean-field level. The momentum distribution of quantum fluctuations around the deformed ground state is obtained analytically, and finally the resulting quantum depletion is calculated. The depletion due to the external potential, or potential depletion for short, is a small correction to the homogeneous depletion, validating our inhomogeneous Bogoliubov theory. Analytical results are derived for weak lattices and spatially correlated random potentials, with simple, universal results in the Thomas-Fermi limit of very smooth potentials.Comment: 17 pages, 4 figures. v2: published version, minor change

Rotordynamic Computation of a Permanent-Magnetic excited Synchronous Machine due to Electromagnetic Force Excitation

For the acoustical computation of electromagnetic noise, it is very important to consider both, the rotor and stator vibrations of the electrical machine. Rotor vibrations can be transmitted as structure-borne sound to connected systems which might be excited at their resonances and radiate airborne sound. In order to predict the dynamical behaviour of complex electrical machine rotors (such like rotors of permanent-magnetic excited synchronous machines) in frequency domain, finite element (FE) computations can be efficiently applied using rotating coordinates. Hereby, it has to be taken into account that rotor vibrations are mainly influenced by stiffness and damping of the built-in laminated stacks and mechanical joints. Therefore, a FE model of the rotor is required which takes these parameters into account. In order to obtain the material properties, two experimental set-ups are considered. On the one hand, a generic lap joint is considered to determine the stiffness and damping of mechanical joints. On the other hand, a test rig for laminated stacks is presented which allows for the determination of direction-dependent stiffness and damping of laminated stacks by a shear and dilatation test. All identified parameters are included into the FE model. Thereby, local stiffness and damping of mechanical joints are modelled by so-called thin-layer elements. In order to prove the quality of the rotor FE model, a numerical modal analysis without considering rotor spin speed is carried out and compared to experimental results. Electromagnetic force densities are computed in the air gap of the electrical machine using an electromagnetic FE model. To cover different FE meshes of the mechanical and electromagnetic model, a method is presented which allows for converting force densities into equivalent nodal forces on the rotor surface. These excitation forces are used to compute electromagnetically caused rotor vibrations dependent on rotor spin speed by a frequency domain rotor dynamic analysis

Spin foam model from canonical quantization

We suggest a modification of the Barrett-Crane spin foam model of 4-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found as a space of the so-called projected spin networks. These spin networks are identified with the boundary states of a spin foam model and provide a generalization of the unique Barrette-Crane intertwiner. We propose a way to modify the Barrett-Crane quantization procedure to arrive at this generalization: the B field (bi-vectors) should be promoted not to generators of the gauge algebra, but to their certain projection. The modification is also justified by the canonical analysis of Plebanski formulation. Finally, we compare our construction with other proposals to modify the Barret-Crane model.Comment: 26 pages; presentation improved, important changes concerning the closure constraint and the vertex amplitude; minor correctio

On the Universality of the Entropy-Area Relation

We present an argument that, for a large class of possible dynamics, a canonical quantization of gravity will satisfy the Bekenstein-Hawking entropy-area relation. This result holds for temperatures low compared to the Planck temperature and for boundaries with areas large compared to Planck area. We also relate our description, in terms of a grand canonical ensemble, to previous geometric entropy calculations using area ensembles.Comment: 6 page

Harmonic Balance and Averaging Techniques for Stick-Slip Limit-Cycle Determination in Mode-Coupling Friction Self-Excited Systems

A minimal model for mode-coupling friction induced instability with Coulomb-type frictional nonlinearity is set up to investigate the applicability and quality of approximative methods to determine the limit cycles of unstable system configurations. It turns out that - due to the multi-degree-of-freedom nature of the mode-coupling instability - harmonic balance approaches yield reasonable results only if applied carefully, i.e. with respect to the special effects of the nonlinearities under consideration. The Krylov-Bogoliubov-Mitropolsky approach yields good results in a straightforward manner, the technique is however formally much more cumbersome

Xenopus Development from Late Gastrulation to Feeding Tadpole in Simulated Microgravity

Microgravity (microG) is known to influence cytoskeletal structure, but its effects on cell migration are not well understood. To examine the effects of altered gravity on neural crest cell (NCC) migration, we inserted Xenopus laevis embryos into two separate microG-simulating slow turning lateral vessels (STLVs) just before neurulation (stage 11-12), and exposed them until feeding stage (stage 45), when the jaws and branchial apparatus are fully functional. To evaluate apparatus-related artifacts, we used two different STLVs and a vibration control as well as a stationary control vessel. Larval growth, pattern of NCC-derived cartilage formation, and incidence of malformations were analyzed using immunolocalization and wholemount staining of cartilage with Alcian blue. Interestingly, the two STLVs often yielded different or conflicting results. Many differences, such as increased cartilage size, attenuated Hoxa2 expression, and increased cell division, may be attributed mainly to vibration of the rotating vessels. However, tadpoles that developed in simulated microgravity (both STLVs, but not the vibration control) showed significantly more skeletal abnormalities, with stronger effects on cartilages derived from NCCs than those derived mainly from mesoderm. We conclude that migrating NCCs of Xenopus are sensitive to the altered gravitational environment of STLVs, and that studies relying on bioreactors to simulate microgravity also need to take variation in apparatus into account

A generalized Hamiltonian Constraint Operator in Loop Quantum Gravity and its simplest Euclidean Matrix Elements

We study a generalized version of the Hamiltonian constraint operator in nonperturbative loop quantum gravity. The generalization is based on admitting arbitrary irreducible SU(2) representations in the regularization of the operator, in contrast to the original definition where only the fundamental representation is taken. This leads to a quantization ambiguity and to a family of operators with the same classical limit. We calculate the action of the Euclidean part of the generalized Hamiltonian constraint on trivalent states, using the graphical notation of Temperley-Lieb recoupling theory. We discuss the relation between this generalization of the Hamiltonian constraint and crossing symmetry.Comment: 35 pp, 20 eps figures; minor corrections, references added; version to appear in Class. Quant. Gra

Anisotropic scattering of Bogoliubov excitations

We consider elementary excitations of an interacting Bose-Einstein condensate in the mean-field framework. As a building block for understanding the dynamics of systems comprising interaction and disorder, we study the scattering of Bogoliubov excitations by a single external impurity potential. A numerical integration of the Gross-Pitaevskii equation shows that the single-scattering amplitude has a marked angular anisotropy. By a saddle-point expansion of the hydrodynamic mean-field energy functional, we derive the relevant scattering amplitude including the crossover from sound-like to particle-like excitations. The very different scattering properties of these limiting cases are smoothly connected by an angular envelope function with a well-defined node of vanishing scattering amplitude. We find that the overall scattering is most efficient at the crossover from phonon-like to particle-like Bogoliubov excitations.Comment: 5 pages, 5 figure

Regularized Hamiltonians and Spinfoams

We review a recent proposal for the regularization of the scalar constraint of General Relativity in the context of LQG. The resulting constraint presents strengths and weaknesses compared to Thiemann's prescription. The main improvement is that it can generate the 1-4 Pachner moves and its matrix elements contain 15j Wigner symbols, it is therefore compatible with the spinfoam formalism: the drawback is that Thiemann anomaly free proof is spoiled because the nodes that the constraint creates have volume.Comment: 4 pages, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS