Local characterization of hindered Brownian motion by using digital video microscopy and 3D particle tracking

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.In this article we present methods for measuring hindered Brownian motion in the confinement of complex 3D geometries using digital video microscopy. Here we discuss essential features of automated 3D particle tracking as well as diffusion data analysis. By introducing local mean squared displacement-vs-time curves, we are able to simultaneously measure the spatial dependence of diffusion coefficients, tracking accuracies and drift velocities. Such local measurements allow a more detailed and appropriate description of strongly heterogeneous systems as opposed to global measurements. Finite size effects of the tracking region on measuring mean squared displacements are also discussed. The use of these methods was crucial for the measurement of the diffusive behavior of spherical polystyrene particles (505 nm diameter) in a microfluidic chip. The particles explored an array of parallel channels with different cross sections as well as the bulk reservoirs. For this experiment we present the measurement of local tracking accuracies in all three axial directions as well as the diffusivity parallel to the channel axis while we observed no significant flow but purely Brownian motion. Finally, the presented algorithm is suitable also for tracking of fluorescently labeled particles and particles driven by an external force, e.g., electrokinetic or dielectrophoretic forces.S.L.D. acknowledges funding from the German Academic Exchange Service (DAAD) and the German National Academic Foundation. S.P. and U.F.K. were supported by an ERC starting grant. S.P. also acknowledges the support from the Leverhulme Trust and the Newton Trust through an Early Career Fellowship

Channel-facilitated diffusion boosted by particle binding at the channel entrance

This is the final version of the article. Available from the publisher via the DOI in this record.We investigate single-file diffusion of Brownian particles in arrays of closely confining microchannels permeated by a variety of attractive optical potentials and connecting two baths with equal particle concentration. We simultaneously test free diffusion in the channel, diffusion in optical traps coupled in the center of the channel, and diffusion in traps extending into the baths. We found that both classes of attractive optical potentials enhance the translocation rate through the channel with respect to free diffusion. Surprisingly, for the latter class of potentials we measure a 40-fold enhancement in the translocation rate with respect to free diffusion and find a sublinear power law dependence of the translocation rate on the average number of particles in the channel. Our results reveal the function of particle binding at the channel entrances for diffusive transport and open the way to a better understanding of membrane transport and design of synthetic membranes with enhanced diffusion rate.S. P. acknowledges support from the Leverhulme and Newton Trust through an Early Career Fellowship. S. L. D. acknowledges funding from the German Academic Exchange Service (DAAD) and the German National Academic Foundation. U. F. K. was supported by an ERC starting grant

Phase Fluctuations in Bose-Einstein Condensates

We demonstrate the existence of phase fluctuations in elongated Bose-Einstein Condensates (BECs) and study the dependence of those fluctuations on the system parameters. A strong dependence on temperature, atom number, and trapping geometry is observed. Phase fluctuations directly affect the coherence properties of BECs. In particular, we observe instances where the phase coherence length is significantly smaller than the condensate size. Our method of detecting phase fluctuations is based on their transformation into density modulations after ballistic expansion. An analytic theory describing this transformation is developed.Comment: 11 pages, 7 figure

Localization and Anomalous Transport in a 1-D Soft Boson Optical Lattice

We study the dynamics of Bose-Einstein condensed atoms in a 1-D optical lattice potential in a regime where the collective (Josephson) tunneling energy is comparable with the on-site interaction energy, and the number of particles per lattice site is mesoscopically large. By directly imaging the motion of atoms in the lattice, we observe an abrupt suppression of atom transport through the array for a critical ratio of these energies, consistent with quantum fluctuation induced localization. Directly below the onset of localization, the frequency of the observed superfluid transport can be explained by a phonon excitation but deviates substantially from that predicted by the hydrodynamic/Gross-Pitaevskii equations.Comment: 14 pages, 5 figure

A rare low-grade myofibroblastic sarcoma in lower jaw with the resemblance to benign lesions.

BACKGROUND Low-grade myofibroblastic sarcoma (LGMS) is a rare solid infiltrative soft tissue tumor with a predilection for the head and neck region. CASE PRESENTATION We report the diagnostic steps of a fast-growing lesion of the lower left jaw in a 45-year-old otherwise healthy woman. A first biopsy and subsequent histopathological examination showed potential differentials of a benign myofibroma, benign nodular fasciitis or an LGMS. This diagnostic overlap was a challenge for the decision of the further treatment approach. The treatment consisted of a segmental en bloc resection of the mandible including the second premolar, first and second molar. Histopathological examination of the resected tumor confirmed an LGMS. CONCLUSION The histopathologic resemblance of LGMS to a range of benign and reactive tumors may lead to misdiagnosis and mistreatment. The rarity of LGMS explains the lack of established treatment protocols. This case shows the importance of adequate clinical decisions, expertise in the histopathology of rare tumors and interdisciplinary exchange to achieve state-of-the-art patient management

Dynamics of apparent horizons in quantum gravitational collapse

We study the gravitational collapse of a massless scalar field within the effective scenario of loop quantum gravity. Classical singularity is avoided and replaced by a quantum bounce in this model. It is shown that, quantum gravity effects predict a threshold scale below which no horizon can form as the collapse evolves towards the bounce.Comment: Contribution to the Spanish Relativity Meeting in Portugal 2012 (ERE2012), Guimaraes, Portuga

Maximal length of trapped one-dimensional Bose-Einstein condensates

I discuss a Bogoliubov inequality for obtaining a rigorous bound on the maximal axial extension of inhomogeneous one-dimensional Bose-Einstein condensates. An explicit upper limit for the aspect ratio of a strongly elongated, harmonically trapped Thomas-Fermi condensate is derived.Comment: 6 pages; contributed paper for Quantum Fluids and Solids, Trento 2004, to appear in JLT

The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions

We show that the Lieb-Liniger model for one-dimensional bosons with repulsive $\delta$-function interaction can be rigorously derived via a scaling limit from a dilute three-dimensional Bose gas with arbitrary repulsive interaction potential of finite scattering length. For this purpose, we prove bounds on both the eigenvalues and corresponding eigenfunctions of three-dimensional bosons in strongly elongated traps and relate them to the corresponding quantities in the Lieb-Liniger model. In particular, if both the scattering length $a$ and the radius $r$ of the cylindrical trap go to zero, the Lieb-Liniger model with coupling constant $g \sim a/r^2$ is derived. Our bounds are uniform in $g$ in the whole parameter range $0\leq g\leq \infty$, and apply to the Hamiltonian for three-dimensional bosons in a spectral window of size $\sim r^{-2}$ above the ground state energy.Comment: LaTeX2e, 19 page

Observation of Phase Fluctuations in Bose-Einstein Condensates

The occurrence of phase fluctuations due to thermal excitations in Bose-Einstein condensates (BECs) is studied for a variety of temperatures and trap geometries. We observe the statistical nature of the appearence of phase fluctuations and characterize the dependence of their average value on temperature, number of particles and the trapping potential. We find pronounced phase fluctuations for condensates in very elongated traps in a broad temperature range. The results are of great importance for the realization of BEC in quasi 1D geometries, for matter wave interferometry with BECs, as well as for coherence properties of guided atom laser beams.Comment: 4 pages, 4 figure