A random wave model for the Aharonov-Bohm effect

We study an ensemble of random waves subject to the Aharonov-Bohm effect. The introduction of a point with a magnetic flux of arbitrary strength into a random wave ensemble gives a family of wavefunctions whose distribution of vortices (complex zeros) are responsible for the topological phase associated with the Aharonov-Bohm effect. Analytical expressions are found for the vortex number and topological charge densities as functions of distance from the flux point. Comparison is made with the distribution of vortices in the isotropic random wave model. The results indicate that as the flux approaches half-integer values, a vortex with the same sign as the fractional part of the flux is attracted to the flux point, merging with it at half-integer flux. Other features of the Aharonov-Bohm vortex distribution are also explored.Comment: 16 pages, 5 figure

Spacetime structure and vacuum entanglement

We study the role that both vacuum fluctuations and vacuum entanglement of a scalar field play in identifying the spacetime topology, which is not prescribed from first principles---neither in general relativity or quantum gravity. We analyze how the entanglement and observable correlations acquired between two particle detectors are sensitive to the spatial topology of spacetime. We examine the detector's time evolution to all orders in perturbation theory and then study the phenomenon of vacuum entanglement harvesting in Minkowski spacetime and two flat topologically distinct spacetimes constructed from identifications of the Minkowski space. We show that, for instance, if the spatial topology induces a preferred direction, this direction may be inferred from the dependence of correlations between the two detectors on their orientation. We therefore show that vacuum fluctuations and vacuum entanglement harvesting makes it, in principle, possible to distinguish spacetimes with identical local geometry that differ only in their topology

A wave function based ab initio non-equilibrium Green's function approach to charge transport

We present a novel ab initio non-equilibrium approach to calculate the current across a molecular junction. The method rests on a wave function based description of the central region of the junction combined with a tight binding approximation for the electrodes in the frame of the Keldysh Green's function formalism. In addition we present an extension so as to include effects of the two-particle propagator. Our procedure is demonstrated for a dithiolbenzene molecule between silver electrodes. The full current-voltage characteristic is calculated. Specific conclusions for the contribution of correlation and two-particle effects are derived. The latter are found to contribute about 5% to the current. The order of magnitude of the current coincides with experiments.Comment: 21 pages, 3 figure

Resolution of Nested Neuronal Representations Can Be Exponential in the Number of Neurons

Collective computation is typically polynomial in the number of computational elements, such as transistors or neurons, whether one considers the storage capacity of a memory device or the number of floating-point operations per second of a CPU. However, we show here that the capacity of a computational network to resolve real-valued signals of arbitrary dimensions can be exponential in N, even if the individual elements are noisy and unreliable. Nested, modular codes that achieve such high resolutions mirror the properties of grid cells in vertebrates, which underlie spatial navigation

Optimal Population Codes for Space: Grid Cells Outperform Place Cells

Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal’s position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population. We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, using maximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial “tuning curves” for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons

Polaron Physics in Optical Lattices

We investigate the effects of a nearly uniform Bose-Einstein condensate (BEC) on the properties of immersed trapped impurity atoms. Using a weak-coupling expansion in the BEC-impurity interaction strength, we derive a model describing polarons, i.e., impurities dressed by a coherent state of Bogoliubov phonons, and apply it to ultracold bosonic atoms in an optical lattice. We show that, with increasing BEC temperature, the transport properties of the impurities change from coherent to diffusive. Furthermore, stable polaron clusters are formed via a phonon-mediated off-site attraction.Comment: 4 pages, 4 figure

Vitamin D3receptor is highly expressed in Hodgkin’s lymphoma

BACKGROUND: Hodgkin lymphoma (HL) is one of the most frequent lymphoma in the western world. Despite a good overall prognosis, some patients suffer relapsing tumors which are difficult to cure. Over a long period Vitamin D has been shown to be a potential treatment for cancer. Vitamin D acts via the vitamin D receptor, a nuclear receptor, acting as an inducible transcription factor. We aimed to investigate the expression of vitamin D receptor as a possible diagnostic marker and potential therapeutic target in HL as well as in B-cell derived non-Hodgkin lymphoma (B-NHL). METHODS: We used a panel of 193 formalin fixed tissues of lymphoma cases consisting of 55 cases of HL and 138 cases on several B-NHL entities. RESULTS: Vitamin D receptor is strongly expressed in tumor cells of HL, regardless of the sub entity with an overall positivity of 80% of all HL cases. In contrast, only about 17% of the analyzed origin-NHL showed positivity for vitamin D receptor. The detection of nuclear localization of vitamin D receptor in the tumor cells of HL suggests activated status of the vitamin D receptor. CONCLUSIONS: Our study suggests VDR as a specific marker for tumor cells of HL, but not of B-NHL subtypes. Further, the observed nuclear localization suggests an activated receptor status in tumor cells of HL. Further investigations of mutational status and functional studies may shed some light in functional relevance of vitamin D receptor signaling in HL

How frequent are close supermassive binary black holes in powerful jet sources?

24 pages, 36 figures. © 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)Supermassive black hole binariesmay be detectable by an upcoming suite of gravitationalwave experiments. Their binary nature can also be revealed by radio jets via a short-period precession driven by the orbital motion as well as the geodetic precession at typically longer periods. We have investigated Karl G. Jansky Very Large Array and Multi-Element Radio Linked Interferometer Network (MERLIN) radio maps of powerful jet sources for morphological evidence of geodetic precession. For perhaps the best-studied source, Cygnus A, we find strong evidence for geodetic precession. Projection effects can enhance precession features, for which we find indications in strongly projected sources. For a complete sample of 33 3CR radio sources, we find strong evidence for jet precession in 24 cases (73 per cent). The morphology of the radio maps suggests that the precession periods are of the order of 10 6- 10 7 yr. We consider different explanations for the morphological features and conclude that geodetic precession is the best explanation. The frequently observed gradual jet angle changes in samples of powerful blazars can be explained by orbital motion. Both observations can be explained simultaneously by postulating that a high fraction of powerful radio sources have subparsec supermassive black hole binaries.We consider complementary evidence and discuss if any jetted supermassive black hole with some indication of precession could be detected as individual gravitational wave source in the near future. This appears unlikely, with the possible exception of M87.Peer reviewedFinal Published versio