Berry phase in a non-isolated system

We investigate the effect of the environment on a Berry phase measurement involving a spin-half. We model the spin+environment using a biased spin-boson Hamiltonian with a time-dependent magnetic field. We find that, contrary to naive expectations, the Berry phase acquired by the spin can be observed, but only on timescales which are neither too short nor very long. However this Berry phase is not the same as for the isolated spin-half. It does not have a simple geometric interpretation in terms of the adiabatic evolution of either bare spin-states or the dressed spin-resonances that remain once we have traced out the environment. This result is crucial for proposed Berry phase measurements in superconducting nanocircuits as dissipation there is known to be significant.Comment: 4 pages (revTeX4) 2 fig. This version has MAJOR changes to equation

Water We Putting in the Mohawk

The Hudson River Watershed consists of 11 major sub-watersheds, one of which is the Mohawk River (MKR).1 The Schoharie Creek (SCH) contributes 1,650 of the 4,086 river miles to the Mohawk River watershed, making it the largest contributor to the Mohawk. 2,3 The Cobleskill Creek (CBL), located in Schoharie County, flows in the east-northeast d irection to Schoharie Creek.4 The map shows how the bodies of water flow together to create a large watershed that provides active sites for recreational activities, such as fishing and swimming, across New York State. Since the Cobleskill Creek flows to the Schoharie Creek, which flows in to the Mohawk, the goal of this project is to assess common substances found in each of these rivers. The samples were analyzed to see whether or not these elements and compounds get carried from one body of water to the next due to their interconnected nature.https://digitalworks.union.edu/waterprojectposters/1005/thumbnail.jp

Dessins, their delta-matroids and partial duals

Given a map $\mathcal M$ on a connected and closed orientable surface, the delta-matroid of $\mathcal M$ is a combinatorial object associated to $\mathcal M$ which captures some topological information of the embedding. We explore how delta-matroids associated to dessins d'enfants behave under the action of the absolute Galois group. Twists of delta-matroids are considered as well; they correspond to the recently introduced operation of partial duality of maps. Furthermore, we prove that every map has a partial dual defined over its field of moduli. A relationship between dessins, partial duals and tropical curves arising from the cartography groups of dessins is observed as well.Comment: 34 pages, 20 figures. Accepted for publication in the SIGMAP14 Conference Proceeding

Scaling and the Metal-Insulator Transition in Si/SiGe Quantum Wells

The existence of a metal-insulator transition at zero magnetic field in two- dimensional electron systems has recently been confirmed in high mobility Si-MOSFETs. In this work, the temperature dependence of the resistivity of gated Si/SiGe/Si quantum well structures has revealed a similar metal- insulator transition as a function of carrier density at zero magnetic field. We also report evidence for a Coulomb gap in the temperature dependence of the resistivity of the dilute 2D hole gas confined in a SiGe quantum well. In addition, the resistivity in the insulating phase scales with a single parameter, and is sample independent. These results are consistent with the occurrence of a metal-insulator transition at zero magnetic field in SiGe square quantum wells driven by strong hole-hole interactions.Comment: 3 pages, 3 figures, LaTe

Nerve-targeted probes for fluorescence-guided intraoperative imaging.

A fundamental goal of many surgeries is nerve preservation, as inadvertent injury can lead to patient morbidity including numbness, pain, localized paralysis and incontinence. Nerve identification during surgery relies on multiple parameters including anatomy, texture, color and relationship to surrounding structures using white light illumination. We propose that fluorescent labeling of nerves can enhance the contrast between nerves and adjacent tissue during surgery which may lead to improved outcomes. Methods: Nerve binding peptide sequences including HNP401 were identified by phage display using selective binding to dissected nerve tissue. Peptide dye conjugates including FAM-HNP401 and structural variants were synthesized and screened for nerve binding after topical application on fresh rodent and human tissue and in-vivo after systemic IV administration into both mice and rats. Nerve to muscle contrast was quantified by measuring fluorescent intensity after topical or systemic administration of peptide dye conjugate. Results: Peptide dye conjugate FAM-HNP401 showed selective binding to human sural nerve with 10.9x fluorescence signal intensity (1374.44 ± 425.96) compared to a previously identified peptide FAM-NP41 (126.17 ± 61.03). FAM-HNP401 showed nerve-to-muscle contrast of 3.03 ± 0.57. FAM-HNP401 binds and highlight multiple human peripheral nerves including lower leg sural, upper arm medial antebrachial as well as autonomic nerves isolated from human prostate. Conclusion: Phage display has identified a novel peptide that selectively binds to ex-vivo human nerves and in-vivo using rodent models. FAM-HNP401 or an optimized variant could be translated for use in a clinical setting for intraoperative identification of human nerves to improve visualization and potentially decrease the incidence of intra-surgical nerve injury

Can the trace formula describe weak localisation?

We attempt to systematically derive perturbative quantum corrections to the Berry diagonal approximation of the two-level correlation function (TLCF) for chaotic systems. To this end, we develop a ``weak diagonal approximation'' based on a recent description of the first weak localisation correction to conductance in terms of the Gutzwiller trace formula. This semiclassical method is tested by using it to derive the weak localisation corrections to the TLCF for a semiclassically disordered system. Unfortunately the method is unable to correctly reproduce the ``Hikami boxes'' (the relatively small regions where classical paths are glued together by quantum processes). This results in the method failing to reproduce the well known weak localisation expansion. It so happens that for the first order correction it merely produces the wrong prefactor. However for the second order correction, it is unable to reproduce certain contributions, and leads to a result which is of a different form to the standard one.Comment: 23 pages in Latex (with IOP style files), 3 eps figures included, to be a symposium paper in a Topical Issue of Waves in Random Media, 199

Form factor for a family of quantum graphs: An expansion to third order

For certain types of quantum graphs we show that the random-matrix form factor can be recovered to at least third order in the scaled time $\tau$ from periodic-orbit theory. We consider the contributions from pairs of periodic orbits represented by diagrams with up to two self-intersections connected by up to four arcs and explain why all other diagrams are expected to give higher-order corrections only. For a large family of graphs with ergodic classical dynamics the diagrams that exist in the absence of time-reversal symmetry sum to zero. The mechanism for this cancellation is rather general which suggests that it may also apply at higher-orders in the expansion. This expectation is in full agreement with the fact that in this case the linear-$\tau$ contribution, the diagonal approximation, already reproduces the random-matrix form factor for $\tau<1$. For systems with time-reversal symmetry there are more diagrams which contribute at third order. We sum these contributions for quantum graphs with uniformly hyperbolic dynamics, obtaining $+2\tau^{3}$, in agreement with random-matrix theory. As in the previous calculation of the leading-order correction to the diagonal approximation we find that the third order contribution can be attributed to exceptional orbits representing the intersection of diagram classes.Comment: 23 pages (including 4 fig.) - numerous typos correcte

Application of Discrete Differential Forms to Spherically Symmetric Systems in General Relativity

In this article we describe applications of Discrete Differential Forms in computational GR. In particular we consider the initial value problem in vacuum space-times that are spherically symmetric. The motivation to investigate this method is mainly its manifest coordinate independence. Three numerical schemes are introduced, the results of which are compared with the corresponding analytic solutions. The error of two schemes converges quadratically to zero. For one scheme the errors depend strongly on the initial data.Comment: 22 pages, 6 figures, accepted by Class. Quant. Gra