Probing a topological quantum critical point in semiconductor-superconductor heterostructures

Quantum ground states on the non-trivial side of a topological quantum critical point (TQCP) have unique properties that make them attractive candidates for quantum information applications. A recent example is provided by s-wave superconductivity on a semiconductor platform, which is tuned through a TQCP to a topological superconducting (TS) state by an external Zeeman field. Despite many attractive features of TS states, TQCPs themselves do not break any symmetries, making it impossible to distinguish the TS state from a regular superconductor in conventional bulk measurements. Here we show that for the semiconductor TQCP this problem can be overcome by tracking suitable bulk transport properties across the topological quantum critical regime itself. The universal low-energy effective theory and the scaling form of the relevant susceptibilities also provide a useful theoretical framework in which to understand the topological transitions in semiconductor heterostructures. Based on our theory, specific bulk measurements are proposed here in order to characterize the novel TQCP in semiconductor heterostructures.Comment: 8+ pages, 5 figures, Revised version as accepted in PR

How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array

Semiconducting nanowires in proximity to superconductors are promising experimental systems for Majorana fermions, which may ultimately be used as building blocks for topological quantum computers. A serious challenge in the experimental realization of the Majorana fermions is the supression of topological superconductivity by disorder. We show that Majorana fermions protected by a robust topological gap can occur at the ends of a chain of quantum dots connected by s-wave superconductors. In the appropriate parameter regime, we establish that the quantum dot/superconductor system is equivalent to a 1D Kitaev chain, which can be tuned to be in a robust topological phase with Majorana end modes even in the case where the quantum dots and superconductors are both strongly disordered. Such a spin-orbit coupled quantum dot - s-wave superconductor array provides an ideal experimental platform for the observation of non-Abelian Majorana modes.Comment: 8 pages; 3 figures; version 2: Supplementary material updated to include more general proof for localized Majorana fermion

Solidarity in Creation: Toward an Ecological Ethic for Christian Discipleship

Thesis advisor: Mary Ann HinsdaleThesis advisor: Richard J. CliffordThesis (STL) — Boston College, 2017.Submitted to: Boston College. School of Theology and Ministry.Discipline: Sacred Theology

Fokker-Planck equation with variable diffusion coefficient in the Stratonovich approach

We consider the Langevin equation with multiplicative noise term which depends on time and space. The corresponding Fokker-Planck equation in Stratonovich approach is investigated. Its formal solution is obtained for an arbitrary multiplicative noise term given by $g(x,t)=D(x)T(t)$, and the behaviors of probability distributions, for some specific functions of $D(x)$% , are analyzed. In particular, for $D(x)\sim | x| ^{-\theta /2}$, the physical solutions for the probability distribution in the Ito, Stratonovich and postpoint discretization approaches can be obtained and analyzed.Comment: 6 pages in LATEX cod

Compound Logics for Modification Problems

We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of sentences, expressing graph modification: the modulator sentence, defining some property of the modified part of the graph, and the target sentence, defining some property of the resulting graph. In our framework, modulator sentences are in counting monadic second-order logic (CMSOL) and have models of bounded treewidth, while target sentences express first-order logic (FOL) properties along with minor-exclusion. Our logic captures problems that are not definable in first-order logic and, moreover, may have instances of unbounded treewidth. Also, it permits the modeling of wide families of problems involving vertex/edge removals, alternative modulator measures (such as elimination distance or $\mathcal{G}$-treewidth), multistage modifications, and various cut problems. Our main result is that, for this compound logic, model-checking can be done in quadratic time. All derived algorithms are constructive and this, as a byproduct, extends the constructibility horizon of the algorithmic applications of the Graph Minors theorem of Robertson and Seymour. The proposed logic can be seen as a general framework to capitalize on the potential of the irrelevant vertex technique. It gives a way to deal with problem instances of unbounded treewidth, for which Courcelle's theorem does not apply. The proof of our meta-theorem combines novel combinatorial results related to the Flat Wall theorem along with elements of the proof of Courcelle's theorem and Gaifman's theorem. We finally prove extensions where the target property is expressible in FOL+DP, i.e., the enhancement of FOL with disjoint-paths predicates

A Case of Multiple Myeloma Presenting with Diabetes Insipidus

Multiple myeloma (MM) can present with involvement of the central nervous system in the form of nerve palsy, plasma cell masses or, rarely, with endocrinological effects due to involvement of the pituitary gland. Usually, in such cases, the disease has a rapid progression and poor prognosis. We report a 52-year-old man who was admitted to the Kolkata Medical College, Kolkata, India, in 2016 with a prolonged low-grade fever and hypernatremia. Shortly afterwards, the patient began to complain of increased urinary frequency and drowsiness. The hypernatremia was treated with intranasal desmopressin and free water replacement. Serum protein electrophoresis and an immunofixation study revealed an immunoglobulin G-κ monoclonal band. Magnetic resonance imaging of the pituitary gland revealed the absence of a posterior bright spot and spotty infiltration of the pituitary fossa. A bone marrow biopsy confirmed a diagnosis of cranial diabetes insipidus due to posterior pituitary MM infiltration

Prospects for the Search for a Standard Model Higgs Boson in ATLAS using Vector Boson Fusion

The potential for the discovery of a Standard Model Higgs boson in the mass range m_H < 2 m_Z in the vector boson fusion mode has been studied for the ATLAS experiment at the LHC. The characteristic signatures of additional jets in the forward regions of the detector and of low jet activity in the central region allow for an efficient background rejection. Analyses for the H -> WW and H -> tau tau decay modes have been performed using a realistic simulation of the expected detector performance. The results obtained demonstrate the large discovery potential in the H -> WW decay channel and the sensitivity to Higgs boson decays into tau-pairs in the low-mass region around 120 GeV.Comment: 20 pages, 13 ps figures, uses EPJ style fil

Topological properties of superconducting junctions

Motivated by recent developments in the field of one-dimensional topological superconductors, we investigate the topological properties of s-matrix of generic superconducting junctions where dimension should not play any role. We argue that for a finite junction the s-matrix is always topologically trivial. We resolve an apparent contradiction with the previous results by taking into account the low-energy resonant poles of s-matrix. Thus no common topological transition occur in a finite junction. We reveal a transition of a different kind that concerns the configuration of the resonant poles