The “Forgotten” Pseudomomenta and Gauge Changes in Generalized Landau Level Problems: Spatially Nonuniform Magnetic and Temporally Varying Electric Fields

By perceiving gauge invariance as an analytical tool in order to get insight into the states of the “generalized Landau problem” (a charged quantum particle moving inside a magnetic, and possibly electric field), and motivated by an early article that correctly warns against a naive use of gauge transformation procedures in the usual Landau problem (i.e. with the magnetic field being static and uniform), we first show how to bypass the complications pointed out in that article by solving the problem in full generality through gauge transformation techniques in a more appropriate manner. Our solution provides in simple and closed analytical forms all Landau Level-wavefunctions without the need to specify a particular vector potential. This we do by proper handling of the so-called pseudomomentum \(\vec {{K}}\) (or of a quantity that we term pseudo-angular momentum L _z ), a method that is crucially different from the old warning argument, but also from standard treatments in textbooks and in research literature (where the usual Landau-wavefunctions are employed - labeled with canonical momenta quantum numbers). Most importantly, we go further by showing that a similar procedure can be followed in the more difficult case of spatially-nonuniform magnetic fields: in such case we define \(\vec {{K}}\) and L _z as plausible generalizations of the previous ordinary case, namely as appropriate line integrals of the inhomogeneous magnetic field – our method providing closed analytical expressions for all stationary state wavefunctions in an easy manner and in a broad set of geometries and gauges. It can thus be viewed as complementary to the few existing works on inhomogeneous magnetic fields, that have so far mostly focused on determining the energy eigenvalues rather than the corresponding eigenkets (on which they have claimed that, even in the simplest cases, it is not possible to obtain in closed form the associated wavefunctions). The analytical forms derived here for these wavefunctions enable us to also provide explicit Berry’s phase calculations and a quick study of their connection to probability currents and to some recent interesting issues in elementary Quantum Mechanics and Condensed Matter Physics. As an added feature, we also show how the possible presence of an additional electric field can be treated through a further generalization of pseudomomenta and their proper handling.     

An efficient string sorting algorithm for weighing matrices of small weight

In this paper, we demonstrate that the search for weighing matrices of small weights constructed from two circulants can be viewed as a string sorting problem together with a linear time algorithm to locate common strings in two sorted arrays. We also introduce a sparse encoding of the periodic autocorrelation function vector, based on concepts from Algorithmic Information Theory, also known as Kolmogorov complexity, that allows us to speed up the algorithm considerably. Finally, we use these ideas to find new weighing matrices W(2 · n, 9) constructed from two circulants, for many values of n in the range 100 ≤  n ≤  300. These matrices are given here for the first time. We also discuss briefly a connection with Combinatorial Optimization.     

Extremal metrics for the first eigenvalue of the Laplacian in a conformal class

Let be a compact manifold. First, we give necessary and sufficient conditions for a Riemannian metric on to be extremal for with respect to conformal deformations of fixed volume. In particular, these conditions show that for any lattice of , the flat metric induced on from the standard metric of is extremal (in the previous sense). In the second part, we give, for any , an upper bound of on the conformal class of and exhibit a class of lattices for which the metric maximizes on its conformal class.

     

Lumina: an adaptive,automated and extensible prototype for exploring,enriching and visualizing data

Journal of Visualization - Given a tabular dataset which should be graphically represented, how could the current complex visualization pipeline be improved? Could we produce a more visually...     

Jahn-Teller and related effects in the silver trimer. II: vibrational analysis of the A 2E"-X 2E' electronic transition

The laser-excited, jet-cooled A 2E"-X 2E' electronic spectrum of the silver trimer yields detailed information about its A- and X-state vibronic structure. Following extensive parameter fitting, the absorption and emission spectra are simulated and the bands are assigned. The Jahn-Teller analysis includes both linear and quadratic coupling terms, considered simultaneously with spin-orbit coupling. The spin-orbit splitting is shown to be largely quenched in both the A and X electronic states. The Jahn-Teller analysis of the A and X vibronic structures reveals the distortion of their corresponding potential energy surfaces.     

Electrocatalytic Functionalized Specialty Paper as Low-Cost Porous Transport Layer Material in CO2-Electrolysis

The development of low-cost and efficient electrolyzer components is crucial for practical electrochemical carbon dioxide reduction (ECR). In this study, facile non-woven cellulose-based porous transport layers (PTLs) were developed for high current density CO₂-to-CO conversion. By depositing a cobalt phthalocyanine (CoPc) catalyst-layer over the PTLs, we fabricated ECR-functioning gas-diffusion-electrodes (GDEs) for both flow-cell and zero-gap electrolyzers. Under optimal conditions, the Faradaic efficiency of CO (FE_CO) reached 92 % at a high current density of 200 mA cm⁻². Furthering the architecture of the GDEs, CoPc was incorporated into the initial PTL slurry, forming ECR-active PTLs without the need for an additional catalyst-layer. The new GDE-architecture favored the CoPc-distribution by enhancing the contact and interactions with the carbon substrate and demonstrated a stable electrolysis process for over 50 h in a zero-gap cell at 200 mA cm⁻² with a FE_CO of 80 %.     

Natural Products Inhibitors of Monoamine Oxidases—Potential New Drug Leads for Neuroprotection,Neurological Disorders,and Neuroblastoma

Monoamine oxidase inhibitors (MAOIs) are an important class of drugs prescribed for treatment of depression and other neurological disorders. Evidence has suggested that patients with atypical depression preferentially respond to natural product MAOIs. This review presents a comprehensive survey of the natural products, predominantly from plant sources, as potential new MAOI drug leads. The psychoactive properties of several traditionally used plants and herbal formulations were attributed to their MAOI constituents. MAO inhibitory constituents may also be responsible for neuroprotective effects of natural products. Different classes of MAOIs were identified from the natural product sources with non-selective as well as selective inhibition of MAO-A and -B. Selective reversible natural product MAOIs may be safer alternatives to the conventional MAOI drugs. Characterization of MAO inhibitory constituents of natural products traditionally used as psychoactive preparations or for treatment of neurological disorders may help in understanding the mechanism of action, optimization of these preparations for desired bioactive properties, and improvement of the therapeutic potential. Potential therapeutic application of natural product MAOIs for treatment of neuroblastoma is also discussed.     

Experimental investigation of the Jahn-Teller effect in the ground and excited electronic states of the tropyl radical. Part II. Vibrational analysis of the A 2E"3-X 2E"2 electronic transition

Laser-induced fluorescence (LIF) and laser-excited dispersed fluorescence (LEDF) spectra of the cycloheptatrienyl (tropyl) radical C7H7 have been observed under supersonic jet-cooling conditions. Assignment of the LIF excitation spectrum yields detailed information about the A-state vibronic structure. The LEDF emission was collected by pumping different vibronic bands of the A 2E"3<--X 2E"2 electronic spectrum. Analysis of the LEDF spectra yields valuable information about the vibronic levels of the X 2E"2 state. The X- and A-state vibronic structures characterize the Jahn-Teller distortion of the respective potential energy surfaces. A thorough analysis reveals observable Jahn-Teller activity in three of the four e'3 modes for the X 2E"2 state and two of the three e'1 modes for the A 2E"3 state and provides values for their deperturbed vibrational frequencies as well as linear Jahn-Teller coupling constants. The molecular parameters characterizing the Jahn-Teller interaction in the X and A states of C7H7 are compared to theoretical results and to those previously obtained for C5H5 and C6H6+.     

Caccioppoli’s inequalities on constant mean curvature hypersurfaces in Riemannian manifolds

We prove some Caccioppoli’s inequalities for the traceless part of the second fundamental form of a complete, noncompact, finite index, constant mean curvature hypersurface of a Riemannian manifold, satisfying some curvature conditions. This allows us to unify and clarify many results scattered in the literature and to obtain some new results. For example, we prove that there is no stable, complete, noncompact hypersurface in ${{\mathbb R}^{n+1}, n \leq 5}$ , with constant mean curvature ${H \not=0}$ , provided that, for suitable p, the L ^p norm of the traceless part of second fundamental form satisfies some growth condition.