1,353 research outputs found
Closed form solution for a double quantum well using Gr\"obner basis
Analytical expressions for spectrum, eigenfunctions and dipole matrix
elements of a square double quantum well (DQW) are presented for a general case
when the potential in different regions of the DQW has different heights and
effective masses are different. This was achieved by Gr\"obner basis algorithm
which allows to disentangle the resulting coupled polynomials without
explicitly solving the transcendental eigenvalue equation.Comment: 4 figures, Mathematica full calculation noteboo
On the numerical evaluation of algebro-geometric solutions to integrable equations
Physically meaningful periodic solutions to certain integrable partial
differential equations are given in terms of multi-dimensional theta functions
associated to real Riemann surfaces. Typical analytical problems in the
numerical evaluation of these solutions are studied. In the case of
hyperelliptic surfaces efficient algorithms exist even for almost degenerate
surfaces. This allows the numerical study of solitonic limits. For general real
Riemann surfaces, the choice of a homology basis adapted to the
anti-holomorphic involution is important for a convenient formulation of the
solutions and smoothness conditions. Since existing algorithms for algebraic
curves produce a homology basis not related to automorphisms of the curve, we
study symplectic transformations to an adapted basis and give explicit formulae
for M-curves. As examples we discuss solutions of the Davey-Stewartson and the
multi-component nonlinear Schr\"odinger equations.Comment: 29 pages, 20 figure
Application of the Frobenius method to the Schrodinger equation for a spherically symmetric potential: anharmonic oscillator
The power series method has been adapted to compute the spectrum of the
Schrodinger equation for central potential of the form . The bound-state energies
are given as zeros of a calculable function, if the potential is confined in a
spherical box. For an unconfined potential the interval bounding the energy
eigenvalues can be determined in a similar way with an arbitrarily chosen
precision. The very accurate results for various spherically symmetric
anharmonic potentials are presented.Comment: 16 pages, 5 figures, published in J. Phys
Neoplastic transformation of porcine mammary epithelial cells in vitro and tumor formation in vivo
Magnetization of a two-dimensional electron gas with a second filled subband
We have measured the magnetization of a dual-subband two-dimensional electron
gas, confined in a GaAs/AlGaAs heterojunction. In contrast to two-dimensional
electron gases with a single subband, we observe non-1/B-periodic, triangularly
shaped oscillations of the magnetization with an amplitude significantly less
than per electron. All three effects are explained by a
field dependent self-consistent model, demonstrating the shape of the
magnetization is dominated by oscillations in the confining potential.
Additionally, at 1 K, we observe small oscillations at magnetic fields where
Landau-levels of the two different subbands cross.Comment: 4 pages, 4 figure
Empagliflozin Use and Fournier’s Gangrene: Case Report and Systematic Literature Review
Background: Fournier’s gangrene (FG) is a rare necrotising soft tissue infection localised in the genital areas with possible dramatic outcomes. Recently, sodium glucose co-transporter-2 (SGLT2) inhibitors were identified as a risk factor. Methods: We present a case report of a 57-year-old female patient with type 2 diabetes mellitus (T2DM) in treatment with empagliflozin which led to the development of FG. Moreover, we performed a systematic review assessing the association between empagliflozin use and FG. Results: The female patient with 15-years treated diabetes presented a massive FG after 6 months from starting empagliflozin. Over the period of two months, she was successfully treated in a low-income setting. The systematic review included two studies with a total of 9915 participants. Although no participant had FG, there was an increased rate of urinary and genital infection in patients treated with empagliflozin compared to those treated with other antidiabetics or placebo. Conclusions: FG should be considered as a possible complication in patients using SGLT2. Patients should be educated to report early signs of genital infection and healthy behaviours as well as a balanced diet should be promoted to aid in the prevention of FG
Comment on Higgs Inflation and Naturalness
We rebut the recent claim (arXiv:0912.5463) that Einstein-frame scattering in
the Higgs inflation model is unitary above the cut-off energy Lambda ~ Mp/xi.
We show explicitly how unitarity problems arise in both the Einstein and Jordan
frames of the theory. In a covariant gauge they arise from non-minimal Higgs
self-couplings, which cannot be removed by field redefinitions because the
target space is not flat. In unitary gauge, where there is only a single scalar
which can be redefined to achieve canonical kinetic terms, the unitarity
problems arise through non-minimal Higgs-gauge couplings.Comment: 5 pages, 1 figure V3: Journal Versio
Off-Critical Logarithmic Minimal Models
We consider the integrable minimal models , corresponding
to the perturbation off-criticality, in the {\it logarithmic
limit\,} , where are coprime and the
limit is taken through coprime values of . We view these off-critical
minimal models as the continuum scaling limit of the
Forrester-Baxter Restricted Solid-On-Solid (RSOS) models on the square lattice.
Applying Corner Transfer Matrices to the Forrester-Baxter RSOS models in Regime
III, we argue that taking first the thermodynamic limit and second the {\it
logarithmic limit\,} yields off-critical logarithmic minimal models corresponding to the perturbation of the critical
logarithmic minimal models . Specifically, in accord with the
Kyoto correspondence principle, we show that the logarithmic limit of the
one-dimensional configurational sums yields finitized quasi-rational characters
of the Kac representations of the critical logarithmic minimal models . We also calculate the logarithmic limit of certain off-critical
observables related to One Point Functions and show that the
associated critical exponents
produce all conformal dimensions in the infinitely extended Kac table. The corresponding Kac labels
satisfy . The exponent is obtained from the logarithmic limit of the free energy giving the
conformal dimension for the perturbing field . As befits a non-unitary
theory, some observables diverge at criticality.Comment: 18 pages, 5 figures; version 3 contains amplifications and minor
typographical correction
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