677 research outputs found
Nonperturbative Quantum Physics from Low-Order Perturbation Theory
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish
examples of quantum systems where the perturbation results in a certain
ionization probability by tunneling processes. Accordingly, the perturbed
ground-state energy is shifted and broadened, thus acquiring an imaginary part
which is considered to be a paradigm of nonperturbative behavior. Here we
demonstrate how the low order coefficients of a divergent perturbation series
can be used to obtain excellent approximations to both real and imaginary parts
of the perturbed ground state eigenenergy. The key is to use analytic
continuation functions with a built in analytic structure within the complex
plane of the coupling constant, which is tailored by means of Bender-Wu
dispersion relations. In the examples discussed the analytic continuation
functions are Gauss hypergeometric functions, which take as input fourth order
perturbation theory and return excellent approximations to the complex
perturbed eigenvalue. These functions are Borel-consistent and dramatically
outperform widely used Pad\'e and Borel-Pad\'e approaches, even for rather
large values of the coupling constant.Comment: 5 pages, 3 figures, PDFLaTe
Hypergeometric resummation of self-consistent sunset diagrams for electron-boson quantum many-body systems out of equilibrium
A newly developed hypergeometric resummation technique [H. Mera et al., Phys.
Rev. Lett. 115, 143001 (2015)] provides an easy-to-use recipe to obtain
conserving approximations within the self-consistent nonequilibrium many-body
perturbation theory. We demonstrate the usefulness of this technique by
calculating the phonon-limited electronic current in a model of a
single-molecule junction within the self-consistent Born approximation for the
electron-phonon interacting system, where the perturbation expansion for the
nonequilibrium Green function in powers of the free bosonic propagator
typically consists of a series of non-crossing \sunset" diagrams.
Hypergeometric resummation preserves conservation laws and it is shown to
provide substantial convergence acceleration relative to more standard
approaches to self-consistency. This result strongly suggests that the
convergence of the self-consistent \sunset" series is limited by a branch-cut
singularity, which is accurately described by Gauss hypergeometric functions.
Our results showcase an alternative approach to conservation laws and
self-consistency where expectation values obtained from conserving perturbation
expansions are \summed" to their self-consistent value by analytic continuation
functions able to mimic the convergence-limiting singularity structure.Comment: 13 pages, 6 figure
WKB Approximation to the Power Wall
We present a semiclassical analysis of the quantum propagator of a particle
confined on one side by a steeply, monotonically rising potential. The models
studied in detail have potentials proportional to for ; the
limit would reproduce a perfectly reflecting boundary, but at
present we concentrate on the cases and 2, for which exact
solutions in terms of well known functions are available for comparison. We
classify the classical paths in this system by their qualitative nature and
calculate the contributions of the various classes to the leading-order
semiclassical approximation: For each classical path we find the action ,
the amplitude function and the Laplacian of . (The Laplacian is of
interest because it gives an estimate of the error in the approximation and is
needed for computing higher-order approximations.) The resulting semiclassical
propagator can be used to rewrite the exact problem as a Volterra integral
equation, whose formal solution by iteration (Neumann series) is a
semiclassical, not perturbative, expansion. We thereby test, in the context of
a concrete problem, the validity of the two technical hypotheses in a previous
proof of the convergence of such a Neumann series in the more abstract setting
of an arbitrary smooth potential. Not surprisingly, we find that the hypotheses
are violated when caustics develop in the classical dynamics; this opens up the
interesting future project of extending the methods to momentum space.Comment: 30 pages, 8 figures. Minor corrections in v.
Alat Bantu Pengajaran Interaktif Teknik Digital Berbasis Web
Karnaugh Map (K-map), a method to simplify the logic equations in a logic circuit, was a compulsory topic on Digital Electronics\u27 subject, yet the learning process in TE-PNJ was still done manually. Therefore, the result of this research was a web-based software which was used as an interactive tool for teaching K-map. Furthermore, the main purpose of that tool was so that the learning process becomes more attractive, easily understood, and interactive for the students. Besides that, a web-based programming was applied to build that so it was considered as an open source application. More over, It could simplify logic circuits with 2 to 4 input variables and DON\u27T CARE conditions. In addition, it could display both input and output logic equations and also number of logic gates (AND, OR and NOT) contained in each of those logic equations.
Keywords: K-map, variable input , DON\u27T CARE conditions, logic gate
Analisis Penerapan Metode Konvolusi Untuk Untuk Reduksi Derau Pada Citra Digital
Noise in digital image processing is a disorder caused by deviations of the data received. There are three types of noise, Additive, Gaussian and Speckle. Currently, there are many methods for reducing noise in digital images. One method that can be used for reducing noise is convolution method, which consists of Low Pass Filter, High Pass Filter, Median Filter, Mean Filter and Gaussian Filter. This research will analyze an output by applying the convolution method for noise reduction with various parameters such as histogram, Timing- Run calculation and SNR calculation. Noise reduction will be imposed on the three types of noise.
Keywords : digital image, noise reduction, convolution method, histogram, Timing-Run, SNR
Asymptotic self-consistency in quantum transport calculations
Ab initio simulations of quantum transport commonly focus on a central region which is considered to be connected to infinite leads through which the current flows. The electronic structure of these distant leads is normally obtained from an equilibrium calculation, ignoring the self-consistent response of the leads to the current. We examine the consequences of this, and show that the electrostatic potential Delta phi is effectively being approximated by the difference between electrochemical potentials Delta mu, and that this approximation is incompatible with asymptotic charge neutrality. In a test calculation for a simple metal-vacuum-metal junction, we find significant errors in the nonequilibrium properties calculated with this approximation, in the limit of small vacuum gaps. We provide a scheme by which these errors may be corrected
Fast Summation of Divergent Series and Resurgent Transseries in Quantum Field Theories from Meijer-G Approximants
We demonstrate that a Meijer-G-function-based resummation approach can be
successfully applied to approximate the Borel sum of divergent series, and thus
to approximate the Borel-\'Ecalle summation of resurgent transseries in quantum
field theory (QFT). The proposed method is shown to vastly outperform the
conventional Borel-Pad\'e and Borel-Pad\'e-\'Ecalle summation methods. The
resulting Meijer-G approximants are easily parameterized by means of a
hypergeometric ansatz and can be thought of as a generalization to arbitrary
order of the Borel-Hypergeometric method [Mera {\it et al.} Phys. Rev. Lett.
{\bf 115}, 143001 (2015)]. Here we illustrate the ability of this technique in
various examples from QFT, traditionally employed as benchmark models for
resummation, such as: 0-dimensional theory, with degenerate
minima, self-interacting QFT in 0-dimensions, and the computation of one- and
two-instanton contributions in the quantum-mechanical double-well problem.Comment: 18 pages, 9 figures, PDFTe
Stark effect in low-dimension hydrogen
Studies of atomic systems in electric fields are challenging because of the
diverging perturbation series. However, physically meaningful Stark shifts and
ionization rates can be found by analytical continuation of the series using
appropriate branch cut functions. We apply this approach to low-dimensional
hydrogen atoms in order to study the effects of reduced dimensionality. We find
that modifications by the electric field are strongly suppressed in reduced
dimensions. This finding is explained from a Landau-type analysis of the
ionization process
Current Applications of Mesenchymal Stem Cells for Cartilage Tissue Engineering
Articular cartilage injuries caused by traumatic/mechanical progressive degeneration result in joint pain, swelling, the consequent loss of joint function, and eventually osteoarthritis. Articular tissue possesses a poor ability to regenerate that further complicates the therapeutic approaches. Mesenchymal stem cells (MSCs) have emerged as a promising alternative treatment. Recently, it has been reported that a wide variety of strategies ranging from merely using cells in the injured area to employ biofunctional substitutes in which cells are harmonizing with scaffolding and growth factors to create an engineered cartilage tissue
Porosities and dimensions of measures
We introduce a concept of porosity for measures and study relations between
dimensions and porosities for two classes of measures: measures on which
satisfy the doubling condition and strongly porous measures on .Comment: Jarvenpaa = J\"arvenp\"a\"
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