Comparing a current-carrying circular wire with polygons of equal perimeter; Magnetic field versus magnetic flux

We compare the magnetic field at the center of and the self-magnetic flux through a current-carrying circular loop, with those obtained for current-carrying polygons with the same perimeter. As the magnetic field diverges at the position of the wires, we compare the self-fluxes utilizing several regularization procedures. The calculation is best performed utilizing the vector potential, thus highlighting its usefulness in practical applications. Our analysis answers some of the intuition challenges students face when they encounter a related simple textbook example. These results can be applied directly to the determination of mutual inductances in a variety of situations.Comment: 9 pages, 4 figure

Auxiliary field method and analytical solutions of the Schr\"{o}dinger equation with exponential potentials

The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schr\"{o}dinger equation with exponential potentials of the form $-\alpha r^\lambda \exp(-\beta r)$ can also be analytically solved by using the auxiliary field method. Formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn on the Yukawa potential and the pure exponential one

Duality relations in the auxiliary field method

The eigenenergies $\epsilon^{(N)}(m;\{n_i,l_i\})$ of a system of $N$ identical particles with a mass $m$ are functions of the various radial quantum numbers $n_i$ and orbital quantum numbers $l_i$. Approximations $E^{(N)}(m;Q)$ of these eigenenergies, depending on a principal quantum number $Q(\{n_i,l_i\})$, can be obtained in the framework of the auxiliary field method. We demonstrate the existence of numerous exact duality relations linking quantities $E^{(N)}(m;Q)$ and $E^{(p)}(m';Q')$ for various forms of the potentials (independent of $m$ and $N$) and for both nonrelativistic and semirelativistic kinematics. As the approximations computed with the auxiliary field method can be very close to the exact results, we show with several examples that these duality relations still hold, with sometimes a good accuracy, for the exact eigenenergies $\epsilon^{(N)}(m;\{n_i,l_i\})$

Tetraquark bound states in a constituent quark model and the nature of the a_0(980) and f_0(980)

In this work we study tetraquark bound states in the framework of the constituent quark model of Ref. [2], which has been used for the description of non-strange two- and three-baryon systems and later on applied to the hadron spectra.Comment: Contribution to the MESON 2002 Workshop. Krakow 24-28 May 200

Extensions of the auxiliary field method to solve Schr\"{o}dinger equations

It has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schr\"{o}dinger equation. This technique can generate the spectrum associated with an arbitrary potential $V(r)$ starting from the analytically known spectrum of a particular potential $P(r)$. In the present work, general important properties of the auxiliary field method are proved, such as scaling laws and independence of the results on the choice of $P(r)$. The method is extended in order to find accurate analytical energy formulae for radial potentials of the form $a P(r)+V(r)$, and several explicit examples are studied. Connections existing between the perturbation theory and the auxiliary field method are also discussed

Full-vector analysis of a realistic photonic crystal fiber

We analyze the guiding problem in a realistic photonic crystal fiber using a novel full-vector modal technique, a biorthogonal modal method based on the nonselfadjoint character of the electromagnetic propagation in a fiber. Dispersion curves of guided modes for different fiber structural parameters are calculated along with the 2D transverse intensity distribution of the fundamental mode. Our results match those achieved in recent experiments, where the feasibility of this type of fiber was shown.Comment: 3 figures, submitted to Optics Letter

Price level convergence, purchasing power parity and multiple structural breaks: An application to US cities

This article provides a fresh methodological and empirical approach for assessing price level convergence and its relation to purchasing power parity (PPP) using annual price data for seventeen US cities. We suggest a new procedure that can handle a wide range of PPP concepts in the presence of multiple structural breaks using all possible pairs of real exchange rates. To deal with cross-sectional dependence, we use both cross-sectional demeaned data and a parametric bootstrap approach. In general, we find more evidence for stationarity when the parity restriction is not imposed, while imposing parity restriction provides leads toward the rejection of the panel stationarity. Our results can be embedded on the view of the Balassa-Samuelson approach, but where the slope of the time trend is allowed to change in the long-run. The median half-life point estimate are found to be lower than the consensus view regardless of the parity restriction.