arXiv subjects
Publications and source records attributed to Paolo Amore.
We propose an approximate solution of the time-dependent Schrödinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of the method by applying it to the time development of the wave-function in the quantum-mechanical version of the inflationary slow-roll transition.
A method devised by the author is used to calculate analytical expressions for one loop integrals at finite temperature. A non-perturbative regularization of the integrals is performed, yielding expressions of non-polynomial nature. A comparison with previuosly published results is presented and the advantages of the present technique are discussed.
We introduce the study of neutrino scattering off protons in the deeply virtual kinematics, which describes under a unified formalism elastic and deep inelastic neutrino scattering. A real final state photon and a recoiling nucleon are detected in the few GeV ($|t|\sim 0.2-5$ GeV) region of momentum transfer. This is performed via an extension of the notion of deeply virtual Compton scattering, or DVCS, to the case of a neutral current exchange. The relevance of this process and of other similar exclusive processes for the study of neutrino interactions in neutrino factories for GeV neutrinos is pointed out.
Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly convergent series, completely analytical, which can be used to obtain arbitrarily accurate estimates of $Γ(a,x)$ for any value of $a$ or $x$. Applications of these formulas are discussed.
We discuss and compare two alternative perturbation approaches for the calculation of the period of nonlinear systems based on the Lindstedt--Poincaré technique. As illustrative examples we choose one--dimensional anharmonic oscillators and the Van der Pol equation. Our results show that each approach is better for just one type of model considered here.
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be greatly improved by means of a variational parameter in the basis functions determined by the principle of minimal sensitivity. In the case of the quartic anharmonic oscillator and of a symmetrical double-well potential we choose an effective oscillator frequency. In the case of nonsymmetrical potential we add a coordinate shift in a two-parameter variational calculation. The method not only gives the spectrum, but also an approximation to the energy eigenfunctions. Consequently it can be used to solve the time-dependent Schrödinger equation using the method of stationary states. We apply it to the time development of two different initial wave functions in the double-well slow roll potential.
We discuss two alternative methods, based on the Lindstedt--Poincaré technique, for the removal of secular terms from the equations of perturbation theory. We calculate the period of an anharmonic oscillator by means of both approaches and show that one of them is more accurate for all values of the coupling constant.
In many physical problems it is not possible to find an exact solution. However, when some parameter in the problem is small, one can obtain an approximate solution by expanding in this parameter. This is the basis of perturbative methods, which have been applied and developed practically in all areas of Physics. Unfortunately many interesting problems in Physics are of non-perturbative nature and it is not possible to gain insight on these problems only on the basis of perturbation theory: as a matter of fact it often happens that the perturbative series are not even convergent. In this paper we will describe a method which allows to obtain arbitrarily precise analytical approximations for the period of a classical oscillator. The same method is then also applied to obtain an analytical approximation to the spectrum of a quantum anharmonic potential by using it with the WKB method. In all these cases we observe exponential rates of convergence to the exact solutions. An application of the method to obtain a fastly convergent series for the Riemann zeta function is also discussed.
In this paper we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulas for the period of anharmonic oscillators and other problems of interest in classical mechanics.
We apply a method recently devised by one of the authors to obtain an approximate analytical formula for the spectrum of a quantum anharmonic potential. Due to its general features the method can be applied with minimal effort to general quantum potentials thus allowing very promising applications.
In this paper we generalize and improve a method for calculating the period of a classical oscillator and other integrals of physical interest, which was recently developed by some of the authors. We derive analytical expressions that prove to be more accurate than those commonly found in the literature, and test the convergence of the series produced by the approach.
We develop a simple method to obtain approximate analytical expressions for the period of a particle moving in a given potential. The method is inspired to the Linear Delta Expansion (LDE) and it is applied to a large class of potentials. Precise formulas for the period are obtained.
In this letter we apply a method recently devised in \cite{aapla03} to find precise approximate solutions to a certain class of nonlinear differential equations. The analysis carried out in \cite{aapla03} is refined and results of much higher precision are obtained for the problems previously considered (Duffing equation, sextic oscillator). Fast convergence to the exact results is observed both for the frequency and for the Fourier coefficients. The method is also applied with success to more general polynomial potentials (the octic oscillator) and to the Van Der Pol equation.
We perform a study of various anharmonic potentials using a recently developed method. We calculate both the wave functions and the energy eigenvalues for the ground and first excited states of the quartic, sextic and octic potentials with high precision, comparing the results with other techniques available in the literature.
We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wave function and, finally, a short distance scale, in which the wave function is sizable. The key feature of our method is the introduction of an arbitrary parameter in the last two scales, which is then used to optimize a perturbative expansion in a suitable parameter. We apply the method to the quantum anharmonic oscillator and find excellent results.
We apply the Linear Delta Expansion (LDE) to the Lindstedt-Poincare (``distorted time'') method to find improved approximate solutions to nonlinear problems. We find that our method works very well for a wide range of parameters in the case of the anharmonic oscillator (Duffing equation) and of the non-linear pendulum. The approximate solutions found with this method are better behaved and converge more rapidly to the exact ones than in the simple Lindstedt-Poincaré method.
We present a method for the resolution of (oscillatory) nonlinear problems. It is based on the application of the Linear Delta Expansion to the Lindstedt-Poincaré method. By applying it to the Duffing equation, we show that our method substantially improves the approximation given by the simple Lindstedt-Poincaré method.
In this paper we study the effect of finite size on the two-flavour colour superconducting state. As well as restricting the quarks to a box, we project onto states of good baryon number and onto colour singlets, these being necessary restrictions on any observable ``quark nuggets''. We find that whereas finite size alone has a significant effect for very small boxes, with the superconducting state often being destroyed, the effect of projection is to restore it again. The infinite-volume limit is a good approximation even for quite small systems.