Search results for " Fisica Matematica"
showing 10 items of 384 documents
Generation of Frames
2004
It is well known that, given a generic frame, there exists a unique frame operator which satisfies, together with its adjoint, a double operator inequality. In this paper we start considering the inverse problem, that is how to associate a frame to certain operators satisfying the same kind of inequality. The main motivation of our analysis is the possibility of using frame theory in the discussion of some aspects of the quantum time evolution, both for open and for closed physical systems.
A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
2012
Abstract We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.
Analytic solutions and Singularity formation for the Peakon b--Family equations
2012
This paper deals with the well-posedness of the b-family equation in analytic function spaces. Using the Abstract Cauchy-Kowalewski theorem we prove that the b-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to H s with s>3/2, and the momentum density u 0-u 0, xx does not change sign, we prove that the solution stays analytic globally in time, for b≥1. Using pseudospectral numerical methods, we study, also, the singularity formation for the b-family equations with the singularity tracking method. This method allows us to follow the process of the singularity formation in the complex plane as the singularity a…
Some remarks on few recent results on the damped quantum harmonic oscillator
2020
Abstract In a recent paper, Deguchi et al. (2019), the authors proposed an analysis of the damped quantum harmonic oscillator in terms of ladder operators. This approach was shown to be partly incorrect in Bagarello et al. (2019), via a simple no-go theorem. More recently, (Deguchi and Fujiwara, 2019), Deguchi and Fujiwara claimed that our results in Bagarello et al. (2019) are wrong, and compute what they claim is the square integrable vacuum of their annihilation operators. In this brief note, we show that their vacuum is indeed not a vacuum, and we try to explain what is behind their mistakes in Deguchi et al. (2019) and Deguchi and Fujiwara (2019). We also propose a very simple example …
Solutions via double wave ansatz to the 1-D non-homogeneous gas-dynamics equations
2020
Abstract In this paper classes of double wave solutions of the 1D Euler system describing a ideal fluid in the non-homogeneous case have been determined. In order that the analytical procedure under interest to hold, suitable model laws for the source term involved in the governing model were characterized. Finally such a class of exact double wave solutions has been used for solving some problems of interest in nonlinear wave propagation.
Thermal duality and thermodynamics of micro black holes
2015
Starting from a generalized black hole entropy with logarithmic area corrections, in this paper we obtain (for positive value of the coefficient of the correction term) a generalized equation of state for black holes with two dual branches. In one of them (the usual one for macro black holes) T ≃ 1/M, with T temperature and M mass. In the other one, for micro black holes, instead, T ≃ M. We compare the equilibrium and stability between macro black holes and electromagnetic radiation in a finite box with reflecting walls, with the dual situation corresponding to micro black holes and cosmic string loops, also in a finite box. In this model, the dual phenomenon of evaporation of unstable mac…
Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems
2001
We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to determine the threshold of the break-up of invariant tori with a specific frequency vector. We apply two techniques: the frequency map analysis and renormalization-group methods. The renormalization transformation acting on a Hamiltonian is a canonical change of coordinates which is a combination of a partial elimination of the irrelevant modes of the Hamiltonian and a rescaling of phase space around the considered torus. We give numerical evidence that the critical coupling at which the renormalization transformation starts to diverg…
Dynamics of Confined Crowd Modelled Using Fermionic Operators
2014
An operatorial method based on fermionic operators is used to describe the dynamics of a crowd made of different kind of populations mutually interacting and moving in a two–dimensional bounded closed region. The densities of the populations are recovered through the Heisenberg equation and the diffusion process is driven by the Hamiltonian operator defined by requiring that the populations move along optimal paths. We apply the model obtained in a concrete situation and we discuss the effect of the interaction between the populations during their motion.
Large-scale normal fluid circulation in helium superflows
2017
We perform fully-coupled numerical simulations of helium II pure superflows in a channel, with vortex- line density typical of experiments. Peculiar to our model is the computation of the back-reaction of the superfluid vortex motion on the normal fluid and the presence of solid boundaries. We recover the uniform vortex-line density experimentally measured employing second sound resonators and we show that pure superflow in helium II is associated with a large-scale circulation of the normal fluid which can be detected using existing particle-tracking visualization techniques.
Alternative Vinen equation and its extension to rotating counterflow superfluid turbulence
2007
Two alternative Vinen's evolution equations for the vortex line density L in counterflow superfluid turbulence, are physically admissible and lead to analogous results in steady states. In Phys. Rev. B, 69, 094513 (2004) the most used of them was generalized to counterflow superfluid turbulence in rotating containers. Here, the analogous generalization for the alternative Vinen's equation is proposed. Both generalized Vinen's equations are compared with the experimental results, not only in steady-states but also in some unsteady situations. From this analysis follows that the solutions of the alternative Vinen's equation tend significantly faster to the corresponding final steady state val…