Search results for " Fisica Matematica"
showing 10 items of 384 documents
Effective thermal conductivity of superuid helium: Laminar, turbulent and ballistic regimes
2016
Abstract In this paper we extend previous results on the effective thermal conductivity of liquid helium II in cylindrical channels to rectangular channels with high aspect ratio. The aim is to compare the results in the laminar regime, the turbulent regime and the ballistic regime, all of them obtained within a single mesoscopic formalism of heat transport, with heat flux as an independent variable.
Wavelet-like orthonormal bases for the lowest Landau level
1994
As a first step in the description of a two-dimensional electron gas in a magnetic field, such as encountered in the fractional quantum Hall effect, we discuss a general procedure for constructing an orthonormal basis for the lowest Landau level, starting from an arbitrary orthonormal basis in L2(R). We discuss in detail two relevant examples coming from wavelet analysis, the Haar and the Littlewood-Paley bases.
Two-Parameters Pseudo-Bosons
2010
We construct a two-parameters example of {\em pseudo-bosons}, and we show that they are not regular, in the sense previously introduced by the author. In particular, we show that two biorthogonal bases of $\Lc^2(\Bbb R)$ can be constructed, which are not Riesz bases, in general.
Some analytical considerations on two-scale relations
1994
Scaling functions that generate a multiresolution analysis (MRA) satisfy, among other conditions, the so-called «two-scale relation» (TSR). In this paper we discuss a number of properties that follow from the TSR alone, independently of any MRA: position of zeros (mainly for continuous scaling functions), existence theorems (using fixed point and eigenvalue arguments) and orthogonality relation between integer translates. © 1994 Società Italiana di Fisica.
Applications of wavelets to quantum mechanics: A pedagogical example
1995
We discuss in many details two quantum mechanical models of planar electrons which are very much related to the Fractional Quantum Hall Effect. In particular, we discuss the localization properties of the trial ground states of the models starting from considerations on the numerical results on the energy. We conclude that wavelet theory can be conveniently used in the description of the system. Finally we suggest applications of our results to the Fractional Quantum Hall Effect.
A mathematical description of glitches in neutron stars
2017
In a pulsar, there are gaps and difficulties in our knowledge of glitches, mainly because of the absence of information about the physics of the matter of the star. This has motivated several authors to suggest dynamical models that interpret most of the astronomical data. Many predictions are based on the assumption that the inner part is analogous to the structure of matter of superfluids. Here, we illustrate a new mathematical model, partially inspired by the dynamics of superfluid helium. We obtain two evolution equations for the angular velocities (of the crust and of superfluid), which are supported by another evolution equation for the average vortex line length per unit volume. This…
Vortex density waves and high-frequency second sound in superfluid turbulence hydrodynamics
2010
In this paper we show that a recent hydrodynamical model of superfluid turbulence describes vortex density waves and their effects on the speed of high-frequency second sound. In this frequency regime, the vortex dynamics is not purely diffusive, as for low frequencies, but exhibits ondulatory features, whose influence on the second sound is here explored.
Energy of string loops and thermodynamics of dark energy
2011
We discuss the thermodynamic aspects of a simple model of cosmic string loops, whose energy is nonlinearly related to their lengths. We obtain in a direct way an equation of state having the form p=-(1+{alpha}){rho}/3, with {rho} the energy density and 1+{alpha} the exponent which relates the energy u{sub l} of a loop with its length l as u{sub l}{approx}l{sup 1+{alpha}}. In the linear situation ({alpha}=0) one has p=-{rho}/3, in the quadratic one ({alpha}=1) p=-2{rho}/3, and in the cubic case ({alpha}=2) p=-{rho}. For all values of {alpha} the entropy goes as S{approx}(2-{alpha})L{sup 3/2} (L being the string length density). The expression of S is useful to explore the behavior of such st…
Duality-invariant Einstein-Planck relation and the speed of light at very short wavelengths
2011
We propose a generalized Einstein-Planck relation for photons which is invariant under the change $\ensuremath{\lambda}/a{l}_{P}$ to $a{l}_{P}/\ensuremath{\lambda}$, $\ensuremath{\lambda}$ being the photon wavelength, ${l}_{P}$ Planck's length, and $a$ a numerical constant. This yields a wavelength-dependent speed of light $v(\ensuremath{\lambda})=c/(1+{a}^{2}({l}_{P}/\ensuremath{\lambda}{)}^{2})$, with $c$ the usual speed of light in vacuo, indicating that the speed of light should decrease for sufficiently short wavelengths. We discuss the conceptual differences with the previous proposals related to a possible decrease of the speed of light for very short wavelengths based on quantum flu…
Relations between the Hepp-Lieb and the Alli-Sewell Laser Models
2009
In this paper we show that the dissipative version of the laser model proposed by Alli and Sewell can be obtained by considering the stochastic limit of the (open system) hamiltonian introduced by Hepp and Lieb in their seminal work. We also prove that the Dicke-Haken-Lax hamiltonian produces, after the stochastic limit is considered, the generator of a semigroup with equations of motion very similar to those of Alli-Sewell, and coinciding with these under suitable conditions.