Search results for " Fisica Matematica"

Phase transition in liquid 4HE by a mean field model

2013

In this work the transition of 4He at the lambda line in presence of a Cattaneo- Maxwell heat flux is studied. A hydrodynamical model is formulated, which chooses as fundamental fields the velocity, the temperature, the heat flux and a phase field function f, for which a time dependent Ginzburg-Landau equation is proposed. Using this model we are able to describe the phase transition and to obtain the pressure-temperature phase diagram which represents the transition, the thermodynamic restrictions and a maximum theorem for the phase field.

Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians

2015

We discuss systematically several possible inequivalent ways to describe the dynamics and the transition probabilities of a quantum system when its hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly restrict our analysis to finite dimensional Hilbert spaces. In particular, we propose some experiments which could discriminate between the various possibilities considered in the paper. An example taken from the literature is discussed in detail.

The Stochastic Limit of the Fröhlich Hamiltonian: Relations with the Quantum Hall Effect

2003

We propose a model of an approximatively two-dimensional electron gas in a uniform electric and magnetic field and interacting with a positive background through the Fröhlich Hamiltonian. We consider the stochastic limit of this model and we find the quantum Langevin equation and the generator of the master equation. This allows us to calculate the explicit form of the conductivity and the resistivity tensors and to deduce a fine tuning condition (FTC) between the electric and the magnetic fields. This condition shows that the x-component of the current is zero unless a certain quotient, involving the physical parameters, takes values in a finite set of physically meaningful rational number…

Waves Propagation in Turbulent Superfluid Helium in Presence of Combined Rotation and Counterflow

2010

A complete study of the propagation of waves (namely longitudinal density and temperature waves, longitudinal and transversal velocity waves and heat waves) in turbulent superfluid helium is made in three situations: a rotating frame, a thermal counterflow, and the simultaneous combination of thermal counterflow and rotation. Our analysis aims to obtain as much as possible information on the tangle of quantized vortices from the wave speed and attenuation factor of these different waves, depending on their relative direction of propagation with respect to the rotation vector.

Singular behavior of a vortex layer in the zero thickness limit

2017

The aim of this paper is to study the Euler dynamics of a 2D periodic layer of non uniform vorticity. We consider the zero thickness limit and we compare the Euler solution with the vortex sheet evolution predicted by the Birkhoff-Rott equation. The well known process of singularity formation in shape of the vortex sheet correlates with the appearance of several complex singularities in the Euler solution with the vortex layer datum. These singularities approach the real axis and are responsible for the roll-up process in the layer motion.

Nonstandard analysis in classical physics and quantum formal scattering

1988

After a rigorous introduction to hyperreal numbers, we give in terms of non standard analysis, (1) a Lagrangian statement of classical physics, and (2) a statement of formal quantum scattering. © 1988 Plenum Publishing Corporation.

Supersymmetric associated vector coherent states and generalized Landau levels arising from two-dimensional supersymmetry

2008

We describe a method for constructing vector coherent states for quantum supersymmetric partner Hamiltonians. The method is then applied to such partner Hamiltonians arising from a generalization of the fractional quantum Hall effect. Explicit examples are worked out.

Super-critical and sub-critical bifurcations in a reaction-diffusion Schnakenberg model with linear cross-diffusion

2016

In this paper the Turing pattern formation mechanism of a two components reaction-diffusion system modeling the Schnakenberg chemical reaction is considered. In Ref. (Madzavamuse et al., J Math Biol 70(4):709–743, 2015) it was shown how the presence of linear cross-diffusion terms favors the destabilization of the constant steady state. We perform the weakly nonlinear multiple scales analysis to derive the equations for the amplitude of the Turing patterns and to show how the cross-diffusion coefficients influence the occurrence of super-critical or sub-critical bifurcations. We present a numerical exploration of far from equilibrium regimes and prove the existence of multistable stationary…

Hydrodynamic Equations of Anisotropic, Polarized, Turbulent Superfluids

2009

HYDRODYNAMICAL MODELS OF SUPERFLUID TURBULENCE

2011

This review paper puts together some of our results concerning the application of non equilibrium Thermodynamics to superfluid liquid helium. Two of the most important situations of this quantum fluid are rotating superfluid and superfluid turbulence, both characterized by the presence of quantized vortices (vortex lines whose core is about 1 Angstrom and the quantum of circulation is $h/m$, $h$ being the Plank's constant and $m$ the mass of helium atom). In the first part of the work a non-standard model of superfluid helium, which considers heat flux as independent variable, is briefly recalled, and compared with the well known two-fluid model, in absence of vortices, proposed by Tisza an…