arXiv subjects

L. Moriconi

Publications and source records attributed to L. Moriconi.

47 records · Page 3Linked to original sources

arXiv2004

Statistics of Intense Turbulent Vorticity Events

We investigate statistical properties of vorticity fluctuations in fully developed turbulence, which are known to exhibit a strong intermittent behavior. Taking as the starting point the Navier-Stokes equations with a random force term correlated at large scales, we obtain in the high Reynolds number regime a closed analytical expression for the probability distribution function of an arbitrary component of the vorticity field. The central idea underlying the analysis consists in the phase-space restriction to a particular sector where the rate of strain and the rotation tensors can be locally regarded as slow and fast degrees of freedom, respectively. This prescription is implemented along the Martin-Siggia-Rose functional framework, whereby instantons and perturbations around them are taken into account within a steepest-descent approach.

cond-mat.stat-mech↗

arXiv2003

Hidden Scaling in the Quantum Hall Metal-Insulator Transition

Scaling properties of the quantum Hall metal-insulator transition are severely affected by finite size effects in small systems. Surprisingly, despite the narrow spatial range where probability structure functions exhibit multifractal scaling, we clearly verify the existence of extended self-similarity -- a hidden infrared scaling phenomenon related to the peculiar form of the crossover at the onset of nonmultifractal behavior. As finite size effects get stronger for structure functions with negative orders, the parabolic approximation for the multifractal spectrum loses accuracy. However, by means of an extended self-similarity analysis, an improved evaluation of the multifractal exponents is attained for negative orders too, rendering them consistent with previous results, which rely on computations performed for considerably larger systems.

cond-mat.mes-hall↗

arXiv2003

Extended Self-Similarity in the Two-Dimensional Metal-Insulator Transition

We show that extended self-similarity, a scaling phenomenon firstly observed in classical turbulent flows, holds for a two-dimensional metal-insulator transition that belongs to the universality class of random Dirac fermions. Deviations from multifractality, which in turbulence are due to the dominance of diffusive processes at small scales, appear in the condensed matter context as a large scale, finite size effect related to the imposition of an infra-red cutoff in the field theory formulation. We propose a phenomenological interpretation of extended self-similarity in the metal-insulator transition within the framework of the random $β$-model description of multifractal sets. As a natural step our discussion is bridged to the analysis of strange attractors, where crossovers between multifractal and non-multifractal regimes are found and extended self-similarity turns to be verified as well.

cond-mat.dis-nn↗

arXiv2002

Circulation-Strain Sum Rule in Stochastic Magnetohydrodynamics

We study probability density functions (pdfs) of the circulation of velocity and magnetic fields in magnetohydrodynamics, computed for a circular contour within inertial range scales. The analysis is based on the instanton method as adapted to the Martin-Siggia-Rose field theory formalism. While in the viscous limit the expected gaussian behaviour of fluctuations is indeed verified, the case of vanishing viscosity is not suitable of a direct saddle-point treatment. To study the latter limit, we take into account fluctuations around quasi-static background fields, which allows us to derive a sum rule relating pdfs of the circulation observables and the rate of the strain tensor. A simple inspection of the sum rule definition leads straightforwardly to the algebraic decay $ρ(Γ) \sim 1/ Γ^2$ at the circulation pdf tails.

cond-mat.dis-nn↗

arXiv2001

Phase Space Reduction and the Instanton Crossover in (1+1)-Dimensional Turbulence

We study (1+1)-dimensional turbulence in the framework of the Martin-Siggia-Rose field theory formalism. The analysis is focused on the asymptotic behaviour at the right tail of the probability distribution function (pdf) of velocity differences, where shock waves do not contribute. A BRS-preserving scheme of phase space reduction, based on the smoothness of the relevant velocity fields, leads to an effective theory for a few degrees of freedom. The sum over fluctuations around the instanton solution is written as the expectation value of a functional of the time-dependent physical fields, which evolve according to a set of Langevin equations. A natural regularization of the fluctuation determinant is provided from the fact that the instanton dominates the action for a finite time interval. The transition from the turbulent to the instanton dominated regime is related to logarithmic corrections to the saddle-point action, manifested on their turn as multiplicative power law corrections to the velocity differences pdf.

cond-mat.dis-nn↗

arXiv2001

Charge Density Wave-Assisted Tunneling Between Hall Edge States

We study the intra-planar tunneling between quantum Hall samples separated by a quasi one-dimensional barrier, induced through the interaction of edge degrees of freedom with the charge density waves of a Hall crystal defined in a parallel layer. A field theory formulation is set up in terms of bosonic (2+1)-dimensional excitations coupled to (1+1)-dimensional fermions. Parity symmetry is broken at the quantum level by the confinement of soliton-antisoliton pairs near the tunneling region. The usual Peierls argument allows to estimate the critical temperature $T_c$, so that for $T > T_c$ mass corrections due to longitudinal density fluctuations disappear from the edge spectrum. We compute the gap dependence upon the random global phase of the pinned charge density wave, as well as the effects of a voltage bias applied across the tunneling junction.

cond-mat.mes-hall↗

arXiv1999

Vortex Reconnection as the Dissipative Scattering of Dipoles

We propose a phenomenological model of vortex tube reconnection at high Reynolds numbers. The basic picture is that squeezed vortex lines, formed by stretching in the region of closest approach between filaments, interact like dipoles (monopole-antimonopole pairs) of a confining electrostatic theory. The probability of dipole creation is found from a canonical ensemble spanned by foldings of the vortex tubes, with temperature parameter estimated from the typical energy variation taking place in the reconnection process. Vortex line reshuffling by viscous diffusion is described in terms of directional transitions of the dipoles. The model is used to fit with reasonable accuracy experimental data established long ago on the symmetric collision of vortex rings. We also study along similar lines the asymmetric case, related to the reconnection of non-parallel vortex tubes.

cond-mat.soft↗

arXiv1998

Circulation Statistics in Three-Dimensional Turbulent Flows

We study the large $λ$ limit of the loop-dependent characteristic functional $Z(λ)=<\exp(iλ\oint_c \vec v \cdot d \vec x)>$, related to the probability density function (PDF) of the circulation around a closed contour $c$. The analysis is carried out in the framework of the Martin-Siggia-Rose field theory formulation of the turbulence problem, by means of the saddle-point technique. Axisymmetric instantons, labelled by the component $σ_{zz}$ of the strain field -- a partially annealed variable in our formalism -- are obtained for a circular loop in the $xy$ plane, with radius defined in the inertial range. Fluctuations of the velocity field around the saddle-point solutions are relevant, leading to the lorentzian asymptotic behavior $Z(λ) \sim 1/{λ^2}$. The ${\cal O}(1 / {λ^4})$ subleading correction and the asymmetry between right and left PDF tails due to parity breaking mechanisms are also investigated.

cond-mat.stat-mech↗

arXiv1998

Renormalization Group Derivation of the Localization Length Exponent in the Integer Quantum Hall Effect

We compute, neglecting possible effects of subleading irrelevant couplings, the localization length exponent in the integer quantum Hall effect, for the case of white noise random potentials. The result obtained is $ν=2$ for all Landau levels. Our approach consists in a renormalization group transformation of Landau orbitals, which iterates the generating functional of Green's functions for the localization problem. The value of $ν$ is obtained from the asymptotic form of the renormalization group mapping. The basic assumptions in our derivation are the existence of a scaling law for the localization length and the absence of Landau level mixing.

cond-mat↗

arXiv1998

3-D Perturbations in Conformal Turbulence

The effects of three-dimensional perturbations in two-dimensional turbulence are investigated, through a conformal field theory approach. We compute scaling exponents for the energy spectra of enstrophy and energy cascades, in a strong coupling limit, and compare them to the values found in recent experiments. The extension of unperturbed conformal turbulence to the present situation is performed by means of a simple physical picture in which the existence of small scale random forces is closely related to deviations of the exact two-dimensional fluid motion.

hep-th↗

arXiv1994

Quantum Field Theory Description of Tunneling in the Integer Quantum Hall Effect

We study the tunneling between two quantum Hall systems, along a quasi one-dimensional interface. A detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field theory model for the tunneling. It is shown that the phenomenon of fermion number fractionalization is expected to occur, either localized in conveniently modulated barriers or in the form of free excitations, once lattice effects are taken into account. This opens the experimental possibility of an observation of fractional charges with internal structure, close to the magnetic length scale. The coupling of the system to external gauge fields is performed, leading us to the exact quantization of the Hall conductivity at the interface. The field theory approach is well supported by a numerical diagonalization of the microscopic Hamiltonian.

cond-mat↗