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L. Pietronero

Publications and source records attributed to L. Pietronero.

At least 37 records · Page 2Linked to original sources
arXiv2005

Basic properties of galaxy clustering in the light of recent results from the Sloan Digital Sky Survey

We discuss some of the basic implications of recent results on galaxy correlations published by the SDSS collaboration. In particular we focus on the evidence which has been recently presented for the scale and nature of the transition to homogeneity in the galaxy distribution, and results which describe the dependence of clustering on luminosity. The two questions are in fact strictly entangled, as the stability of the measure of the amplitude of the correlation function depends on the scale at which the mean density becomes well defined. We note that the recent results which indicate the convergence to well defined homogeneity in a volume equivalent to that of a sphere of radius 70 Mpc/h, place in doubt previous detections of ``luminosity bias'' from measures of the amplitude of the correlation function. We emphasize that the way to resolve these issues is to first use, in volume limited samples corresponding to different ranges of luminosity, the unnormalized two point statistics to establish the scale (and value) at which the mean density becomes well defined. We note also that the recent SDSS results for these statistics are in good agreement with those obtained by us through analyses of many previous samples, confirming in particular that the galaxy distribution is well described by a fractal dimension D ~ 2 up to a scale of at least 20 Mpc/h. We discuss critically the agreement of this new data with current theoretical models.

astro-ph↗
arXiv2005

Fractals vs. halos: Asymptotic scaling without fractal properties

Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical tools permitting to discriminate accurately different spatial patterns is highly desiderable. This is specially the case when non-fractal distributions have power law two-point correlation functions, which are usually signatures of fractal properties. Here we review some possible methods used in the literature and introduce a new variable called "scaling gradient". This tool and the conditional variance are shown to be effective in providing an unambiguous way for such a distinction. Their application is expected to be of outmost importance in the analysis of upcoming galaxy catalogues.

astro-ph↗
arXiv2004

Small Fermi energy, zero point fluctuations and nonadiabaticity in MgB$_2$

Small Fermi energy effects are induced in MgB$_2$ by the low hole doping in the $σ$ bands which are characterized by a Fermi energy $E_{\rm F}^σ\sim 0.5$ eV. We show that, due to the particularly strong deformation potential relative to the $E_{2g}$ phonon mode, lattice fluctuations are reflected in strong fluctuations in the electronic band structure. Quantum fluctuations associated to the zero-point lattice motion are responsible for an uncertainty of the Fermi energy of the order of the Fermi energy itself, leading to the breakdown of the adiabatic principle underlying the Born-Oppenheimer approximation in MgB$_2$ even if $ω_{\rm ph}/E_{\rm F} \sim 0.1-0.2$, where $ω_{\rm ph}$ are the characteristic phonon frequencies. This amounts to a new nonadiabatic regime, which could be relevant to other unconventional superconductors.

cond-mat.supr-con↗
arXiv2004

A topological approach to neural complexity

Considerable efforts in modern statistical physics is devoted to the study of networked systems. One of the most important example of them is the brain, which creates and continuously develops complex networks of correlated dynamics. An important quantity which captures fundamental aspects of brain network organization is the neural complexity C(X)introduced by Tononi et al. This work addresses the dependence of this measure on the topological features of a network in the case of gaussian stationary process. Both anlytical and numerical results show that the degree of complexity has a clear and simple meaning from a topological point of view. Moreover the analytical result offers a straightforward algorithm to compute the complexity than the standard one.

nlin.AO↗
arXiv2004

Relevance of multiband Jahn-Teller effects on the electron-phonon interaction in $A_3$C$_{60}$

Assessing the effective relevance of multiband effects in the fullerides is of fundamental importance to understand the complex superconducting and transport properties of these compounds. In this paper we investigate in particular the role of the multiband effects on the electron-phonon (el-ph) properties of the $t_{1u}$ bands coupled with the Jahn-Teller intra-molecular $H_g$ vibrational modes in the C$_{60}$ compounds. We show that, assuming perfect degeneracy of the electronic bands, vertex diagrams arising from the breakdown of the adiabatic hypothesis, are one order of magnitude smaller than the non-crossing terms usually retained in the Migdal-Eliashberg (ME) theory. These results permit to understand the robustness on ME theory found by numerical calculations. The effects of the non degeneracy of the $t_{1u}$ in realistic systems are also analyzed. Using a tight-binding model we show that the el-ph interaction is mainly dominated by interband scattering within a single electronic band. Our results question the reliability of a degenerate band modeling and show the importance of these combined effects in the $A_3$C$_{60}$ family.

cond-mat.supr-con↗
arXiv2004

Polaronic and nonadiabatic phase diagram from anomalous isotope effects

Isotope effects (IEs) are powerful tool to probe directly the dependence of many physical properties on the lattice dynamics. In this paper we invenstigate the onset of anomalous IEs in the spinless Holstein model by employing the dynamical mean field theory. We show that the isotope coefficients of the electron effective mass and of the dressed phonon frequency are sizeable also far away from the strong coupling polaronic crossover and mark the importance of nonadiabatic lattice fluctuations in the weak to moderate coupling region. We characterize the polaronic regime by the appearence of huge IEs. We draw a nonadiabatic phase diagram in which we identify a novel crossover, not related to polaronic features, where the IEs attain their largest anomalies.

cond-mat.str-el↗
arXiv2003

Charge fluctuations and electron-phonon interaction in the finite-$U$ Hubbard model

In this paper we employ a gaussian expansion within the finite-$U$ slave-bosons formalism to investigate the momentum structure of the electron-phonon vertex function in the Hubbard model as function of $U$ and $n$. The suppression of large momentum scattering and the onset a small-${\bf q}$ peak structure, parametrized by a cut-off $q_c$, are shown to be essentially ruled by the band narrowing factor $Z_{\rm MF}$ due to the electronic correlation. A phase diagram of $Z_{\rm MF}$ and $q_c$ in the whole $U$-$n$ space is presented. Our results are in more than qualitative agreement with a recent numerical analysis and permit to understand some anomalous features of the Quantum Monte Carlo data.

cond-mat.str-el↗
arXiv2003

Poor screening and nonadiabatic superconductivity in correlated systems

In this paper we investigate the role of the electronic correlation on the hole doping dependence of electron-phonon and superconducting properties of cuprates. We introduce a simple analytical expression for the one-particle Green's function in the presence of electronic correlation and we evaluate the reduction of the screening properties as the electronic correlation increases by approaching half-filling. The poor screening properties play an important role within the context of the nonadiabatic theory of superconductivity. We show that a consistent inclusion of the reduced screening properties in the nonadiabatic theory can account in a natural way for the $T_c$-$δ$ phase diagram of cuprates. Experimental evidences are also discussed.

cond-mat.str-el↗
arXiv2003

Electron-phonon renormalization in small Fermi energy systems

The puzzling features of recent photoemission data in cuprates have been object of several analysis in order to identity the nature of the underlying electron-boson interaction. In this paper we point out that many basilar assumptions of the conventional analysis as expected to fail in small Fermi energy systems when, as the cuprates, the Fermi energy $E_{\rm F}$ is comparable with the boson energy scale. We discuss in details the novel features appearing in the self-energy of small Fermi energy systems and the possible implications on the ARPES data in cuprates.

cond-mat.supr-con↗
arXiv2003

Comment on ``Electron-phonon Vertex in the Two-dimensional One-band Hubbard Model''

In cond-mat/0306131 Huang {\em et al.} reported for the first time a numerical evidence for the predominance of small phonon momenta in the electron-phonon coupling induced by electronic correlation. They report also an upturn of the electron-phonon vertex function for small momenta as function of the Hubbard repulsion $U$ for sufficient large $U$. In this comment we compare their Quantum Monte Carlo data with analytical results based on slave-boson techniques for generic $U$. We associate the upturn of the electron-phonon vertex function with the tendency towards a phase separation instability at large temperatures.

cond-mat.str-el↗
arXiv2003

Band-filling effects on electron-phonon properties of normal and superconducting state

We address the effect of band filling on the effective electron mass $m^*$ and the superconducting critical temperature $T_c$ in a electron-phonon system. We compare the vertex corrected theory with the non-crossing approximation of the Holstein model within a local approximation. We identify two regions of the electron density where $m^*$ and $T_c$ are enhanced or decreased by the inclusion of the vertex diagrams. We show that the crossover between the enhancement at low density and the decrease towards half filling is almost independent of the microscopic electron-phonon parameters. These different behaviors are explained in terms of the net sign of the vertex diagrams which is positive at low densities and negative close to half filling. Predictions of the present theory for doped MgB$_2$, which is argued to be in the low density regime, are discussed.

cond-mat.supr-con↗
arXiv2002

Generation of Primordial Cosmological Perturbations from Statistical Mechanical Models

The initial conditions describing seed fluctuations for the formation of structure in standard cosmological models, i.e.the Harrison-Zeldovich distribution, have very characteristic ``super-homogeneous'' properties: they are statistically translation invariant, isotropic, and the variance of the mass fluctuations in a region of volume V grows slower than V. We discuss the geometrical construction of distributions of points in ${\bf R}^3$ with similar properties encountered in tiling and in statistical physics, e.g. the Gibbs distribution of a one-component system of charged particles in a uniform background (OCP). Modifications of the OCP can produce equilibrium correlations of the kind assumed in the cosmological context. We then describe how such systems can be used for the generation of initial conditions in gravitational $N$-body simulations.

astro-ph↗
arXiv2002

Spin susceptibility in small Fermi energy systems: effects of nonmagnetic impurities

In small Fermi energy metals, disorder can deeply modify superconducting state properties leading to a strong suppression of the critical temperature $T_c$. In this paper, we show that also normal state properties can be seriously influenced by disorder when the Fermi energy $E_{\rm F}$ is sufficiently small. We calculate the normal state spin susceptibility $χ$ for a narrow band electron-phonon coupled metal as a function of the non-magnetic impurity scattering rate $γ_{\rm imp}$. We find that as soon as $γ_{\rm imp}$ is comparable to $E_{\rm F}$, $χ$ is strongly reduced with respect to its value in the clean limit. The effects of the electron-phonon interaction including the nonadiabatic corrections are discussed. Our results strongly suggest that the recent finding on irradiated MgB$_2$ samples can be naturally explained in terms of small $E_{\rm F}$ values associated with the $σ$-bands of the boron plane, sustaining therefore the hypothesis that MgB$_2$ is a nonadiabatic metal.

cond-mat.supr-con↗
arXiv2002

Local Rigidity in Sandpile Models

We address the problem of the role of the concept of local rigidity in the family of sandpile systems. We define rigidity as the ratio between the critical energy and the amplitude of the external perturbation and we show, in the framework of the Dynamically Driven Renormalization Group (DDRG), that any finite value of the rigidity in a generalized sandpile model renormalizes to an infinite value at the fixed point, i.e. on a large scale. The fixed point value of the rigidity allows then for a non ambiguous distinction between sandpile-like systems and diffusive systems. Numerical simulations support our analytical results.

cond-mat.stat-mech↗
arXiv2002

High $T_c$ superconductivity in MgB$_2$ by nonadiabatic pairing

The evidence for the key role of the $σ$ bands in the electronic properties of MgB$_2$ points to the possibility of nonadiabatic effects in the superconductivity of these materials. These are governed by the small value of the Fermi energy due to the vicinity of the hole doping level to the top of the $σ$ bands. We show that the nonadiabatic theory leads to a coherent interpretation of $T_c = 39$ K and the boron isotope coefficient $α_{\rm B} = 0.30$ without invoking very large couplings and it naturally explains the role of the disorder on $T_c$. It also leads to various specific predictions for the properties of MgB$_2$ and for the material optimization of these type of compounds.

cond-mat.supr-con↗
arXiv2001

The Holtsmark distribution of forces and its role in gravitational clustering

The evolution and the statistical properties of an infinite gravitating system represent an interesting and widely investigated subject of research. In cosmology, the standard approach is based on equations of hydrodynamics. In the present paper, we analyze the problem from a different perspective, which is usually neglected. We focus our attention on the fact that at small scale the distribution is point-like, or granular, and not fluid-like. The basic result is that the discrete nature of the system is a fundamental ingredient to understand its evolution. The initial configuration is a Poisson distribution in which the distribution of forces is governed by the Holtsmark function. Computer simulations show that the structure formation corresponds to the shift of the granularity from small to large scales. We also present a simple cellular automaton model that reproduces this phenomenon.

cond-mat.stat-mech↗
arXiv2001

Scaling in cosmic structures

The study of the properties of cosmic structures in the universe is one of the most fascinating subject of the modern cosmology research. Far from being predicted, the large scale structure of the matter distribution is a very recent discovery, which continuosly exhibits new features and issues. We have faced such topic along two directions; from one side we have studied the correlation properties of the cosmic structures, that we have found substantially different from the commonly accepted ones. From the other side, we have studied the statistical properties of the very simplified system, in the attempt to capture the essential ingredients of the formation of the observed structures.

cond-mat.stat-mech↗