arXiv subjects

Luca Guido Molinari

Publications and source records attributed to Luca Guido Molinari.

48 records · Page 3Linked to original sources

arXiv2016

A note on extended Lorentzian recurrent manifolds

Extended recurrent pseudo-Riemannian manifolds were introduced by Mileva Prvanovic'. We reconsider her work in the light of recent results and show that the manifold is conformally flat, and it is a space of quasi-constant curvature. We also show that an extended recurrent Lorentzian manifold, with time-like associated covector, is a perfect fluid Robertson-Walker space-time. We obtain the equation of state; in n = 4 and if the scalar curvature is zero, a model for incoherent radiation is obtained.

math.DG↗

arXiv2016

On the Weyl and Ricci tensors of Generalized Robertson-Walker space-times

We prove theorems about the Ricci and the Weyl tensors on generalized Robertson-Walker space-times of dimension $n\ge 3$. In particular, we show that the concircular vector introduced by Chen decomposes the Ricci tensor as a perfect fluid term plus a term linear in the contracted Weyl tensor. The Weyl tensor is harmonic if and only if it is annihilated by Chen's vector, and any of the two conditions is necessary and sufficient for the GRW space-time to be a quasi-Einstein (perfect fluid) manifold. Finally, the general structure of the Riemann tensor for Robertson-Walker space-times is given, in terms of Chen's vector. A GRW space-time in n = 4 with null conformal divergence is a Robertson-Walker space-time.

math-ph↗

arXiv2016

Random Antagonistic Matrices

The ensemble of antagonistic matrices is introduced and studied. In antagonistic matrices the entries $\mathcal A_{i,j}$ and $\mathcal A_{j,i}$ are real and have opposite signs, or are both zero, and the diagonal is zero. This generalization of antisymmetric matrices is suggested by the linearized dynamics of competitive species in ecology.

math-ph↗

arXiv2016

Devil's staircase phase diagram of the fractional quantum Hall effect in the thin-torus limit

After more than three decades the fractional quantum Hall effect still poses challenges to contemporary physics. Recent experiments point toward a fractal scenario for the Hall resistivity as a function of the magnetic field. Here, we consider the so-called thin-torus limit of the Hamiltonian describing interacting electrons in a strong magnetic field, restricted to the lowest Landau level, and we show that it can be mapped onto a one-dimensional lattice gas with repulsive interactions, with the magnetic field playing the role of a chemical potential. The statistical mechanics of such models leads to interpret the sequence of Hall plateaux as a fractal phase diagram, whose landscape shows a qualitative agreement with experiments.

cond-mat.str-el↗

arXiv2016

A condition for a perfect-fluid space-time to be a generalized Robertson-Walker space-time

A perfect-fluid space-time of dimension n>3 with 1) irrotational velocity vector field, 2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with Einstein fiber. Condition 1) is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl tensor with the velocity vector field is zero. Conversely, a generalized Robertson-Walker space-time with null divergence of the Weyl tensor is a perfect-fluid space-time.

math.DG↗

arXiv2011

Counting the exponents of single transfer matrices

The eigenvalue equation of a band or a block tridiagonal matrix, the tight binding model for a crystal, a molecule, or a particle in a lattice with random potential or hopping amplitudes: these and other problems lead to three-term recursive relations for (multicomponent) amplitudes. Amplitudes n steps apart are linearly related by a transfer matrix, which is the product of n matrices. Its exponents describe the decay lengths of the amplitudes. A formula is obtained for the counting function of the exponents, based on a duality relation and the Argument Principle for the zeros of analytic functions. It involves the corner blocks of the inverse of the associated Hamiltonian matrix. As an illustration, numerical evaluations of the counting function of quasi 1D Anderson model are shown.

math-ph↗

arXiv2011

Extended Derdzinski-Shen theorem for the Riemann tensor

We extend a classical result by Derdzinski and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. The new conditions of the theorem include Codazzi tensors (i.e. closed 1-forms) as well as tensors with gauged Codazzi condition (i.e. "recurrent 1-forms"), typical of some well known differential structures.

math.DG↗

arXiv2009

A second-order identity for the Riemann tensor and applications

A second-order differential identity for the Riemann tensor is obtained, on a manifold with symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors descend from it. Applications to manifolds with Recurrent or Symmetric structures are discussed. The new structure of K-recurrency naturally emerges from an invariance property of an old identity by Lovelock.

math.DG↗

arXiv2008

Non-Hermitian spectra and Anderson localization

The spectrum of exponents of the transfer matrix provides the localization lengths of Anderson's model for a particle in a lattice with disordered potential. I show that a duality identity for determinants and Jensen's identity for subharmonic functions, give a formula for the spectrum in terms of eigenvalues of the Hamiltonian with non-Hermitian boundary conditions. The formula is exact; it involves an average over a Bloch phase, rather than disorder. A preliminary investigation of non-Hermitian spectra of Anderson's model in D=1,2 and on the smallest exponent is presented.

math-ph↗

arXiv2007

Ab-initio self-energy corrections in systems with metallic screening

The calculation of self-energy corrections to the electron bands of a metal requires the evaluation of the intraband contribution to the polarizability in the small-q limit. When neglected, as in standard GW codes for semiconductors and insulators, a spurious gap opens at the Fermi energy. Systematic methods to include intraband contributions to the polarizability exist, but require a computationally intensive Fermi-surface integration. We propose a numerically cheap and stable method, based on a fit of the power expansion of the polarizability in the small-q region. We test it on the homogeneous electron gas and on real metals such as sodium and aluminum.

cond-mat.mtrl-sci↗

arXiv2006

Another proof of Gell-Mann and Low's theorem

The theorem by Gell-Mann and Low is a cornerstone in QFT and zero-temperature many-body theory. The standard proof is based on Dyson's time-ordered expansion of the propagator; a proof based on exact identities for the time-propagator is here given.

math-ph↗

arXiv2005

Enumeration of many-body skeleton diagrams

The many-body dynamics of interacting electrons in condensed matter and quantum chemistry is often studied at the quasiparticle level, where the perturbative diagrammatic series is partially resummed. Based on Hedin's equations for self-energy, polarization, propagator, effective potential, and vertex function in zero dimension of space-time, dressed Feynman (skeleton) diagrams are enumerated. Such diagram counts provide useful basic checks for extensions of the theory for future realistic simulations.

cond-mat.str-el↗