arXiv subjects

A. De Martino

Publications and source records attributed to A. De Martino.

At least 19 recordsLinked to original sources

arXiv2026

A unified approach to the Dirac fine structures on the $S$-spectrum and a connection with Gegenbauer polynomials

This paper contributes to the recently introduced theory of fine structures on the $S$-spectrum. We study, in a unified way, the functional calculi for axially Poly-Analytic-Harmonic functions on the $S$-spectrum. Axially Poly-Analytic-Harmonic functions of type $(β, m)$, for $β, m \in \mathbb{N}_0$ belong to the kernel of the Dirac-Laplace operators $D^βΔ^m$ of type $(β, m)$ and contain as particular cases axially Poly-Analytic and axially Poly-Harmonic functions. By applying these operators to the Cauchy kernels $S^{-1}_L(s,x)$ of (left) slice hyperholomorphic functions, we obtain an integral representation for axially Poly-Analytic-Harmonic functions. We point out that the kernels $D^βΔ^mS^{-1}_L(s,x)$ have a remarkable connection with Gegenbauer polynomials. By replacing the paravector operator $T$ with commuting components in the kernels $D^βΔ^m S^{-1}_L(s,x)$, we obtain the associated resolvent operators. With these resolvent operators, denoted by $S^{-1}_{L, D^βΔ^m}(s,T)$, we define the associated functional calculi based on the $S$-spectrum and study their properties.

math.FA↗

arXiv2025

Magnetic Bloch bands and Weiss oscillations in Dirac mass superlattices

We study two-dimensional Dirac fermions in a one-dimensional mass superlattice under a perpendicular magnetic field. Using exact solutions for isolated and finite arrays of domain walls, we demonstrate the persistence of Jackiw-Rebbi modes with a field-dependent renormalized velocity. For the periodic case, we adopt a gauge-invariant projection method onto magnetic Bloch states, valid for arbitrary fields and mass profiles, which yields dispersive Landau levels, and confirm its accuracy by comparison with finite arrays spectra. From the miniband spectra we predict modified quantum Hall plateaus and Weiss-like magnetoconductivity oscillations, characterized by a strongly reduced amplitude and a $π/2$ phase shift compared to electrostatic superlattices.

cond-mat.mes-hall↗

arXiv2023

Two-dimensional Dirac fermions in a mass superlattice

We study two-dimensional (2D) Dirac fermions in the presence of a periodic mass term alternating between positive and negative values along one direction. This scenario could be realized for a graphene monolayer or for the surface states of topological insulators. The low-energy physics is governed by chiral Jackiw-Rebbi modes propagating along zero-mass lines, with the energy dispersion of the Bloch states given by an anisotropic Dirac cone. By means of the transfer matrix approach, we obtain exact results for a piece-wise constant mass superlattice. On top of Bloch states, two different classes of boundary and/or interface modes can exist in a finite-size geometry or in a nonuniform electrostatic potential, respectively. We compute the dispersion relation for both types of boundary and interface modes, which originate either from states close to the superlattice Brillouin zone (BZ) center or, via a Lifshitz transition, from states near the BZ boundary. In the presence of a potential step, we predict that the interface modes, the Bloch wave functions, and the electrical conductance will sensitively depend on the step position relative to the mass superlattice.

cond-mat.mes-hall↗

arXiv2019

The Essential Role of Thermodynamics in metabolic network modeling: physical insights and computational challenges

Quantitative studies of cell metabolism are often based on large chemical reaction network models. A steady state approach is suited to analyze phenomena on the timescale of cell growth and circumvents the problem of incomplete experimental knowledge on kinetic laws and parameters, but it shall be supported by a correct implementation of thermodynamic constraints. In this article we review the latter aspect highlighting its computational challenges and physical insights. The simple introduction of Gibbs inequalities avoids the presence of unfeasible loops allowing for correct timescale analysis but leads to possibly non-convex feasible flux spaces, whose exploration needs efficient algorithms. We shorty review on the implementation of thermodynamics through variational principles in constraints based models of metabolic networks.

q-bio.MN↗

arXiv2017

Proximity-induced superconductivity in Landau-quantized graphene monolayers

We consider massless Dirac fermions in a graphene monolayer subject to both a perpendicular magnetic field $B$ and a proximity-induced pairing gap $Δ$. When the chemical potential is at the Dirac point, our exact solution of the Bogoliubov-de Gennes equation yields $Δ$-independent relativistic Landau levels. Since eigenstates depend on $Δ$, many observables nevertheless are sensitive to pairing, e.g., the local density of states or the edge state spectrum. By solving the problem with an additional in-plane electric field, we also discuss how snake states are influenced by a pairing gap.

cond-mat.mes-hall↗

arXiv2017

Two-electron bound states near a Coulomb impurity in gapped graphene

We formulate and solve the perhaps simplest two-body bound state problem for interacting Dirac fermions in two spatial dimensions. A two-body bound state is predicted for gapped graphene monolayers in the presence of weakly repulsive electron-electron interactions and a Coulomb impurity with charge $Ze>0$, where the most interesting case corresponds to $Z=1$. We introduce a variational Chandrasekhar-Dirac spinor wave function and show the existence of at least one bound state. This state leaves clear signatures accessible by scanning tunneling microscopy. One may thereby obtain direct information about the strength of electron-electron interactions in graphene.

cond-mat.mes-hall↗

arXiv2016

Chiral interface states in graphene $p$-$n$ junctions

We present a theoretical analysis of unidirectional interface states which form near $p$-$n$ junctions in a graphene monolayer subject to a homogeneous magnetic field. The semiclassical limit of these states corresponds to trajectories propagating along the $p$-$n$ interface by a combined skipping-snaking motion. Studying the two-dimensional Dirac equation with a magnetic field and an electrostatic potential step, we provide and discuss the exact and essentially analytical solution of the quantum-mechanical eigenproblem for both a straight and a circularly shaped junction. The spectrum consists of localized Landau-like and unidirectional snaking-skipping interface states, where we always find at least one chiral interface state. For a straight junction and at energies near the Dirac point, when increasing the potential step height, the group velocity of this state interpolates in an oscillatory manner between the classical drift velocity in a crossed electromagnetic field and the semiclassical value expected for a purely snaking motion. Away from the Dirac point, chiral interface states instead resemble the conventional skipping (edge-type) motion found also in the corresponding Schrödinger case. We also investigate the circular geometry, where chiral interface states are predicted to induce sizeable equilibrium ring currents.

cond-mat.mes-hall↗

arXiv2015

A mid-infrared Mueller ellipsometer with pseudo-achromatic optical elements

The purpose of this article is to present a new broadband Mueller ellipsometer designed to work in the mid-infrared range, from 3 to 14 microns. The Mueller ellipsometer, which can be mounted in reflection or in transmission configuration, consists of a polarization state generator (PSG), a sample holder, and a polarization state analyzer (PSA). The PSG consists in one linear polarizer and a retarder sequentially rotated to generate a set of four optimal polarization states. The retarder consists in a bi-prism made of two identical Fresnel rhombs disposed symmetrically and joined by optical contact, giving the ensemble a "V" shape. Retardation is induced by the four total internal reflections that the beam undergoes when it propagates through the bi-prism. Total internal reflection allows to generate a quasi-achromatic retardation. The PSA is identical to the PSG, but with its optical elements mounted in reverse order. After a measurement run, the instrument yields a set of sixteen independent values, which is the minimum amount of data required to calculate the Mueller matrix of the sample. The design of the Mueller ellipsometer is based on the optimization of an objective criterion that allows minimizing the propagation of errors from raw data to the Mueller matrix of the sample. The pseudo-achromatic optical elements ensure a homogeneous quality of the measurements for all wavelengths. The performance of the Mueller ellipsometer in terms of precision, and accuracy, is discussed and illustrated with a few examples.

physics.optics↗

arXiv2014

Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities

We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear combination of atomic orbitals (LCAO) approach. For opposite charges of the Coulomb centers, an electric dipole potential results at large distances. We provide a nonperturbative analysis of the corresponding low-energy scattering problem.

cond-mat.mes-hall↗

arXiv2014

Electric dipole induced universality for Dirac fermions in graphene

We study electric dipole effects for massive Dirac fermions in graphene and related materials. The dipole potential accomodates towers of infinitely many bound states exhibiting a universal Efimov-like scaling hierarchy. The dipole moment determines the number of towers, but there is always at least one tower. The corresponding eigenstates show a characteristic angular asymmetry, observable in tunnel spectroscopy. However, charge transport properties inferred from scattering states are highly isotropic.

cond-mat.mes-hall↗

arXiv2013

Identifying all irreducible conserved metabolite pools in genome-scale metabolic networks: a general method and the case of Escherichia coli

The stoichiometry of metabolic networks usually gives rise to a family of conservation laws for the aggregate concentration of specific pools of metabolites, which not only constrain the dynamics of the network, but also provide key insight into a cell's production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all integer solutions to an NP-hard programming problem. Here we propose a novel and efficient computational strategy that combines Monte Carlo, message passing, and relaxation algorithms to compute the complete set of irreducible integer conservation laws of a given stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. The method is deployed for the analysis of the complete set of irreducible integer pools of two large-scale reconstructions of the metabolism of the bacterium Escherichia coli in different growth media. In addition, we uncover a scaling relation that links the size of the irreducible pool basis to the number of metabolites, for which we present an analytical explanation.

q-bio.MN↗

arXiv2013

Bound States and Supercriticality in Graphene-Based Topological Insulators

We study the bound state spectrum and the conditions for entering a supercritical regime in graphene with strong intrinsic and Rashba spin-orbit interactions within the topological insulator phase. Explicit results are provided for a disk-shaped potential well and for the Coulomb center problem

cond-mat.mes-hall↗

arXiv2011

Landau levels, edge states, and strained magnetic waveguides in graphene monolayers with enhanced spin-orbit interaction

The electronic properties of a graphene monolayer in a magnetic and a strain-induced pseudo-magnetic field are studied in the presence of spin-orbit interactions (SOI) that are artificially enhanced, e.g., by suitable adatom deposition. For the homogeneous case, we provide analytical results for the Landau level eigenstates for arbitrary intrinsic and Rashba SOI, including also the Zeeman field. The edge states in a semi-infinite geometry are studied in the absence of the Rashba term. For a critical value of the magnetic field, we find a quantum phase transition separating two phases with spin-filtered helical edge states at the Dirac point. These phases have opposite spin current direction. We also discuss strained magnetic waveguides with inhomogeneous field profiles that allow for chiral snake orbits. Such waveguides are practically immune to disorder-induced backscattering, and the SOI provides non-trivial spin texture to these modes.

cond-mat.mes-hall↗

arXiv2010

Fluctuation relations and rare realizations of transport observables

Fluctuation relations establish rigorous identities for the nonequilibrium averages of observables. Starting from a general transport master equation with time-dependent rates, we employ the stochastic path integral approach to study statistical fluctuations around such averages. We show how under nonequilibrium conditions, rare realizations of transport observables are crucial and imply massive fluctuations that may completely mask such identities. Quantitative estimates for these fluctuations are provided. We illustrate our results on the paradigmatic example of a mesoscopic RC circuit.

cond-mat.stat-mech↗

arXiv2010

Transient fluctuation relations for time-dependent particle transport

We consider particle transport under the influence of time-varying driving forces, where fluctuation relations connect the statistics of pairs of time reversed evolutions of physical observables. In many "mesoscopic" transport processes, the effective many-particle dynamics is dominantly classical, while the microscopic rates governing particle motion are of quantum-mechanical origin. We here employ the stochastic path integral approach as an optimal tool to probe the fluctuation statistics in such applications. Describing the classical limit of the Keldysh quantum nonequilibrium field theory, the stochastic path integral encapsulates the quantum origin of microscopic particle exchange rates. Dynamically, it is equivalent to a transport master equation which is a formalism general enough to describe many applications of practical interest. We apply the stochastic path integral to derive general functional fluctuation relations for current flow induced by time-varying forces. We show that the successive measurement processes implied by this setup do not put the derivation of quantum fluctuation relations in jeopardy. While in many cases the fluctuation relation for a full time-dependent current profile may contain excessive information, we formulate a number of reduced relations, and demonstrate their application to mesoscopic transport. Examples include the distribution of transmitted charge, where we show that the derivation of a fluctuation relation requires the combined monitoring of the statistics of charge and work.

cond-mat.stat-mech↗

arXiv2010

Spin-orbit coupling and spectral function of interacting electrons in carbon nanotubes

The electronic spin-orbit coupling in carbon nanotubes is strongly enhanced by the curvature of the tube surface and has important effects on the single-particle spectrum. Here, we include the full spin-orbit interaction in the formulation of the effective low-energy theory for interacting electrons in metallic single-wall carbon nanotubes and study its consequences. The resulting theory is a four-channel Luttinger liquid, where spin and charge modes are mixed. We show that the analytic structure of the spectral function is strongly affected by this mixing, which can provide an experimental signature of the spin-orbit interaction.

cond-mat.mes-hall↗

arXiv2010

One way to grow, many ways to shrink: the reversible Von Neumann expanding model

We study the solutions of Von Neumann's expanding model with reversible processes for an infinite reaction network. We show that, contrary to the irreversible case, the solution space need not be convex in contracting phases (i.e. phases where the concentrations of reagents necessarily decrease over time). At optimality, this implies that, while multiple dynamical paths of global contraction exist, optimal expansion is achieved by a unique time evolution of reaction fluxes. This scenario is investigated in a statistical mechanics framework by a replica symmetric theory. The transition from a non-convex to a convex solution space, which turns out to be well described by a phenomenological order parameter (the fraction of unused reversible reactions) is analyzed numerically.

cond-mat.dis-nn↗

arXiv2010

Multiparticle equations for interacting Dirac Fermions in graphene nanostructures

We study the energy of quasi-particles in graphene within the Hartree-Fock approximation. The quasi-particles are confined via an inhomogeneous magnetic field and interact via the Coulomb potential. We show that the associated functional has a minimizer and determine the stability conditions for the N-particle problem in such a graphene quantum dot.

cond-mat.mes-hall↗