# Luigi MartinaINFN - Istituto Nazionale di Fisica Nucleare | INFN · Lecce

Luigi Martina

Associate Professor

## About

155

Publications

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1,681

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Introduction

Additional affiliations

September 1995 - December 2000

January 1982 - December 2012

## Publications

Publications (155)

We analyze the interaction with uniform external fields of nematic liquid crystals within a recent generalized free energy posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i.e., uniform heliconical structures, which correspond to the so-cal...

The capture of scintillation light emitted by liquid Argon and Xenon under molecular excitations by charged particles is still a challenging task. Here we present a first attempt to design a device able to have a sufficiently high photon detection efficiency, in order to reconstruct the path of ionizing particles. The study is based on the use of m...

We consider a family of thermodynamic models such that the energy density can be expressed as an asymptotic expansion in the scale formal parameter and whose terms are suitable functions of the volume density. We examine the possibility to construct solutions for the Maxwell thermodynamic relations relying on their symmetry properties and deduce th...

We analyze the interaction with uniform external fields of nematic liquid crystals within a recent generalized free-energy posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i. e., uniform heliconical structures, which correspond to the so-ca...

The capture of scintillation light emitted by liquid Argon and Xenon under molecular excitations by charged particles is still a challenging task. Here we present a first attempt to design a device able to grab sufficiently high luminosity in order to reconstruct the path of ionizing particles. This preliminary study is based on the use of masks to...

We analyze a recent generalized free-energy for liquid crystals posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i.e., uniform heliconical structures, and we find new liquid crystal configurations, which closely resemble some novel, experim...

We analyse a recent generalised free-energy for liquid crystals posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i. e. uniform heliconical structures, and we find new liquid crystal configurations, which closely resemble some novel, experim...

Cholesteric liquid crystals, subject to externally applied magnetic fields and confined between two parallel planar surfaces with strong homeotropic anchoring conditions, are found to undergo transitions to different types of helicoidal configurations with disclinations. Analytical and numerical studies are performed in order to characterize their...

Cholesteric Liquid Crystals (CLCs), in presence of an external uniform electric field and confined between two parallel planes with strong homeotropic anchoring conditions, are found to admit different types of helicoidal solutions with disclinations. Analytical and numerical analysis are performed in order to characterise their properties. In part...

In this work, we analyze the scattering of light by the so-called spherulites or skyrmions in cholesteric liquid crystals. These are quasi-planar localized excitations of the director configuration. We compute the cross section of the polarization conversion for polarized incident light in the Born approximation, considering the anisotropic optical...

The symmetry algebra of the real elliptic Liouville equation is an infinite-dimensional loop algebra with the simple Lie algebra o(3, 1) as its maximal finite-dimensional subalgebra. The entire algebra generates the conformal group of the Euclidean plane E2. This infinite-dimensional algebra distinguishes the elliptic Liouville equation from the hy...

We study the light scattering by localized quasi planar excitations of a Cholesteric Liquid Crystal known as spherulites. Due to the anisotropic optical properties of the medium and the peculiar shape of the excitations, we quantitatively evaluate the cross section of the axis-rotation of polarized light. Because of the complexity of the system und...

In this work, we study surface modifications of AISI 420 stainless steel specimens in order to improve their surface properties. Oxidation resistance and surface micro-hardness were analyzed. Using an ion beam delivered by a Laser Ion Source (LIS) coupled to an electrostatic accelerator, we performed implantation of low energy yttrium ions on the s...

Within the framework of Oseen-Frank theory, we analyse the static configurations for chiral liquid crystals. In particular, we find numerical solutions for localised axisymmetric states in confined chiral liquid crystals with weak homeotropic anchoring at the boundaries. These solutions describe the distortions of two-dimensional skyrmions, known a...

The complex Liouville equation as well as the real hyperbolic one are invariant under the direct product of two Virasoro groups. The Lie algebra of the real elliptic Liouville equation does not have the structure of a direct sum. We discretize this equation on a lattice that is rotationally symmetric. The obtained difference system is invariant und...

We consider the $\Omega$-deformed $\mathcal{N}=2$ $SU(2)$ gauge theory in four dimensions with $N_{f}=4$ massive fundamental hypermultiplets. The low energy effective action depends on the deformation parameters $\varepsilon_{1}, \varepsilon_{2}$, the scalar field expectation value $a$, and the hypermultiplet masses ${\bf m}=(m_{1}, m_{2}, m_{3}, m...

This paper is devoted to a study of the connections between three different analytic descriptions for the immersion functions of 2D-surfaces corresponding to the following three types of symmetries: gauge symmetries of the linear spectral problem, conformal transformations in the spectral parameter and generalized symmetries of the associated integ...

The main purpose of this article is to show how structure reflected in
partial differential equations can be preserved in a discrete world and
reflected in difference schemes.
Three different structure preserving discretizations of the Liouville
equation are presented and then used to solve specific boundary value problems.
The results are compared...

The Liouville equation is well known to be linearizable by a point
transformation. It has an infinite dimensional Lie point symmetry algebra
isomorphic to a direct sum of two Virasoro algebras. We show that it is not
possible to discretize the equation keeping the entire symmetry algebra as
point symmetries. We do however construct a difference sys...

Modern theory of nonlinear integrable equations is nowdays an important and effective tool of study for numerous nonlinear phenomena in various branches of physics from hydrodynamics and optics to quantum filed theory and gravity. It includes the study of nonlinear partial differential and discrete equations, regular and singular behaviour of their...

The Skyrme-Faddeev model admits exact analytical non localized solutions, which describe magnetic domain wall solutions when multivalued singularities appear or, differently, always regular periodic nonlinear waves, which may degenerate into linear spin waves or solitonic structures. Here both classes of solutions are derived and discussed and a ge...

In the present article we perform the symmetry analysis of the Skyrme-Faddeev system at the level of point symmetries. We provide a new simple approximate expression for the axisymmetric solutions, with an accuracy of 10−4 in the static energy value. Furthermore, we proceed to a reduction with respect to all discrete Platonic rotation subgroups, pr...

We show that the Skyrme-Faddeev model can be reduced in different ways to completely integrable sectors; the corresponding classes of solutions can be parametrized by specific sets of arbitrary functions. Moreover, using the ansatz of a phase and pseudo-phase reduction, the corresponding ordinary nonlinear wave solutions can be integrated in terms...

We consider an electrically charged particle simultaneously interacting with a magnetic monopole and a dual monopole in the momentum space. It is a prototype of a three-dimensional system involving noncommuting and/or noncanonical variables but having geometric and also gauge symmetries in both the position and momentum spaces. We discuss the main...

Recent results on the semiclassical dynamics of an electron in a solid are explained using techniques developed for "exotic" Galilean dynamics. The system is indeed Hamiltonian and Liouville's theorem holds for the symplectic volume form. Suitably defined quantities satisfy hydrodynamic equations.

A system of partial differential equations, describing one-dimensional nematic liquid crystals is studied by Lie group analysis. These equations are the Euler–Lagrange equations associated with a free energy functional that depends on the mass density and the gradient of the mass density. The group analysis is an algorithmic approach that allows us...

Inspired by the geometrical methods allowing the introduction of mechanical systems confined in the plane and endowed with exotic galilean symmetry, we resort to the Lagrange-Souriau 2-form formalism, in order to look for a wide class of 3D systems, involving not commuting and/or not canonical variables, but possessing geometric as well gauge symme...

The coupling of nonrelativistic anyons (called exotic particles) to an electromagnetic field is considered. Anomalous coupling is introduced by adding a spin-orbit term to the Lagrangian. Alternatively, one has two Hamiltonian structures, obtained by either adding the anomalous term to the Hamiltonian, or by redefining the mass and the NC parameter...

Inspired by the geometrical methods allowing the introduction of mechanical
systems confined in the plane and endowed with exotic galilean symmetry, we
resort to the Lagrange-Souriau 2-form formalism, in order to look for a wide
class of 3D systems, involving not commuting and/or not canonical variables,
but possessing geometric as well gauge symme...

We consider a chain of SU(2)4
anyons with transitions to a topologically ordered phase state. For half-integer and integer indices of the type of strongly correlated excitations, we find an effective low-energy Hamiltonian that is an analogue of the standard Heisenberg Hamiltonian for quantum magnets. We describe the properties of the Hilbert space...

In terms of the Lagrange-Souriau 2-form formalism, we describe a wide set of Hamiltonian dynamical systems with first-order
Lagrangians. We consider a wide class of systems derived in different phenomenological contexts. The noncommutativity of the
particle position coordinates are a natural consequence. We present various explicit examples.
Keywo...

Our goal is to clarify the relation between entanglement and correlation energy in a bipartite system with infinite dimensional Hilbert space. To this aim we consider the completely solvable Moshinsky's model of two linearly coupled harmonic oscillators. Also for small values of the couplings the entanglement of the ground state is nonlinearly rela...

Some aspects of the "exotic" particle, associated with the two-parameter
central extension of the planar Galilei group are reviewed. A fundamental
property is that it has non-commuting position coordinates. Other and
generalized non-commutative models are also discussed. Minimal as well as
anomalous coupling to an external electromagnetic field is...

One-dimensional lattice model of SU(2)_{4} anyons containing a transition into the topological ordered phase state is considered. An effective low-energy Hamiltonian is found for half-integer and integer indices of the type of strongly correlated non-Abelian anyons. The Hilbert state space properties in the considered modular tensor category are st...

We consider a universal representation for the Hamiltonian of systems in topologically ordered phase states. We show that
for strongly correlated electronic systems, the Hamiltonian expressed in terms of projectors of the Temperley-Lieb algebra
on the spin singlet state has the form of a two-dimensional Bloch matrix in the case of doubly linked exc...

We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We focus on the discrete equations which take place in the case of generalized exclusion principle statistics. We...

We propose a method for automatic lung juxta-pleural nodule detection in thorax CT images, to be used as a Computer Assisted Detection (CAD) tool by radiologists. It is based on the calculation and automatic analysis of local curvature on the lung surface as extracted from high-resolution CT scans, and exploits uniformization to a sphere (e.g. thro...

Semiclassical wave packets for electrons in crystals, subject to an external electromagnetic field, satisfy Hamiltonian equations.
In (2+1)-dimensions and in the limit of uniform fields, the symmetry group results in a two-folded Galilei algebra, incorporating
an “exotic” central charge. It has the physical meaning of the Berry-phase curvature. In...

In this work, the photoemission performance of rough and smooth cathodes is presented. The cathodes were made up of pure yttrium metal bulk. For evaluation of the photocathodes, a KrF excimer laser, operating at 248 nm wavelength, 5 eV photon energy and 23 ns full width at half maximum (FWHM) was used. The targets were tested in a vacuum photodiode...

In this work, we present the experimental study and a theoretical approach of the photoemission of rough and smooth photocathodes. The cathode was made of pure yttrium while its surface was morphologically modified. The cathode surface was irradiated by a KrF excimer at normal incidence. The measurements were performed after electric breakdowns bet...

In this review article some fundamental aspects on the application of entanglement running from quantum optics to some issues of quantum information, are presented. One of the authors (g.s.) dedicates this essay to his wife Gioiella with love and gratitude.

We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We focus on the discrete equations which take place in the case of generalized exclusion principle statistics. We...

The relation between the correlation energy and the entanglement is analytically constructed for the Moshinsky's model of two coupled harmonic oscillators. It turns out that the two quantities are far to be proportional, even at very small couplings. A comparison is made also with the 2-point Ising model.

In this paper we investigate some entanglement properties for the Hydrogen molecule considered as a two interacting spin 1/2 (qubit) model. The entanglement related to the $H_{2}$ molecule is evaluated both using the von Neumann entropy and the Concurrence and it is compared with the corresponding quantities for the two interacting spin system. Man...

We use the concept of quantum entanglement to give a physical meaning to the electron correlation energy in systems of interacting
electrons. The electron correlation is not directly observable, being defined as the difference between the exact ground state
energy of the many-electron Schrödinger equation and the Hartree-Fock energy. Using the conf...

The semiclassical approximation for electron wave packets in crystals leads to equations that can be derived from a Lagrangian
or, under suitable regularity conditions, in a Hamiltonian framework. We use the method of coadjoint orbits applied to the
“enlarged” Galilei group to study these issues in the plane.

The Comment by Duval et al. [PRL 96, 099701 (2006)] addresses an important,
but not the main, result of our Letter [PRL 95, 137204 (2005)]. It does not
contradict our results in substance, and the only objection is really on the
style of approach.

Comment. 2 pages, no figures. Reference date corrected Affiliation of the first author expanded

The exotic Galileian group is realized as a symmetry group of a family of nonrelativistic field theories on the noncommutative
plane. This was obtained in a unique way consistent with the Seiberg—Witten mapping. The symmetry group of the free model
is analyzed and a characterization of the class of the self-interacting theories is given.

In this work the experimental and simulation results of photoemission studies for photoelectrons are presented. The cathode used was a Zn disc having a work function of 4.33 eV. Two different excimer lasers were employed as energy source to apply the photoelectron process: XeCl (308 nm, 10 ns) and KrF (248nm, 23ns). Experimental parameters were the...

The Bogoliubov particle considered in [cond-mat/0507125] admits, contrarily to the claim of the authors, an interesting Hamiltonian structure.

In this work, wave formation in laser-produced plasma is investigated by an analysis of time-of-flight signal of the electron pulse. Electrons are extracted from a non-equilibrium plasma, generated by pulsed laser ablation on a solid Ge target. The process is represented by ion-acoustic waves, which are generated from an external perturbation, give...

We report new developments concerning the symmetry properties and their actions on special solutions allowed by certain field theory models on the noncommutative plane. In particular, we seek Galilean-invariant models. The analysis indicates that this requirement strongly restricts the admissible interactions. Moreover, if a scalar field is coupled...

Affiliation of the first Author expanded. One more reference added. To appear in Mod. Phys. Lett. B. 5 pages

Enlarged planar Galilean symmetry, built of both space-time and field variables and also incorporating the ``exotic'' central extension is introduced. It is used to describe non-relativistic anyons coupled to an electromagnetic field. Our theory exhibits an anomalous velocity relation of the type used to explain the Anomalous Hall Effect. The Hall...

New developments about the symmetries properties and their actions on special solutions allowed by certain field theoretical models on the non commutative plane are reported. In particular we are looking for Galilei invariant models. The analysis indicates that this requirement strongly restricts the admissible interactions. Moreover, looking for t...

We generated electron beams by a Nb polycrystalline photocathode illuminated by different wavelength excimer lasers; an XeCl and a KrCl. The cathode surface roughness was 0.09. At low accelerating voltage, the electron beams were governed by the space-charge effect and their intensity never resulted clipped as previous by the Child-Langmuir law. In...

Noncommutative Chern–Simons gauge theory coupled to nonrelativistic scalars or spinors is shown to admit the “exotic” two-parameter-centrally extended Galilean symmetry, realized in a unique way consistent with the Seiberg–Witten map. Nontopological spinor vortices and topological external-field vortices are constructed by reducing the problem to p...

When the interaction potential is suitably reordered, the Moyal field theory admits two types of Galilean symmetries, namely the conventional mass-parameter-centrally-extended one with commuting boosts, but also the two-fold centrally extended “exotic” Galilean symmetry, where the commutator of the boosts yields the noncommutative parameter. In the...

We present a discretization of the P1 sigma model. We show that the discrete P1 sigma model is described by a nonlinear partial second-order difference equation with rational nonlinearity. To derive discrete surfaces immersed in three-dimensional Euclidean space a 'complex' lattice is introduced. The so-obtained surfaces are characterized in terms...

In a geometrical framework, we prove the integrability of two (1+1)-dimensional spin systems. A unifying approach, based on the integrable spin systems, to the construction of integrable classes of surfaces is proposed. In particular, two classes of integrable surfaces are studied.

The Moyal *-deformed noncommutative Burgers' equation is considered.
Using the *-analog of the Cole-Hopf transformation, the linearization of
the model in terms of the linear heat equation is found. Deformations of
one and two shock soliton solutions are described.

The Moyal *-deformed noncommutative version of Burgers' equation is considered. Using the *-analog of the Cole-Hopf transformation, the linearization of the model in terms of the linear heat equation is found. Noncommutative q-deformations of shock soliton solutions and their interaction are described

The study of the relation between the Weierstrass inducing formulae for constant mean curvature surfaces and the completely integrable euclidean nonlinear sigma-model suggests a connection among integrable sigma -models in a background and other type of surfaces. We show how a generalization of the Weierstrass representation can be achieved and we...