arXiv subjects

Gaetano Fiore

Publications and source records attributed to Gaetano Fiore.

At least 37 records · Page 2Linked to original sources

arXiv2018

Fuzzy circle and new fuzzy sphere through confining potentials and energy cutoffs

Guided by ordinary quantum mechanics we introduce new fuzzy spheres of dimensions d=1,2: we consider an ordinary quantum particle in D=d+1 dimensions subject to a rotation invariant potential well V(r) with a very sharp minimum on a sphere of unit radius. Imposing a sufficiently low energy cutoff to `freeze' the radial excitations makes only a finite-dimensional Hilbert subspace accessible and on it the coordinates noncommutative à la Snyder; in fact, on it they generate the whole algebra of observables. The construction is equivariant not only under rotations - as Madore's fuzzy sphere -, but under the full orthogonal group O(D). Making the cutoff and the depth of the well dependent on (and diverging with) a natural number L, and keeping the leading terms in 1/L, we obtain a sequence S^d_L of fuzzy spheres converging (in a suitable sense) to the sphere S^d as L diverges (whereby we recover ordinary quantum mechanics on S^d). These models may be useful in condensed matter problems where particles are confined on a sphere by an (at least approximately) rotation-invariant potential, beside being suggestive of analogous mechanisms in quantum field theory or quantum gravity.

math-ph↗

arXiv2018

Travelling waves and light-front approach in relativistic electrodynamics

We briefly report on a recent proposal (Fiore in J Phys A Math Theor 51:085203, 2018) for simplifying the equations of motion of charged particles in an electromagnetic (EM) field $F^{μν}$ that is the sum of a plane travelling wave $F_t^{μν}(ct\!-\!z)$ and a static part $F_s^{μν}(x,y,z)$; it adopts the light-like coordinate $ξ=ct\!-\!z$ instead of time $t$ as an independent variable. We illustrate it in a few cases of extreme acceleration, first of an isolated particle, then of electrons in a plasma in plane hydrodynamic conditions: the Lorentz-Maxwell \& continuity PDEs can be simplified or sometimes even completely reduced to a family of decoupled systems of ordinary ones; this occurs e.g. with the impact of the travelling wave on a vacuum-plasma interface (what may produce plasma waves or the slingshot effect).

physics.plasm-ph↗

arXiv2018

On cold diluted plasmas hit by short laser pulses

Adapting a plane hydrodynamical model we briefly revisit the study of the impact of a very short and intense laser pulse onto a diluted plasma, the formation of a plasma wave, its wave-breaking, the occurrence of the slingshot effect.

physics.plasm-ph↗

arXiv2018

Travelling waves and a fruitful `time' reparametrization in relativistic electrodynamics

We simplify the nonlinear equations of motion of charged particles in an external electromagnetic field that is the sum of a plane travelling wave F_t(ct-z) and a static part F_s(x,y,z): by adopting the light-like coordinate ct-z instead of time t as an independent variable in the Action, Lagrangian and Hamiltonian, and deriving the new Euler-Lagrange and Hamilton equations accordingly, we make the unknown z(t) disappear from the argument of F_t. We study and solve first the single particle equations in few significant cases of extreme accelerations. In particular we obtain a rigorous formulation of a Lawson-Woodward-type (no-final-acceleration) theorem and a compact derivation of cyclotron autoresonance, beside new solutions in the presence of uniform F_s. We then extend our method to plasmas in hydrodynamic conditions and apply it to plane problems: the system of partial differential equations may be partially solved and sometimes even completely reduced to a family of decoupled systems of ordinary ones; this occurs e.g. with the impact of the travelling wave on a vacuum-plasma interface (what may produce the slingshot effect). Since Fourier analysis plays no role in our general framework, the method can be applied to all kind of travelling waves, ranging from almost monochromatic to socalled "impulses", which contain few, one or even no complete cycle.

math-ph↗

arXiv2018

On a `time' reparametrization in relativistic electrodynamics with travelling waves

We briefly report on our method [Fiore JPA 2017] of simplifying the equations of motion of charged particles in an electromagnetic field that is the sum of a plane travelling wave and a static part; it is based on changes of the dependent variables and the independent one (light-like coordinate instead of time t). We sketch its application to a few cases of extreme laser-induced accelerations, both in vacuum and in plane problems at the vacuum-plasma interface, where we are able to reduce the system of the (Lorentz-Maxwell and continuity) partial differential equations into a family of decoupled systems of Hamilton equations in 1 dimension. Since Fourier analysis plays no role, the method can be applied to all kind of travelling waves, ranging from almost monochromatic to socalled "impulse".

math-ph↗

arXiv2016

Simple model of the slingshot effect

We present a detailed quantitative description of the recently proposed "slingshot effect" [Fiore, Fedele, De angelis 2014]. Namely, we determine a broad range of conditions under which the impact of a very short and intense laser pulse normally onto a low-density plasma (or matter to be locally completely ionized into a plasma by the pulse) causes the expulsion of a bunch of surface electrons in the direction opposite to the one of propagation of the pulse, and the detailed, ready-for-experiments features of the expelled electrons (energy spectrum, collimation, etc). The effect is due to the combined actions of the ponderomotive force and the huge longitudinal field arising from charge separation. Our predictions are based on estimating 3D corrections to a simple, yet powerful plane magnetohydrodynamic (MHD) model where the equations to be solved are reduced to a system of Hamilton equations in one dimension (or a collection of) which become autonomous after the pulse has overcome the electrons. Experimental tests seem to be at hand. If confirmed by the latter, the effect would provide a new extraction and acceleration mechanism for electrons, alternative to traditional radio-frequency-based or Laser-Wake-Field ones.

physics.plasm-ph↗

arXiv2016

On very short and intense laser-plasma interactions

We briefly report on some results regarding the impact of very short and intense laser pulses on a cold, low-density plasma initially at rest, and the consequent acceleration of plasma electrons to relativistic energies. Locally and for short times the pulse can be described by a transverse plane electromagnetic travelling-wave and the motion of the electrons by a purely Magneto-Fluido-Dynamical (MFD) model with a very simple dependence on the transverse electromagnetic potential, while the ions can be regarded as at rest; the Lorentz-Maxwell and continuity equations are reduced to the Hamilton equations of a Hamiltonian system with 1 degree of freedom, in the case of a plasma with constant initial density, or a collection of such systems otherwise. We can thus describe both the well-known "wakefield" behind the pulse and the recently predicted "slingshot effect", i.e. the backward expulsion of high energy electrons just after the laser pulse has hit the surface of the plasma.

physics.plasm-ph↗

arXiv2016

A "slingshot" laser-driven acceleration mechanism of plasma electrons

We briefly report on the recently proposed [G. Fiore, R. Fedele, U. de Angelis, Phys. Plasmas 21 (2014), 113105], [G. Fiore, S. De Nicola, arXiv:1509.04656] electron acceleration mechanism named "slingshot effect": under suitable conditions the impact of an ultra-short and ultra-intense laser pulse against the surface of a low-density plasma is expected to cause the expulsion of a bunch of superficial electrons with high energy in the direction opposite to that of the pulse propagation; this is due to the interplay of the huge ponderomotive force, huge longitudinal field arising from charge separation, and the finite size of the laser spot.

physics.plasm-ph↗

arXiv2015

On kinks and other travelling-wave solutions of a modified sine-Gordon equation

We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. The perturbation of the equation consists of a constant forcing term and a linear dissipative term. On the real line candidate orbitally stable solutions with bounded energy density are either the constant one, or of kink (i.e. soliton) type, or of array-of-kinks type, or of "half-array-of-kinks" type. While the first three have unperturbed analogs, the last type is essentially new. We also propose a convergent method of successive approximations of the (anti)kink solution based on a careful application of the fixed point theorem.

math-ph↗

arXiv2014

The slingshot effect: a possible new laser-driven high energy acceleration mechanism for electrons

We show that under appropriate conditions the impact of a very short and intense laser pulse onto a plasma causes the expulsion of surface electrons with high energy in the direction opposite to the one of propagation of the pulse. This is due to the combined effects of the ponderomotive force and the huge longitudinal field arising from charge separation ("slingshot effect"). The effect should also be present with other states of matter, provided the pulse is sufficiently intense to locally cause complete ionization. An experimental test seems to be feasible and, if confirmed, would provide a new extraction and acceleration mechanism for electrons, alternative to traditional radio-frequency-based or Laser-Wake-Field ones.

physics.plasm-ph↗

arXiv2014

Modules over the Noncommutative Torus and Elliptic Curves

Using the Weil-Brezin-Zak transform of solid state physics, we describe line bundles over elliptic curves in terms of Weyl operators. We then discuss the connection with finitely-generated projective modules over the algebra $A_θ$ of the noncommutative torus. We show that such $A_θ$-modules have a natural interpretation as Moyal deformations of vector bundles over an elliptic curve $E_τ$, under the condition that the deformation parameter $θ$ and the modular parameter $τ$ satisfy a non-trivial relation.

math.OA↗

arXiv2014

On plane-wave relativistic electrodynamics in plasmas and in vacuum

We revisit the exact microscopic equations (in differential, and equivalent integral form) ruling a relativistic cold plasma after the plane-wave Ansatz, without customary approximations. We show that in the Eulerian description the motion of a very diluted plasma initially at rest and excited by an arbitrary transverse plane electromagnetic travelling-wave has a very simple and explicit dependence on the transverse electromagnetic potential; for a non-zero density plasma the above motion is a good approximation of the real one as long as the back-reaction of the charges on the electromagnetic field can be neglected, i.e. for a time lapse decreasing with the plasma density, and can be used as initial step in an iterative resolution scheme. As one of many possible applications, we use these results to describe how the ponderomotive force of a very intense and short plane laser pulse hitting normally the surface of a plasma boosts the surface electrons into the ion background. Because of this penetration the electrons are then pulled back by the electric force exerted by the ions and may leave the plasma with high energy in the direction opposite to that of propagation of the pulse [G. Fiore, R. Fedele, U. De Angelis, "The slingshot effect: a possible new laser-driven high energy acceleration mechanism for electrons", arXiv:1309.1400].

math-ph↗

arXiv2014

On plane waves in diluted relativistic cold plasmas

We briefly report on some exact results [G. Fiore, arXiv:1312.4665 preprint, to appear in J. Phys. A] regarding plane waves in a relativistic cold plasma. If the plasma, initially at rest, is reached by a transverse plane electromagnetic travelling-wave, then its motion has a very simple dependence on this wave in the limit of zero density, otherwise can be determined by an iterative procedure whose accuracy decreases with time or the plasma density. Thus one can describe in particular the impact of a very intense and short laser pulse onto a plasma and determine conditions for the "slingshot effect" [G. Fiore, R. Fedele, U. De Angelis, arXiv:1309.1400 preprint] to occur. The motion in vacuum of a charged test particle subject to a wave of the same kind is also determined, for any initial velocity.

math-ph↗

arXiv2013

On quantum mechanics with a magnetic field on R^n and on a torus T^n, and their relation

We show in elementary terms the equivalence in a general gauge of a U(1)-gauge theory of a scalar charged particle on a torus T^n = R^n/L to the analogous theory on R^n constrained by quasiperiodicity under translations in the lattice L. The latter theory provides a global description of the former: the quasiperiodic wavefunctions defined on R^n play the role of sections of the associated hermitean line bundle E on T^n, since also E admits a global description as a quotient. The components of the covariant derivatives corresponding to a constant (necessarily integral) magnetic field B = dA generate a Lie algebra g_Q and together with the periodic functions the algebra of observables O_Q . The non-abelian part of g_Q is a Heisenberg Lie algebra with the electric charge operator Q as the central generator; the corresponding Lie group G_Q acts on the Hilbert space as the translation group up to phase factors. Also the space of sections of E is mapped into itself by g in G_Q . We identify the socalled magnetic translation group as a subgroup of the observables' group Y_Q . We determine the unitary irreducible representations of O_Q, Y_Q corresponding to integer charges and for each of them an associated orthonormal basis explicitly in configuration space. We also clarify how in the n = 2m case a holomorphic structure and Theta functions arise on the associated complex torus. These results apply equally well to the physics of charged scalar particles on R^n and on T^n in the presence of periodic magnetic field B and scalar potential. They are also necessary preliminary steps for the application to these theories of the deformation procedure induced by Drinfel'd twists.

math-ph↗

arXiv2012

Existence, uniqueness and stability for a class of third order dissipative problems depending on time

We prove new results regarding the existence, uniqueness, (eventual) boundedness, (total) stability and attractivity of the solutions of a class of initial-boundary-value problems characterized by a quasi-linear third order equation which may contain time-dependent coefficients. The class includes equations arising in Superconductor Theory and in the Theory of Viscoelastic Materials. In the proof we use a Liapunov functional V depending on two parameters, which we adapt to the characteristics of the problem.

math-ph↗

arXiv2012

Existence and uniqueness of solutions of a class of 3rd order dissipative problems with various boundary conditions describing the Josephson effect

We prove existence and uniqueness of solutions of a large class of initial-boundary-value problems characterized by a quasi-linear third order equation (the third order term being dissipative) on a finite space interval with Dirichlet, Neumann or pseudoperiodic boundary conditions. The class includes equations arising in superconductor theory, such as a well-known modified sine-Gordon equation describing the Josephson effect, and in the theory of viscoelastic materials.

math-ph↗

arXiv2012

Learning from Julius' star, *, $\star$

While collecting some personal memories about Julius Wess, I briefly describe some aspects of my recent work on many particle quantum mechanics and second quantization on noncommutative spaces obtained by twisting, and their connection to him.

math-ph↗

arXiv2011

Class of invariants for the 2D time-dependent Landau problem and harmonic oscillator in a magnetic field

We consider an isotropic two dimensional harmonic oscillator with arbitrarily time-dependent mass $M(t)$ and frequency $Ω(t)$ in an arbitrarily time-dependent magnetic field $B(t)$. We determine two commuting invariant observables (in the sense of Lewis and Riesenfeld) $L,I$ in terms of some solution of an auxiliary ordinary differential equation and an orthonormal basis of the Hilbert space consisting of joint eigenvectors $ϕ_λ$ of $L,I$. We then determine time-dependent phases $α_λ(t)$ such that the $ψ_λ(t)=e^{iα_λ}ϕ_λ$ are solutions of the time-dependent Schrödinger equation and make up an orthonormal basis of the Hilbert space. These results apply, in particular to a two dimensional Landau problem with time-dependent $M,B$, which is obtained from the above just by setting $Ω(t) \equiv 0$. By a mere redefinition of the parameters, these results can be applied also to the analogous models on the canonical non-commutative plane.

math-ph↗