27 citations · 128 across the 24 of their papers we have counts for
26 papers
A survey on rigorous results for the dynamics of periodic FPU chains
Dario Bambusi, Andrea Carati, Alberto Maiocchi
In this paper we review some analytic results on the dynamics of the FPU system. In the first part of the paper, having in mind that the FPU Hamiltonian and the Toda Hamiltonian ar…
Approach to equilibrium for a particle interacting with a harmonic thermal bath
Federico Bonetto, Alberto Mario Maiocchi
We study the long time evolution of the position-position correlation function for a harmonic oscillator (the {\it probe}) interacting via a coupling with a larg…
A refinement of Heath-Brown's theorem on quadratic forms
Andrey Dymov, Sergei Kuksin, Alberto Maiocchi +1
In his paper from 1996 on quadratic forms Heath-Brown developed a version of the circle method to count points in the intersection of an unbounded quadric with a lattice of short p…
Some remarks on Heath-Brown's theorem on quadratic forms
Andrey Dymov, Sergei Kuksin, Alberto Maiocchi +1
In his paper from 1996 on quadratic forms Heath-Brown developed a version of circle method to count points in the intersection of an unbounded quadric with a lattice of short perio…
The large-period limit for equations of discrete turbulence
Andrey Dymov, Sergei Kuksin, Alberto Maiocchi +1
We consider the damped/driven cubic NLS equation on the torus of a large period with a small nonlinearity of size , a properly scaled random forcing and dissipation. We exam…
Freezing of the optical--branch energy in a diatomic FPU chain
Alberto Mario Maiocchi
We study the exchange of energy between the modes of the optical branch and those of the acoustic one in a diatomic chain of particles, with masses and . We prove that,…
Classical infrared spectra of ionic crystals and their relevance for statistical mechanics
Andrea Carati, Luigi Galgani, Alberto Maiocchi +2
It was recently shown that the experimental infrared spectra of ionic crystals at room temperature are very well reproduced by classical realistic models, and here new results are…
Infrared optical properties of quartz by molecular dynamics simulations
Fabrizio Gangemi, Roberto Gangemi, Andrea Carati +2
This paper is concerned with theoretical estimates of the refractive--index curves for quartz, obtained by the Kubo formulæ in the classical approximation, through MD simulations f…
A replacement of the Lorentz law for the shape of the spectral lines in the infrared region
Andrea Carati, Alberto Maiocchi
We propose a new phenomenological law for the shape of the spectral lines in the infrared, which accounts for the exponential decay of the extinction coefficient in the high freque…
The Fermi-Pasta-Ulam system as a model for glasses
Andrea Carati, Alberto Maiocchi, Luigi Galgani +1
We show that the standard Fermi--Pasta--Ulam system, with a suitable choice for the interparticle potential, constitutes a model for glasses, and indeed an extremely simple and man…
Agreement of classical Kubo theory with the infrared dispersion curves of ionic crystals
Andrea Carati, Luigi Galgani, Roberto Gangemi +2
The theoretical dispersion curves (refractive index versus frequency) of ionic crystals in the infrared domain are expressed, within the Green--Kubo theory, in terms of a ti…
The effective equation method
Sergei Kuksin, Alberto Maiocchi
In this chapter we present a general method of constructing the effective equation which describes the behaviour of small-amplitude solutions for a nonlinear PDE in finite volume,…
Time-averaging for weakly nonlinear CGL equations with arbitrary potentials
Guan Huang, Sergei Kuksin, Alberto Maiocchi
Consider weakly nonlinear complex Ginzburg--Landau (CGL) equation of the form: under the periodic boundary…
The limit of small Rossby numbers for randomly forced quasi-geostrophic equation on -plane
Sergei Kuksin, Alberto Maiocchi
We consider the 2d quasigeostrophic equation on the -plane for the stream function , with dissipation and a random force: $$ (*)\qquad (-Δ+K)ψ_t - ρJ(ψ, Δψ) -βψ_x= \langle \t…
Some analytic results on the FPU paradox
Dario Bambusi, Andrea Carati, Alberto Maiocchi +1
We present some analytic results aiming at explaining the lack of thermalization observed by Fermi Pasta and Ulam in their celebrated numerical experiment. In particular we focus o…
Derivation of the Kolmogorov-Zakharov equation from the resonant-averaged stochastic NLS equation
Sergei Kuksin, Alberto Maiocchi
We suggest a new derivation of a kinetic equation of Kolmogorov-Zakharov (KZ) type for the spectrum of the weakly nonlinear Schrödinger equation with stochastic forcing. The kyneti…
Resonant averaging for small solutions of stochastic NLS equations
Sergei Kuksin, Alberto Maiocchi
We consider the free linear Schrödinger equation on a torus , perturbed by a hamiltonian nonlinearity, driven by a random force and damped by a linear damping: $$ u_t…
Resonant averaging for weakly nonlinear stochastic Schrödinger equations
Sergei Kuksin, Alberto Maiocchi
We consider the free linear Schroedinger equation on a torus , perturbed by a Hamiltonian nonlinearity, driven by a random force and damped by a linear damping: $$u_t…
An averaging theorem for FPU in the thermodynamic limit
Alberto Maiocchi, Dario Bambusi, Andrea Carati
Consider an FPU chain composed of particles, and endow the phase space with the Gibbs measure corresponding to a small temperature . Given a fixed , we constr…
Statistical Thermodynamics for metaequilibrium or metastable states
A. Carati, A. Maiocchi, L. Galgani
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the…
Transition to chaos in magnetized, weakly coupled plasmas
Andrea Carati, Francesco Benfenati, Alberto Maiocchi +2
We report the results of numerical simulations for a model of a one component plasma (a system of N point electrons with mutual Coulomb interactions) in a uniform stationary magnet…
Transition from order to chaos, and density limit, in magnetized plasmas
A. Carati, M. Zuin, A. Maiocchi +3
It is known that a plasma in a magnetic field, conceived microscopically as a system of point charges, can exist in a magnetized state, and thus remain confined, inasmuch as it is…
Density limit in a first principles model of a magnetized plasma in the Debye--Hückel approximation
A. Carati, M. Zuin, A. Maiocchi +3
A crucial problem concerning a large variety of fusion devices is that the confinement due to an external magnetic field is lost above a critical density, while a widely accepted f…
A series expansion for the time autocorrelation of dynamical variables
Alberto Mario Maiocchi, Andrea Carati, Antonio Giorgilli
We present here a general iterative formula which gives a (formal) series expansion for the time autocorrelation of smooth dynamical variables, for all Hamiltonian systems endowed…