Replacement of the Lorentz law for the shape of the spectral lines in the infrared region

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-frequency region, observed in many spectra. We apply this law to the measured infrared spectra of LiF, NaCl, and MgF2, finding good agreement over a wide range of frequencies

PERTURBATION THEORY AT THE THERMODYNAMIC LIMIT

La presente tesi propone un'estensione della teoria delle perturbazioni Hamiltoniana al limite termodinamico (ossia, per sistemi con un numero infinito di gradi di libert\ue0 e una temperatura, o energia specifica, finita), nello spirito della teoria ergodica (cio\ue8, in presenza di una misura invariante). Per un sistema concreto, il modello \u3a64 discreto, si ottiene una versione debole del teorema di Nehoroscev. Il risultato \ue8 che, nel limite termodinamico, esiste almeno un'osservabile, indipendente dall'energia, la cui funzione di autocorrelazione temporale rimanga significativamente discosta da zero fino a tempi esponenzialmente lunghi nei parametri perturbativi. La tesi \ue8 completata dalla discussione di argomenti correlati, ossia le propriet\ue0 analitiche generali delle funzioni di autocorrelazione temporale e un'applicazione euristica della teoria perturbativa al problema del limite di densit\ue0 nei plasmi magnetizzati.The present thesis provides an extension of Hamiltonian perturbation theory to the thermodynamic limit (i.e., for systems with an infinite number of degrees of freedom and a finite temperature or specific energy), in the spirit of ergodic theory (i.e., in the presence of an invariant measure). For a concrete model, which is the discrete \u3a64 model, a weaker version of classical Nekhoroshev theorem is obtained. The result is that, at the thermodynamic limit, there exists at least one observable, independent of energy, such that its time\u2013autocorrelation function does not relax to zero up to times exponentially long in the perturbation parameters. In the thesis, further related subjects are discussed, namely, analytical properties of generic time-autocorrelation functions and a heuristic application of perturbation theory to the problem of the density limit in magnetized plasmas

The virtual restoration of the former ducal chapel of San Ludovico in Parma

This text deals with the issues related to the fruition of illusory spaces and to the dissemination of cultural heritage through the illustration of an experience conducted by professors of DICATeA of the University of Parma in the context of an exhibition dedicated to Maria Luigia of Hapsburg. In this context, a digital model of the former church of St. Ludovico in its original configuration was created to be loaded on special visors that visitors of the exhibition can wear in order to virtually immerse themselves in a reality today largely changed. The goal of this work is to show how a scientific approach, resulting from a strong synergy between different disciplines, can lead to the implementation of important tools aimed at knowledge, enhancement and communication of cultural heritage

Derivation of a wave kinetic equation from the resonant-averaged stochastic NLS equation

We suggest a new derivation of a wave kinetic equation for the spectrum of the weakly nonlinear Schr\uf6dinger equation with stochastic forcing. The kinetic equation is obtained as a result of a double limiting procedure. Firstly, we consider the equation on a finite box with periodic boundary conditions and send the size of the nonlinearity and of the forcing to zero, while the time is correspondingly rescaled; then, the size of the box is sent to infinity (with a suitable rescaling of the solution). We report here the results of the first limiting procedure, analysed with full rigour in Kuksin and Maiocchi (0000), and show how the second limit leads to a kinetic equation for the spectrum, if some further hypotheses (commonly employed in the weak turbulence theory) are accepted. Finally we show how to derive from these equations the Kolmogorov-Zakharov spectra

Relaxation times for Hamiltonian systems

Usually, the relaxation times of a gas are estimated in the frame of the Boltzmann equation. In this paper, instead, we deal with the relaxation problem in the frame of the dynamical theory of Hamiltonian systems, in which the definition itself of a relaxation time is an open question. We introduce a lower bound for the relaxation time, and give a general theorem for estimating it. Then we give an application to a concrete model of an interacting gas, in which the lower bound turns out to be of the order of magnitude of the relaxation times observed in dilute gases.Comment: 26 page

An Averaging Theorem for FPU in the Thermodynamic Limit

Consider an FPU chain composed of N 6b1 particles, and endow the phase space with the Gibbs measure corresponding to a small temperature \u3b2^(-1). Given a fixed K , we construct K packets of normal modes whose energies are adiabatic invariants (i.e., are approximately constant for times of order \u3b2^(1 12a), a>0 ) for initial data in a set of large measure. Furthermore, the time autocorrelation function of the energy of each packet does not decay significantly for times of order \u3b2. The restrictions on the shape of the packets are very mild. All estimates are uniform in the number N of particles and thus hold in the thermodynamic limit N\u2192 1e , \u3b2>0

Statistical thermodynamics for metaequilibrium or metastable states

We show how statistical thermodynamics can be formulated in situations of metaequilibrium or metastability (as in the cases of supercooled liquids or of glasses respectively). By analogy with phenomenological thermodynamics, the primary quantities considered are the heat Q absorbed and the work W performed by the system of interest. These are defined through the energy exchanges which occur when the system is put in contact with a thermostat and with a barostat, the whole system being dealt with as a global Hamiltonian dynamical system. The coefficients of the fundamental form (Formula presented.) turn out to have such expressions that the closure of the form is manifest: this gives the first principle. A further step is performed by making use of time reversibility. This provides new expressions for the coefficients, such that the second principle in the form of Clausius is also manifest. Such coefficients are expressed in terms of time-autocorrelations of suitable dynamical variables, in a way analogous to that of fluctuation dissipation theory for equilibrium states. All these results are independent of the ergodicity properties of the global dynamical system