luigi galgani - Academia.edu (original) (raw)
Papers by luigi galgani
International Journal of Modern Physics B, 2004
We reexamine the model of matter–radiation interaction considered by Planck in his studies on the... more We reexamine the model of matter–radiation interaction considered by Planck in his studies on the black-body problem, and point out that its consistency seems to be in doubt. The key point is that Planck's model deals in principle with a system of n material resonators interacting with the field, but in fact Planck actually deals with a single resonator, because he explicitly makes the assumption that the resonators act independently of each other, i.e. perform incoherent motions. We point out that it would be more appropriate to deal from the start with the dynamics of the complete system, and that, in view of the long range character of the electrodynamical forces, motions of a coherent or correlated type might thus be found to occur.
The attempt of Carati and Galgani [Phys. Rev. E 61, 4791 (2000)] to derive the Planck formula as ... more The attempt of Carati and Galgani [Phys. Rev. E 61, 4791 (2000)] to derive the Planck formula as though it were due to long relaxation times is shown to be correct only if there is a single temperature and therefore no transients.
Physica A: Statistical Mechanics and its Applications, 2021
Abstract We investigate the thermal fluctuations of the ionic motions in a Born model of ionic cr... more Abstract We investigate the thermal fluctuations of the ionic motions in a Born model of ionic crystals, namely, a model in which the electrons are eliminated, being replaced by suitable effective potentials among the ions. The model is studied in its classical version, computing the Newtonian trajectories of the ions. The general motivation is that, although being an essential ingredient within Green-Kubo linear response theory, thermal fluctuations apparently were not studied systematically by molecular dynamics methods, as was done instead for the approach to equilibrium in the Fermi-Pasta–Ulam problem. The time evolution of the fluctuations is studied in terms of the time-changes of the mode-energies of the system. The stages of the “regression” of the fluctuations are described, from a first stage of strong time-correlations up to a final decorrelation, and a comparison with the process of approach to equilibrium is performed. Finally, the dependence on specific energy is investigated.
Physica A: Statistical Mechanics and its Applications, 2018
It was recently shown that the experimental infrared spectra of ionic crystals at room temperatur... more 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 reported on the temperature dependence of the spectra, for the LiF crystal. The principal aim of the present work is however to highlight the deep analogy existing between the problem of spectra in ionic crystal models on the one hand, and that of energy equipartition in the Fermi-Pasta-Ulam model, on the other. Indeed at low temperatures the computations of the spectra show that the dynamics of the considered system is not completely chaotic, so that the use of the Boltzmann-Gibbs statistics is put in question, as in the Fermi-Pasta-Ulam case. Here, however, at variance with the equipartition problem, a first positive indication is given on the modifications that should be introduced in a classical statistical treatment: the new results at low temperatures show that it is indeed the Clausius identification of temperature that has to be modified. In fact, at very low temperatures the theoretical spectra fail to reproduce the experimental ones, if the temperature is taken as proportional to mean kinetic energy, but agreement is recovered through the only expedient of introducing a suitable temperature rescaling. Analogous results are also found in connection with thermal expansion.
EPL (Europhysics Letters), 2015
The theoretical dispersion curves n(ω) (refractive index versus frequency) of ionic crystals in t... more The theoretical dispersion curves n(ω) (refractive index versus frequency) of ionic crystals in the infrared domain are expressed, within the Green-Kubo theory, in terms of a time correlation function involving the motion of the ions only. The aim of this paper is to investigate how well the experimental data are reproduced by a classical approximation of the theory, in which the time correlation functions are expressed in terms of the ions orbits. We report the results of molecular dynamics (MD) simulations for the ions motions of a LiF lattice of 4096 ions at room temperature. The theoretical curves thus obtained are in surprisingly good agreement with the experimental data, essentially over the whole infrared domain. This shows that at room temperature the motion of the ions develops essentially in a classical regime.
The Foundations of Quantum Mechanics — Historical Analysis and Open Questions, 1995
We refer on some recent studies on classical electrodynamics of point particles, as described by ... more We refer on some recent studies on classical electrodynamics of point particles, as described by the Abraham-Lorentz-Dirac equation. Such studies exploit positively the well known existence of generic runaway solutions. Indeed the additional requirement that has to be imposed, namely the restriction to initial data giving rise to nonrunaway behaviour, turns out to allow for unexpected phenomena, for example a behaviour qualitatively similar to that occurring in the quantum tunnel effect. It is pointed out how this fact might be relevant for the problem of hidden parameters.
Physical Review A, 1976
Numerical investigations of dynamical systems allow one to give estimates of the rate of divergen... more Numerical investigations of dynamical systems allow one to give estimates of the rate of divergence of nearby trajectories, by means of a quantity which is usually assumed to be related to the Kolmogorov (or metric) entropy. In this paper it is shown first, on the basis of mathematical results of Oseledec and Piesin, how such a relation can be made precise. Then, as an example, a numerical study of the Kolmogorov entropy for the Henon-Heiles model is reported.
Calibration of Fundamental Stellar Quantities, 1985
For the calibration of radiation detectors, use is currently made of blackbodies, assuming they s... more For the calibration of radiation detectors, use is currently made of blackbodies, assuming they satisfy Planck's Law. The first problem considered here is then: how well has this law been checked experiment ally? Now, it has been pointed out (Crovini and Galgani 1984) that essentially no new experiments have been made after 1921 (Rubens and Michel 1921), when the data were interpreted as fitting the theoretical law within 1%. But, in fact, this work made use of the value 14300 (in suitable units) of the second radiation constant, while the presently adopted value is 14388. When one inserts this value into the calcul ations, one finds that, indeed, Planck's Law has been checked only to 3%. Furthermore, some theoretical considerations, based on Arnold's diffusion, lead to the idea that Planck's Law could be just a first approximation to the radiation law, and that one could expect some corrections in the Rayleigh-Jeans region for values of x=hv/kT less than 0.2. No experiments on blackbodies are available in that region. Looking, instead, at the data for the Sun, clear deviations are obser ved, giving a plateau.
Il Nuovo Cimento B Series 11, 1985
Summary In the present paper we study by numerical methods a Hamiltonian model describing a chai... more Summary In the present paper we study by numerical methods a Hamiltonian model describing a chain of weakly coupled rotators. The existence of local phenomena of ordered and chaotic motions is illustrated and is interpreted, within classical perturbation theory, in terms of resonances.
Il Nuovo Cimento B Series 11, 1985
Summary We show how to construct a classical perturbation theory at any finite order for an Hami... more Summary We show how to construct a classical perturbation theory at any finite order for an Hamiltonian system describing a chain of weakly coupled rotators, both for the nonresonant and for the resonant cases. In particular, by means of a suitable algebraic scheme, we show how small denominantors and propagation of harmonics can be controlled.
Pure and Applied Chemistry, 1970
It is pointed out that the usual basic postulate of increase of entropy for an isolated system, a... more It is pointed out that the usual basic postulate of increase of entropy for an isolated system, as stated for example by Tisza and Callen, if mathematically formalized, is expressed as a superadditivity property of entropy. This fact has two kinds of implications: (a) it allows one to deduce in a very direct and mathematically clear way stability properties such as Cv ~ 0 and KT ~ 0 and the equivalence of various thermodynamic schemes as expressed for example by the fact that the "minimum' property of the free energy is a consequence of the 'maximum' property of entropy; (b) it makes it possible to establish a link with foundations research, notably the system developed by Giles, where superadditivity of entropy appears as a consequence of other axioms.
Physical Review Letters, 1972
Journal of Statistical Physics, 1982
We make a numerical study of the solutions of the equations of motion for the electromagnetic fie... more We make a numerical study of the solutions of the equations of motion for the electromagnetic field in a one-dimensional model of a radiant cavity. Our main results are as follows: (1) There exist stochasticity thresholds such that below them one has ordered motions without energy exchanges, while chaotic motions with intense energy exchanges occur above them; (2) above thresholds there is a trend toward equipartition of energy (in time average) among the normal modes of the field, but this occurs in the sense of Boltzmann and Jeans, namely, with the higher frequencies requiring longer and longer times in order to be involved in the energy sharing.
Journal of Plasma Physics, 2002
We consider a model of viscoresistive incompressible magnetohydrodynamics in a periodic cylinder,... more We consider a model of viscoresistive incompressible magnetohydrodynamics in a periodic cylinder, with boundary conditions meant to idealize in a tractable way those of a laboratory plasma. The resistivity is described by a tensor presenting a field-dependent anisotropic part suggested by kinetic theory, controlled by a certain anisotropy parameter. An explicit analytical description of the corresponding axisymmetric zero-flow equilibria is given, and it is shown how tokamak-like or paramagnetic-pinch-like field profiles are obtained as the anisotropy parameter is changed. The study of the stability properties of such equilibria is deferred to a later paper.
Journal of Mathematical Physics, 1971
We start from the solution of the problem of the thermodynamic limit for microcanonical entropy a... more We start from the solution of the problem of the thermodynamic limit for microcanonical entropy as given by Ruelle and extend his method to solve the analogous problem of consistency, within the same ensemble, for the Legendre transforms of entropy. We solve then in a unified way the problem of the asymptotic equivalence of ensembles.
Communications in Nonlinear Science and Numerical Simulation, 2008
This article was published in an Elsevier journal. The attached copy is furnished to the author f... more This article was published in an Elsevier journal. The attached copy is furnished to the author for non-commercial research and education use, including for instruction at the author's institution, sharing with colleagues and providing to institution administration. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright
International Journal of Modern Physics B, 2004
We reexamine the model of matter–radiation interaction considered by Planck in his studies on the... more We reexamine the model of matter–radiation interaction considered by Planck in his studies on the black-body problem, and point out that its consistency seems to be in doubt. The key point is that Planck's model deals in principle with a system of n material resonators interacting with the field, but in fact Planck actually deals with a single resonator, because he explicitly makes the assumption that the resonators act independently of each other, i.e. perform incoherent motions. We point out that it would be more appropriate to deal from the start with the dynamics of the complete system, and that, in view of the long range character of the electrodynamical forces, motions of a coherent or correlated type might thus be found to occur.
The attempt of Carati and Galgani [Phys. Rev. E 61, 4791 (2000)] to derive the Planck formula as ... more The attempt of Carati and Galgani [Phys. Rev. E 61, 4791 (2000)] to derive the Planck formula as though it were due to long relaxation times is shown to be correct only if there is a single temperature and therefore no transients.
Physica A: Statistical Mechanics and its Applications, 2021
Abstract We investigate the thermal fluctuations of the ionic motions in a Born model of ionic cr... more Abstract We investigate the thermal fluctuations of the ionic motions in a Born model of ionic crystals, namely, a model in which the electrons are eliminated, being replaced by suitable effective potentials among the ions. The model is studied in its classical version, computing the Newtonian trajectories of the ions. The general motivation is that, although being an essential ingredient within Green-Kubo linear response theory, thermal fluctuations apparently were not studied systematically by molecular dynamics methods, as was done instead for the approach to equilibrium in the Fermi-Pasta–Ulam problem. The time evolution of the fluctuations is studied in terms of the time-changes of the mode-energies of the system. The stages of the “regression” of the fluctuations are described, from a first stage of strong time-correlations up to a final decorrelation, and a comparison with the process of approach to equilibrium is performed. Finally, the dependence on specific energy is investigated.
Physica A: Statistical Mechanics and its Applications, 2018
It was recently shown that the experimental infrared spectra of ionic crystals at room temperatur... more 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 reported on the temperature dependence of the spectra, for the LiF crystal. The principal aim of the present work is however to highlight the deep analogy existing between the problem of spectra in ionic crystal models on the one hand, and that of energy equipartition in the Fermi-Pasta-Ulam model, on the other. Indeed at low temperatures the computations of the spectra show that the dynamics of the considered system is not completely chaotic, so that the use of the Boltzmann-Gibbs statistics is put in question, as in the Fermi-Pasta-Ulam case. Here, however, at variance with the equipartition problem, a first positive indication is given on the modifications that should be introduced in a classical statistical treatment: the new results at low temperatures show that it is indeed the Clausius identification of temperature that has to be modified. In fact, at very low temperatures the theoretical spectra fail to reproduce the experimental ones, if the temperature is taken as proportional to mean kinetic energy, but agreement is recovered through the only expedient of introducing a suitable temperature rescaling. Analogous results are also found in connection with thermal expansion.
EPL (Europhysics Letters), 2015
The theoretical dispersion curves n(ω) (refractive index versus frequency) of ionic crystals in t... more The theoretical dispersion curves n(ω) (refractive index versus frequency) of ionic crystals in the infrared domain are expressed, within the Green-Kubo theory, in terms of a time correlation function involving the motion of the ions only. The aim of this paper is to investigate how well the experimental data are reproduced by a classical approximation of the theory, in which the time correlation functions are expressed in terms of the ions orbits. We report the results of molecular dynamics (MD) simulations for the ions motions of a LiF lattice of 4096 ions at room temperature. The theoretical curves thus obtained are in surprisingly good agreement with the experimental data, essentially over the whole infrared domain. This shows that at room temperature the motion of the ions develops essentially in a classical regime.
The Foundations of Quantum Mechanics — Historical Analysis and Open Questions, 1995
We refer on some recent studies on classical electrodynamics of point particles, as described by ... more We refer on some recent studies on classical electrodynamics of point particles, as described by the Abraham-Lorentz-Dirac equation. Such studies exploit positively the well known existence of generic runaway solutions. Indeed the additional requirement that has to be imposed, namely the restriction to initial data giving rise to nonrunaway behaviour, turns out to allow for unexpected phenomena, for example a behaviour qualitatively similar to that occurring in the quantum tunnel effect. It is pointed out how this fact might be relevant for the problem of hidden parameters.
Physical Review A, 1976
Numerical investigations of dynamical systems allow one to give estimates of the rate of divergen... more Numerical investigations of dynamical systems allow one to give estimates of the rate of divergence of nearby trajectories, by means of a quantity which is usually assumed to be related to the Kolmogorov (or metric) entropy. In this paper it is shown first, on the basis of mathematical results of Oseledec and Piesin, how such a relation can be made precise. Then, as an example, a numerical study of the Kolmogorov entropy for the Henon-Heiles model is reported.
Calibration of Fundamental Stellar Quantities, 1985
For the calibration of radiation detectors, use is currently made of blackbodies, assuming they s... more For the calibration of radiation detectors, use is currently made of blackbodies, assuming they satisfy Planck's Law. The first problem considered here is then: how well has this law been checked experiment ally? Now, it has been pointed out (Crovini and Galgani 1984) that essentially no new experiments have been made after 1921 (Rubens and Michel 1921), when the data were interpreted as fitting the theoretical law within 1%. But, in fact, this work made use of the value 14300 (in suitable units) of the second radiation constant, while the presently adopted value is 14388. When one inserts this value into the calcul ations, one finds that, indeed, Planck's Law has been checked only to 3%. Furthermore, some theoretical considerations, based on Arnold's diffusion, lead to the idea that Planck's Law could be just a first approximation to the radiation law, and that one could expect some corrections in the Rayleigh-Jeans region for values of x=hv/kT less than 0.2. No experiments on blackbodies are available in that region. Looking, instead, at the data for the Sun, clear deviations are obser ved, giving a plateau.
Il Nuovo Cimento B Series 11, 1985
Summary In the present paper we study by numerical methods a Hamiltonian model describing a chai... more Summary In the present paper we study by numerical methods a Hamiltonian model describing a chain of weakly coupled rotators. The existence of local phenomena of ordered and chaotic motions is illustrated and is interpreted, within classical perturbation theory, in terms of resonances.
Il Nuovo Cimento B Series 11, 1985
Summary We show how to construct a classical perturbation theory at any finite order for an Hami... more Summary We show how to construct a classical perturbation theory at any finite order for an Hamiltonian system describing a chain of weakly coupled rotators, both for the nonresonant and for the resonant cases. In particular, by means of a suitable algebraic scheme, we show how small denominantors and propagation of harmonics can be controlled.
Pure and Applied Chemistry, 1970
It is pointed out that the usual basic postulate of increase of entropy for an isolated system, a... more It is pointed out that the usual basic postulate of increase of entropy for an isolated system, as stated for example by Tisza and Callen, if mathematically formalized, is expressed as a superadditivity property of entropy. This fact has two kinds of implications: (a) it allows one to deduce in a very direct and mathematically clear way stability properties such as Cv ~ 0 and KT ~ 0 and the equivalence of various thermodynamic schemes as expressed for example by the fact that the "minimum' property of the free energy is a consequence of the 'maximum' property of entropy; (b) it makes it possible to establish a link with foundations research, notably the system developed by Giles, where superadditivity of entropy appears as a consequence of other axioms.
Physical Review Letters, 1972
Journal of Statistical Physics, 1982
We make a numerical study of the solutions of the equations of motion for the electromagnetic fie... more We make a numerical study of the solutions of the equations of motion for the electromagnetic field in a one-dimensional model of a radiant cavity. Our main results are as follows: (1) There exist stochasticity thresholds such that below them one has ordered motions without energy exchanges, while chaotic motions with intense energy exchanges occur above them; (2) above thresholds there is a trend toward equipartition of energy (in time average) among the normal modes of the field, but this occurs in the sense of Boltzmann and Jeans, namely, with the higher frequencies requiring longer and longer times in order to be involved in the energy sharing.
Journal of Plasma Physics, 2002
We consider a model of viscoresistive incompressible magnetohydrodynamics in a periodic cylinder,... more We consider a model of viscoresistive incompressible magnetohydrodynamics in a periodic cylinder, with boundary conditions meant to idealize in a tractable way those of a laboratory plasma. The resistivity is described by a tensor presenting a field-dependent anisotropic part suggested by kinetic theory, controlled by a certain anisotropy parameter. An explicit analytical description of the corresponding axisymmetric zero-flow equilibria is given, and it is shown how tokamak-like or paramagnetic-pinch-like field profiles are obtained as the anisotropy parameter is changed. The study of the stability properties of such equilibria is deferred to a later paper.
Journal of Mathematical Physics, 1971
We start from the solution of the problem of the thermodynamic limit for microcanonical entropy a... more We start from the solution of the problem of the thermodynamic limit for microcanonical entropy as given by Ruelle and extend his method to solve the analogous problem of consistency, within the same ensemble, for the Legendre transforms of entropy. We solve then in a unified way the problem of the asymptotic equivalence of ensembles.
Communications in Nonlinear Science and Numerical Simulation, 2008
This article was published in an Elsevier journal. The attached copy is furnished to the author f... more This article was published in an Elsevier journal. The attached copy is furnished to the author for non-commercial research and education use, including for instruction at the author's institution, sharing with colleagues and providing to institution administration. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright