1,721,050 research outputs found
Planck’s formula for classical oscillators with stochasticity thresholds
No full textIn this paper a further contribution is given to the attempt of understanding the consequences that occur in statistical mechanics from the hypothesis that there exist stochasticity thresholds in the dynamics of an oscillator weakly coupled to a conservative system of oscillators, following an old idea of Nernst. By taking a point of view due to Boltzmann, and identifying the thermodynamic energy with that fraction of mechanical energy which is highly unstable and thus available to thermal exchanges, it is shown how one is thus led to Planck’s formula
A critical remark on Planck's model of black--body
No full textWe reexamine the model of matter--radiation interaction considered by Planck in his studies on the black--body problem, and point out that it is, in our opinion, inconsistent. The key point is that Planck's model deals in principle with a system of material resonators interacting with the field, but in fact Planck actually deals with a single forced resonator, because he explicitly makes the assumption that the resonators act {\it independently of one another}, i.e. perform incoherent motions. We show that this assumption is inconsistent when the contribution of all the resonators is taken into account.
Moreover we point out that, in view of the long range character of the electrodynamical forces, it would be more appropriate to deal from the start with the dynamics of the complete system, with the mutual
interaction of matter and radiation taken into account, looking for solutions of a coherent or correlated type (normal modes)
Asymptotic character of the series of classical electrodynamics and an application to bremsstrahlung
No full textThe Lorentz-Dirac equation, which describes the self-interaction of a classical charged particle with the electromagnetic field, is studied, for the case of scattering and in the non-relativistic approximation, in the framework of the theory of singular perturbation problems. We prove that the series expansions, which are usually given for the solutions in terms of the electric charge, in general are divergent and have asymptotic character. A closer inspection of such series leads to recognition of two types of particle motions, namely those qualitatively similar to purely mechanical ones (corresponding to vanishing charge), and those qualitatively dissimilar. For an attractive Coulomb potential, the distinction turns out to depend on the value of the initial angular, momentum, the threshold being of the order of magnitude of e2/c. Finally, we discuss the implications for the radiated spectrum, showing that the threshold in angular momentum should correspond to a frequency cutoff of the order of magnitude of the de Broglie frequency
Nonlocality of classical electrodynamics of point particles, and violation of Bell's inequalities
No full textWe show that Bell's inequalities are violated in a model of two charged particles interacting with two potential barriers, which mimic the measuring instruments; the motion of each particle is described by the Abraham-Lorentz-Dirac equation in the nonrelativistic version, and the role of the hidden variables is played by the initial accelerations. The essential nonlocality property of the system is induced by the celebrated Dirac's nonrunaway condition, which makes the measuring instruments have a certain influence on the observed system, by determining the domain of definition of the hidden variable (the Bopp-Haag phenomenon). So this model strongly supports E. Nelson's suggestion, namely that nonlocality properties suited to violate Bell's inequalities appear in classical field theories when regularizing cutoffs are removed
Planck's formula and glassy behavior in classical nonequilibrium statistical mechanics
No full textIn statistical mechanics it is well known that one has to take into account the role of the relaxation times to equilibrium. We discuss the relevance of this fact for systems of weakly coupled harmonic oscillators in a classical framework, showing how one has a behavior similar to that of glassy systems and how one finds an analogue of Planck's formula. From this point of view, quantum equilibrium statistical mechanics thus appears as a first-order approximation in classical nonequilibrium statistical mechanics very far from equilibrium
Einstein Classical Program Revived
Get PDFThe Einstein Classical Program is well known: to prove that, at least in the domain of atomic physics, quantum
mechanics can be recovered from a theory presenting some “realistic character’’. Here we address an extreme form
of the program in which the realistic theory is just classical electrodynamics of point charges, and give concrete
examples in which typical “quantum phenomena’’ are explained. Namely, spectral lines (in the case of ionic crystals)
and chemical bond (in the case of the H 2
+ ion of the Hydrogen molecule). Additionally, an explanation is given of a
phenomenon (existence of polaritons in ionic crystals), for which a quantum explanation is still lacking. Concerning
the general objection that a classical theory would be impossible because of radiative collapse (radiation emission
by accelerated charges), we illustrate how it is removed for charges in a medium, in virtue of the Wheeler-Feynman
cancellation. The impact of such results for the general reductionistic program is also commented
Formal integrals for an autonomous Hamiltonian system near an equilibrium point
No full textIn this paper we give a new method to construct formal integrals for an autonomous Hamiltonian system near an equilibrium point. Our construction is reminiscent of the algorithms introduced by Hori and Deprit; we show however how it presents itself quite naturally if one follows the line of attack of Whittaker, Cherry, and Contopoulos. © 1978 D. Reidel Publishing Company
Metastability in specific heat measurements: simulations with the FPU model
Get PDFIn this letter we report numerical results giving, as a function of time, the energy fluctuation of a Fermi–Pasta–Ulam system in dynamical contact with a heat bath, the initial data of the FPU system being extracted from a Gibbs distribution at the same temperature of
the bath. The aim is to get information on the specific heat of the FPU system in the spirit of the fluctuation–dissipation theorem. While the standard equilibrium result is recovered at high temperatures, there exists a critical temperature below which the energy fluctuation as a function of time tends to an asymptotic value sensibly lower than the one expected at equilibrium. This fact appears to exhibit the existence of a metastable state for generic initial conditions. An analogous phenomenon of metastability was up to now observed in FPU systems only for exceptional initial data having vanishing Gibbs measure, namely excitations of a few low–frequency modes (as in the original FPU work)
Theory of dynamical systems and the relations between classical and quantum mechanics
Get PDFWe give a review of some works where it is shown that certain quantum-like features are exhibited by classical systems. Two kinds of problems are considered. The first one concerns the specific heat of crystals (the so called Fermi-Pasta-Ulam problem), where a glassy behavior is observed, and the energy distribution is found to be of Planck-like type. The second kind of problems concerns the self-interaction of a charged particle with the electromagnetic field, where an analog of the tunnel effect is proven to exist, and moreover some nonlocal effects are exhibited, leading to a natural hidden variable theory which violates Bell's inequalities
Nonradiating normal modes in a classical many-body model of matter-radiation interaction
No full textWe consider a classical model of matter--radiation interaction, in which the matter is represented by a system of infinitely many dipoles on a one--dimensional lattice, and the system is dealt with in the so--called dipole (i.e. linearized) approximation. We prove that there exist normal--mode solutions of the complete system, so that in particular the dipoles, though performing accelerated motions, do not radiate energy away. This comes about in virtue of an exact compensation which we prove to occur, for each dipole, between the ``radiation reaction force'' and a part of the retarded forces due to all the other dipoles. This fact corresponds to a certain identity which we name after Oseen, since it occurs that this researcher did actually propose it, already in the year 1916. We finally make a connection with a paper of Wheeler and Feynman on the foundations of electrodynamics. It turns out indeed that the Oseen identity, which we prove here in a particular model, is in fact a weak form of a general identity that such authors were assuming as an independent postulate
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