52 research outputs found
Classical microscopic theory of dispersion, emission and absorption of light in dielectrics
This paper is a continuation of a recent one in which, apparently for the
first time, the existence of polaritons in ionic crystals was proven in a
microscopic electrodynamic theory. This was obtained through an explicit
computation of the dispersion curves. Here the main further contribution
consists in studying electric susceptibility, from which the spectrum can be
inferred. We show how susceptibility is obtained by the Green--Kubo methods of
Hamiltonian statistical mechanics, and give for it a concrete expression in
terms of time--correlation functions. As in the previous paper, here too we
work in a completely classical framework, in which the electrodynamic forces
acting on the charges are all taken into account, both the retarded forces and
the radiation reaction ones. So, in order to apply the methods of statistical
mechanics, the system has to be previously reduced to a Hamiltonian one. This
is made possible in virtue of two global properties of classical
electrodynamics, namely, the Wheeler--Feynman identity and the Ewald
resummation properties, the proofs of which were already given for ordered
system. The second contribution consists in formulating the theory in a
completely general way, so that in principle it applies also to disordered
systems such as glasses, or liquids or gases, provided the two general
properties mentioned above continue to hold. A first step in this direction is
made here by providing a completely general proof of the Wheeler--Feynman
identity, which is shown to be the counterpart of a general causality property
of classical electrodynamics. Finally it is shown how a line spectrum can
appear at all in classical systems, as a counterpart of suitable stability
properties of the motions, with a broadening due to a coexistence of
chaoticity
Theoretical thermodynamic analysis of a closed-cycle process for the conversion of heat into electrical energy by means of a distiller and an electrochemical cell
We analyse a device aimed at the conversion of heat into electrical energy,
based on a closed cycle in which a distiller generates two solutions at
different concentrations, and an electrochemical cell consumes the
concentration difference, converting it into electrical current. We first study
an ideal model of such a process. We show that, if the device works at a single
fixed pressure (i.e. with a ``single effect''), then the efficiency of the
conversion of heat into electrical power can approach the efficiency of a
reversible Carnot engine operating between the boiling temperature of the
concentrated solution and that of the pure solvent. When two heat reservoirs
with a higher temperature difference are available, the overall efficiency can
be incremented by employing an arrangement of multiple cells working at
different pressures (``multiple effects''). We find that a given efficiency can
be achieved with a reduced number of effects by using solutions with a high
boiling point elevation.Comment: The following article has been submitted to Journal of Renewable and
Sustainable Energy. After it is published, it will be found at
http://scitation.aip.org/content/aip/journal/jrs
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
Relaxation times and ergodicity properties in a realistic ionic--crystal model, and the modern form of the FPU problem
It is well known that Gibbs' statistical mechanics is not justified for
systems presenting long-range interactions, such as plasmas or galaxies. In a
previous work we considered a realistic FPU-like model of an ionic crystal (and
thus with long-range interactions), and showed that it reproduces the
experimental infrared spectra from 1000 K down to 7 K, provided one abandons
the Gibbs identification of temperature in terms of specific kinetic energy, at
low temperatures. Here we investigate such a model in connection with its
ergodicity properties. The conclusion we reach is that at low temperatures
ergodicity does not occur, and thus the Gibbs prescriptions are not dynamically
justified, up to geological time scales. We finally give a preliminary result
indicating how the so-called `nonclassical' q-statistics show up in the
realistic ionic-crystal model. How to formulate a consistent statistical
mechanics, with the corresponding suitable identification of temperature in
such nonergodicity conditions, remains an open problem, which apparently
constitutes the modern form of the FPU problem
- …