Related papers: Inverse problem for Planck formula
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory…
Inverse scattering transform method of the heat equation is developed for a special subclass of potentials nondecaying at space infinity---perturbations of the one-soliton potential by means of decaying two-dimensional functions. Extended…
Electromagnetism is a \textit{relativistic} theory and one must exercise care in coupling this theory with \textit{nonrelativistic} classical mechanics and with \textit{nonrelativistic} classical statistical mechanics. Indeed historically,…
"Negative energy" has been one of the most enduring puzzles in quantum theory, whereas the present work reveals that it actually plays a central role in clarifying various controversies of quantum theory. The basic idea is contained in a…
Temperature is an outsider in the laws of motion given by Newton and Einstein and this oversight is the source of the predictions of time-reversal-invariance made by these two great systems of motion. By taking into consideration Planck's…
A factorization formula for wave functions, which is basic in the inverse spectral transform approach to initial-boundary value problems, is proved in greater generality than before. Applications follow. Related compatibility questions for…
The true- and eccentric-anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits by considering perturbations of the radial part of kinetic energy as a series in the negative powers of the orbital radius. A…
For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time-averages, and the main problem is then how to formulate an appropriate statistical thermodynamics. The common answer is that the…
The second Tisza-Callen postulate of equilibrium thermodynamics states that for any system exists a function of the system's extensive parameters, called entropy, defined for all equilibrium states and having the property that the values…
It has been suggested recently that `$q$-exponential' distributions which form the basis of Tsallis' non-extensive thermostatistical formalism may be viewed as mixtures of exponential (Gibbs) distributions characterized by a fluctuating…
By examining two counterexamples to the existing theory, it is shown, with mathematical rigor, that as far as scattered particles are concerned the true distribution function is in principle not determinable (indeterminacy principle or…
The boundary problem for a two-dimensional elliptical equation -sinh-Gordon has been investigated. The exact solutions have been found and identities of traces have been proposed. The application of the problem to the model of the Coulomb's…
The Planck's radiation law for the blackbody radiation spectrum was capable to explain the experimentally-measured blackbody spectrum. In order to get this result, Planck proposed his radiation law in a two-fold way: 1) by an \textit{ad…
An inverse boundary value problem for the Helmholtz equation in a bounded domain is considered. The problem is to extract information about an unknown obstacle embedded in the domain with unknown impedance boundary condition (the Robin…
The generalized uncertainty principle (GUP) modifies the uncertainty relation between momentum and position giving room for a minimal length, as predicted by candidates theories of quantum gravity. Inspired by GUP, Planck's distribution is…
We suggest an unified presentation to teach fundamental constants to graduate students, by introducing four lower limits to observed phenomena. The reduced Planck constant $\hbar$ is the lowest classically definable action. The inverse of…
We develop a differential theory for the polarity transform parallel to that for the Legendre transform, which is applicable when the functions studied are "geometric convex", namely convex, non-negative and vanish at the origin. This…
We construct a new class of charged rotating solutions of $(n+1)$-dimensional Einstein-Born-Infeld gravity with cylindrical or toroidal horizons in the presence of cosmological constant and investigate their properties. These solutions are…
The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to a thermodynamic force in its first order solution. Both existence and uniqueness of such a…
Using a quantum-kinetic many-body approach, exact results for the interacting system of field and matter in a specified geometry are presented. It is shown that both the spectral function of photons and the field fluctuations split up into…