General properties of kinetic momenta in quantum mechanics

Ilya Prigogine, A.P. Grécos

Hicham Agueny, M Chovancova, J. P. Hansen +1 more

Abstract In recent experiments of single-cycle field ionization of excited Na( nd ) atoms with principal quantum number n ∈ [ 6 , 15 ] (Li and Jones 2014 Phys. Rev. Lett. 112 143006 ) it was shown that the maximum field intensity necessary to ionize 10% of the atoms decreases with increasing n according to an n − 3 power law dependence. This scaling property at the same ionization probability was confirmed in classical trajectory Monte Carlo calculations. In this work we note that the scaling relation in the experiment is much more general, it is in fact valid for all ionization probabilities. When applied to the emitted electron energies it places a very wide distribution of electron momenta from different initial states onto a narrow range. These aspects are investigated in a one-dimensional model with a 3D hydrogen-like spectrum. Calculations confirm the general n − 3 scaling relation for the ionization probability and that this particular scaling of the kinetic emission spectrum puts the ejected electron momenta on a narrow common scale. The ionization mechanism itself is identified as quantum mechanical tunneling and the nature of the tunneling process is the direct origin of the scaling law.

Serghey V. Vonsovsky

M. Bönitz

A. Lavagno, G. Gervino

On the basis of generalized classical kinetic equations, reproducing the sta- tionary distribution of the Tsallis nonextensive thermostatistics, we postulate a nonlinear generalized Schroedinger equation. Such a dynamical equation satisfies the basic assumptions of the quantum mechanics under an appropriate generalization of the operator properties. In this framework, we apply the above introduced classical nonlinear equation to a phenomenological study of observable measured in the relativistic heavy-ion collisions experiments.

Paulo N. Correa, Alexandra N. Correa

Unlike other physical theories, Aetherometry claims that the wave interference phenomena of massbound particles is caused by the diffraction of the electric waves of their kinetic energy, and not by a much misunderstood particle-wave duality. The new analytical treatment proposes that kinetic energy is captured field energy adapted to the inertial and magnetic constraints of massbound charges. The coincidence of two independent, nonclassical and nonrelativistic analyses - one inertial and the other electric - in the determination of the experimentally observed de Broglie wavelengths and momenta of electrons and massbound charges highlights the central contention that the paths of the accelerated charges in a beam are electric functions of its kinetic energy, and reflect in part the more fundamental interference properties of the underlying flux of a massfree electric field. Conversely, the interference properties of photons only directly reflect the interference properties of moving but decelerating charges. Written as an antidote to Richard Feynman's famous lecture, the present communication suggests that there is a method, after all, to count how many electrons pass through a slit, in a double-slit experiment.