arXiv subjects

Zurab K. Silagadze

Publications and source records attributed to Zurab K. Silagadze.

23 records · Page 2Linked to original sources

arXiv2020

Free fall in KvN mechanics and Einstein's principle of equivalence

The implementation of Einstein's principle of equivalence in Koopman-von Neumann (KvN) mechanics is discussed. The implementation is very similar to the implementation of this principle in quantum mechanics. This is not surprising, because KvN mechanics provides a Hilbert space formulation of classical mechanics that is very similar to the quantum mechanical formalism. Both in KvN mechanics and quantum mechanics, a propagator in a homogeneous gravitational field is simply related with a free propagator. As a result, the wave function in a homogeneous gravitational field in a freely falling reference frame differs from the free wave function only in phase. Fisher information, which quantifies our ability to estimate mass from coordinate measurements, does not depend on the magnitude of the homogeneous gravitational field, and this fact constitutes the formulation of Einstein's principle of equivalence, which is valid both in quantum mechanics and KvN mechanics.

gr-qc↗

arXiv2020

Trigonometric identities inspired by atomic form factor

We prove some trigonometric identities involving Chebyshev polynomials of second kind. The identities were inspired by atomic form factor calculations. Generalizations of these identities, if found, will help to increase the numerical stability of atomic form factors calculations for highly excited states.

physics.atom-ph↗

arXiv2018

Two-photon decay of P-wave positronium: a tutorial

A detailed exposition of two-photon decays of P-wave positronium is given to fill an existing gap in the pedagogical literature. Annihilation decay rates of P-wave positronium are negligible compared to the rates of radiative electric dipole transitions to the ground state. This circumstance makes such decays experimentally inaccessible. However the situation is different for quarkonium and the experimental and theoretical research of two-photon and two-gluon decays of P-wave quarkonia is a still flourishing field.

hep-ph↗

arXiv2018

Visceral theory of sleep and origins of mental disorders

Visceral theory of sleep states that the same brain neurons, which process external information in wakefulness, during sleep switch to the processing of internal information coming from various visceral systems. Here we hypothesize that a failure in the commutation of exteroceptive and interoceptive information flows in the brain can manifest itself as a mental illness.

q-bio.NC↗

arXiv2015

Black hole remnants due to Planck-length deformed QFT

It was argued in a number of papers that the gravitational potential calculated by using the modified QFT that follows from the Planck-length deformed uncertainty relation implies the existence of black-hole remnants of the order of the Planck-mass. Usually this sort of QFTs are endowed with two specific features, the modified dispersion relation, which is universal, and the concept of minimum length, which, however, is not universal. While the emergence of the minimum-length most readily leads to the idea of the black hole remnants, here we examine the behaviour of the potential that follows from the Planck-length deformed QFT in absence of the minimum length and show that it might also lead to the formation of the Planck mass black holes in some particular cases. The calculations are made for higher-dimensional case as well. Such black hole remnants might be considered as a possible candidates for the dark-matter.

gr-qc↗