Related papers: The Origin of the Planck's Constant
\noindent Using the techniques connected with the measure of noncompactness we investigate the neutral difference equation of the following form \begin{equation*} \Delta \left(r_{n}\left(\Delta \left(x_{n}+p_{n}x_{n-k}\right) \right)…
In this work, we introduce a new difference equation which is discrete analogue of Diffusion differential equation and analyze some essential spectral properties, Diffusion difference operator is self-adjoint, eigenvalues of this problem…
In this study, we derive the Planck distribution function in noncommutative space. It is found that it is modified by a small factor. It is shown that it is reduced to the usual Planck distribution function in the commutative limit .
For the past two years, measurements have been performed with a watt balance at the National Institute of Standards and Technology (NIST) to determine the Planck constant. A detailed analysis of these measurements and their uncertainties…
The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation, a no-relativistic particle with a time explicitly depending force, a no-relativistic particle with a constant force and time…
We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional…
The Planck scale is considered to be a natural minimum scale, made up as it is solely of fundamental constants. However the Planck scale is well beyond the scales encountered in real life, these latter being at least of the order of the…
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…
The hallmark of quantum physics is Planck's constant $h$, whose finite value entails the quantization that gave the theory its name. The finite value of $h$ gives rise to inevitable zero-point fluctuations even at vanishing temperature. The…
We elaborate on the proposal of [Phys. Rev. Lett. 123 (2019) 13, 131302], about the possibility of hiding the cosmological constant in the complicated topology that one expects to exist at the Planck scale. We build a differential equation…
A thermodynamic analogue of the Pauli problem (reconstruction of a wavefunction from the position and momentum distributions) is formulated. The coordinates of a quantum system are replaced by the inverse absolute temperature and other…
Difference Boltzmann Equation is derived in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors is used as the second…
This article contains a brief pedagogical introduction to various renormalization group related aspects of quantum gravity with an emphasis on the scale dependence of Newton's constant and on black hole physics.
We discuss the naturalness of exponential potentials for quintessence, showing that the resulting almost flat direction in the space of scalar fields, as well as the small time dependent cosmon mass, can be related to an anomalous…
A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation…
We review recent theoretical models and experiments dealing with the diffraction of neutral atoms from a reflection grating, formed by a standing evanescent wave. We analyze diffraction mechanisms proposed for normal and grazing incidence,…
In this work, we study nonlocal differential equations with particular focus on those with reflection in their argument and piecewise constant dependence. The approach entails deriving the explicit expression of the solution to the linear…
The Lamb-Bateman integral equation was introduced to study the solitary wave diffraction and its solution was written in terms of an integral transform. We prove that it is essentially the Abel integral equation and its solution can be…
We present an analysis of the foundations of the well known Clausius inequality. It is shown that, strictly speaking, the inequality is not a logical consequence of the Kelvin-Planck formulation of the second law of thermodynamics. Some…
A transfer matrix formalism applicable to certain reparametrization invariant theories, including quantum gravity, is proposed. In this formulation it is found that every stationary state in quantum gravity satisfies a Wheeler-DeWitt…