Related papers: 2-States and a fifth force
Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
An iterative algorithm for state determination is presented that uses as physical input the probability distributions for the eigenvalues of two or more observables in an unknown state $\Phi$. Starting form an arbitrary state $\Psi_{0}$, a…
The Newtonian concept of force may be useful in some aspects of the dynamics of many-particle quantum systems such as fissioning nuclei. Following Ehrenfest's method, we show that the quantum kinetic force between parts of an extended…
Using the tools of nonstandard analysis, we develop and present an alternative formulation of Bohmian mechanics. This approach allows one to describe a broader assortment of physical systems than the standard formulation of the theory. It…
The kinetic energy operator of a quantum particle with position dependent mass and the associated ordering ambiguity is revisited. We introduce a new form of this operator which is a continues or discreet superposition of the acceptable…
Recently, a proposal has been advanced to detect unconstitutional partisan gerrymandering with a simple formula called the efficiency gap. The efficiency gap is now working its way towards a possible landmark case in the Supreme Court. This…
To address the observation of Max Born (M. Born 1969) that the Newton's second law can emerge from a purely statistical perspective, we derive the evolution equation about the statistical distribution for dilute gas based solely on…
Experimental determination of an unknown quantum state usually requires several incompatible measurements. However, it is also possible to determine the full quantum state from a single, repeated measurement. For this purpose, the quantum…
Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies…
Newton's inverse-square law of universal gravitation assumes constant mass. But mass increases with speed and perhaps with gravity. By SR, mass is increased over the rest mass by gamma. Rest mass is here postulated to increase under…
Nonlinear scalar-tensor theories of gravity have been considered as candidates for dark matter and dark energy. Often, they possess screening mechanisms, which allow the fifth force mediated by the additional scalar degree(s) of freedom to…
We evaluate the second--order (beyond--mean--field) contribution to the equation of state of nuclear matter with the effective Skyrme force and use cutoff and dimensional regularizations to treat the ultraviolet divergence produced by the…
In trying to explain the present accelerated expansion of the universe in the light of a five-dimensional Brans-Dicke theory, it is found that the fifth dimension itself here acts as a source of dark energy. It may be taken as a…
A new thresholding method, based on L-statistics and called order thresholding, is proposed as a technique for improving the power when testing against high-dimensional alternatives. The new method allows great flexibility in the choice of…
Explicit expressions for the hypergeometric series ${}_2F_1(-n, a; 2a\pm j;2)$ and ${}_2F_1(-n, a; -2n\pm j;2)$ for positive integer $n$ and arbitrary integer $j$ are obtained with the help of generalizations of Kummer's second and third…
We give a new example for a proper scoring rule motivated by the form of Anderson--Darling distance of distribution functions and Example 5 in Brehmer and Gneiting (2020).
Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that…
A brief history is given of the factor 2, starting in the most elementary considerations of geometry and kinematics of uniform acceleration, and moving to relativity, quantum mechanics and particle physics. The basic argument is that in all…
From the equilibrium condition $\delta S=0$ applied to an isolated thermodynamic system of electrically charged particles and the fundamental equation of thermodynamics ($dU = T dS-(\mathbf{f}\cdot d\mathbf{r})$) subject to a new procedure,…