Related papers: Spencer Operator and Applications: From Continuum …
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…
The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…
The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches…
This paper continues the program of applying beyond physics the technique of \textbf{probabilistic quantization} and extending to the quantum mechanics associated with the arc--sine distributions our previous results on the semi--circle…
Using five basic principles we treat Gerstenhaber/Lie brackets, BV operators and Master equations appearing in mathematical and physical contexts in a unified way. The different contexts for this are given by the different types of…
In the Fermi Lectures on the obstacle problem in 1998, Caffarelli gave a proof of the mean value theorem which extends to general divergence form uniformly elliptic operators. In the general setting, the result shows that for any such…
Students in quantum mechanics class are taught that the wave function contains all knowable information about an isolated system. Later in the course, this view seems to be contradicted by the mysterious density matrix, which introduces a…
Mercer inequality for convex functions is a variant of Jensen's inequality, with an operator version that is still valid without operator convexity. This paper is two folded. First, we present a Mercer-type inequality for operators without…
The Jordan algebra structure of the bounded real quantum observables was recognized already in the early days of quantum mechanics. While there are plausible reasons for most parts of this structure, the existence of the distributive…
This work starts with the introduction of a family of differential energy operators. Energy operators ($Psi_R^+$, $Psi_R^-$) were defined together with a method to decompose the wave equation in a previous work. Here the energy operators…
We extend the quantum-mechanical results of Muller & Saunders (2008) establishing the weak discernibility of an arbitrary number of similar fermions in finite-dimensional Hilbert-spaces in two ways: (a) from fermions to bosons for all…
This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…
Einstein's article on the EPR paradox is the most cited of his works, but not many know that it was not fully representative of the way he thought about the incompleteness of the quantum formalism. Indeed, his main worry was not…
In this paper we extend the traditional framework of noncommutative geometry in order to deal with spectral truncations of geometric spaces (i.e. imposing an ultraviolet cutoff in momentum space) and with tolerance relations which provide a…
First-order differential operators arising from the representation-theoretic decomposition of the covariant derivative play a central role in Riemannian geometry. In this paper, we study Stein-Weiss $O(n)$-gradients acting on covariant…
Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the…
The Euler-Lagrange equations (EL) are very important in the theoretical description of several physical systems. In this work we have used a simplified form of EL to study one-dimensional motions under the action of a constant force. From…
John von Neumann's spectral theorem for self-adjoint operators is a cornerstone of quantum mechanics. Among other things, it also provides a connection between expectation values of self-adjoint operators and expected values of real-valued…