Related papers: Experimental Mathematics and Mathematical Physics
Writing and argumentation are critical to both professional physics and physics education. However, the skill of making an extended argument in writing is often overlooked in physics classrooms, apart from certain practices like lab…
The article is devoted to new mathematical methods for psychophysical filtering of experimental data and their processing.
We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable | after the Heisenberg evolution associated with the…
In the operational approach to general probabilistic theories one distinguishes two spaces, the state space of the "elementary systems" and the physical space in which "laboratory devices" are embedded. Each of those spaces has its own…
We give a complete analytical computation of three and two-point loop integrals occurring in heavy-particle theories, involving a velocity change, for arbitrary real values of the external masses and residual momenta.
Computer experiments have become ubiquitous in science and engineering. Commonly, runs of these simulations demand considerable time and computing, making experimental design extremely important in gaining high quality information with…
Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is…
The quantum mechanical measurement process is considered. A hypothetical concept of irrational dynamical variables is proposed. A possible definition of measurement is discussed along with a mathematical method to calculate experimental…
Criteria for defining errors of a physical theory are formulated. It is shown that the Special Theory of Relativity (STR) has a solid mathematical basis. An enormous amount of experiments carried out in particle physics use beams of…
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…
We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions.…
We analyze the electromagnetic scattering of massive particles with and without spin wherein one particle (or both) is electrically neutral. Using the techniques of effective field theory, we isolate the leading long distance effects, both…
In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…
Both the topics of entanglement and particle statistics have aroused enormous research interest since the advent of quantum mechanics. Using two pairs of entangled particles we show that indistinguishability enforces a transfer of…
Empirical analysis serves as an important complement to theoretical analysis for studying practical Bayesian optimization. Often empirical insights expose strengths and weaknesses inaccessible to theoretical analysis. We define two metrics…
A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…
Quantum theory is incredibly successful, explaining the microscopic world with great accuracy, from the behaviour of subatomic particles to chemical reactions to solid-state electronics. There is not a single experimental finding…
For some research questions that involve Spin(p, q) representation theory, using symbolic algebra based techniques might be an attractive option for simplifying and manipulating expressions. Yet, for some such problems, especially as they…
We consider the integration of two-dimensional, piecewise constant functions with respect to copulas. By drawing a connection to linear assignment problems, we can give optimal upper and lower bounds for such integrals and construct the…
This paper addresses different aspects of "coupled" model descriptions in computational electromagnetics. This includes domain decomposition, multiscale problems, multiple or hybrid discrete field formulation and multi-physics problems.…