Related papers: Four Lectures on Weierstrass Elliptic Function and…
We establish a version of the Landen's transformation for Weierstrass functions and invariants that is applicable to general lattices in complex plane. Using it we present an effective method for computing Weierstrass functions, their…
Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The…
In statistical mechanics, it is well known that finite-state classical lattice models can be recast as quantum models, with distinct classical configurations identified with orthogonal basis states. This mapping makes classical statistical…
The Physics Education Group at the University of Washington is examining the extent to which students are able to use graphs of potential energy vs. position to infer kinematic and dynamic quantities for a system. The findings indicate that…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
These are the notes from a course of five lectures at the 2009 Park City Math Institute. The focus is on elliptic curves over function fields over finite fields. In the first three lectures, we explain the main classical results (mainly due…
A survey on the dynamical and thermodynamical properties of plasmas with strong Coulomb interactions in the quasi-classical density-temperature region is given. First the basic theoretical concepts describing nonideality are discussed. The…
The Weierstrassian $\wp, \zeta$ and $\sigma $ functions are generalized to ${\bf R}^{n}$. The $n=3$ and $n=4$ cases have already been used in gravitational and Yang-Mills instanton solutions which may be interpreted as explicit realizations…
Using a particular Hilbert space representation of minimum-length deformed quantum mechanics, we show that the resolution of the wave-function singularities for strongly attractive potentials, as well as cosmological singularity in the…
English abstract: In the "Intuitive Quantum Physics" course, we use graphical interpretations of mathematical equations and qualitative reasoning to develop and teach a simplified model of quantum physics. Our course contains three units:…
A short review will be made of elliptic integrals, widely applied in GPS (Global Positioning System) communications (accounting for General Relativity Theory-effects), cosmology, Black hole physics and celestial mechanics. Then a novel…
These are the handouts of an undergraduate minicourse at the Universit\`a di Bari, in the context of the 2017 INdAM Intensive Period "Contemporary Research in elliptic PDEs and related topics". Without any intention to serve as a throughout…
The advent of hybrid computing platforms consisting of quantum processing units integrated with conventional high-performance computing brings new opportunities for algorithm design. By strategically offloading select portions of the…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
After briefly reviewing the definitions of classical probability densities for position, $P_{CL}(x)$, and for momentum, $P_{CL}(p)$, we present several examples of classical mechanical potential systems, mostly variations on such familiar…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
Jacobi elliptic functions are flexible functions that appear in a variety of problems in physics and engineering. We introduce and describe important features of these functions and present a physical example from classical mechanics where…
A formulation of classical electrodynamics on an energy-momentum background of constant, non-zero curvature is given. The procedure consists of taking the formulation of standard electrodynamics in the energy-momentum representation, and…
The composition of the quantum potential and its role in the breakdown of classical symplectic symmetry in quantum mechanics is investigated. General expressions are derived for the quantum potential in both configuration space and momentum…
We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on…