Related papers: Discrete Liouville equation and Teichm\"uller theo…
Here are a few random thoughts on the interpretations of the quantum double slit experiment, the Mach Zehnder experiment, the delayed-choice experiment and the measurement problem.
We adapt some of the methods of quantum Teichm\"uller theory to construct a family of representations of the pure braid group of the sphere.
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
Using the decoherence formalism of Gell-Mann and Hartle, a quantum system is found which is the equivalent of the classical chaotic Duffing oscillator. The similarities and the differences from the classical oscillator are examined; in…
The problem of classical particle in linear potential is studied by using the formalism of Hilbert space and tomographic probability distribution. The Liouville equation for this problem is solved by finding the density matrix satisfying…
We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof…
** The primary topic of this dissertation is the study of the relationships between parts and wholes as described by particular physical theories, namely generalized probability theories in a quasi-classical physics framework and…
The singularity theorems of classical general relativity are briefly reviewed. The extent to which their conclusions might still apply when quantum theory is taken into account is discussed. There are two distinct quantum loopholes: quantum…
A simple implementation of Noether's theorem for discrete symmetries in relativistic continuum field theories is presented. The associated conserved current is exemplified by charge conjugation and a cyclic symmetry. In addition, the…
In this paper, we present a new approachment for Sturm-Liouville problem having special potentials. We acquire the representations of solutions and asymptotic formulas for solutions with regard to initial conditions. Also, a few…
We first compare the mathematical structure of quantum and classical mechanics when both are formulated in a C*-algebraic framework. By using finite von Neumann algebras, a quantum mechanical analogue of Liouville's theorem is then…
In this note we provide a gentle introduction to the concepts and intuition behind the recent breakthrough results on the mathematically rigorous construction of a non-trivial 2D conformal field theory, namely the so-called Liouville…
The Sturm-Liouville equation represents the linearized form of the first-order Riccati equation. This provides an evidence for the connection between Schwarzian derivative and this first-order nonlinear differential equation. Similar…
Here we define a Caputo like discrete fractional difference and we compare it to the earlier defined Riemann-Liouville fractional discrete analog. Then we produce discrete fractional Taylor formulae for the first time, and we estimate their…
We address the relation between quantum metrological resolution and coherence. We examine this dependence in two manners: we develop a quantum Wiener-Kintchine theorem for a suitable model of quantum ruler, and we compute the Fisher…
An introduction to the physical interpretation of the Coulomb logarithm is given with particular emphasis on the quantum-mechanical corrections that are required at high temperatures. Excerpts from the literature are used to emphasize the…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
In this short note, we study the smoothness of the extremal solutions to the Liouville system
We investigate the spin dynamics of a dipole-coupled system by comparing a direct solution of the Schrodinger equation for quantum spins with simulations of classical spins. Although classical spins have long been used in microscopic spin…
We discuss direct and inverse spectral theory of self-adjoint Sturm-Liouville relations with separated boundary conditions in the left-definite setting. In particular, we develop singular Weyl-Titchmarsh theory for these relations.…