Related papers: Quantum-Mechanical interpretation of Riemann zeta …
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for spectra of temporal fluctuations. Such non-local connections…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
We study an integrable vertex model with a periodic boundary condition associated with U_q(A_n^{(1)}) at the crystallizing point q=0. It is an (n+1)-state cellular automaton describing the factorized scattering of solitons. The dynamics…
In general, a finite metric function at the center of a black hole describes a non-singular spacetime but an infinite metric at the center gives a singular spacetime, where the former is associated with convergent Ricci and Kretschmann…
This paper is a summary of the general approach outlined in my previous papers toward proving the riemann hypothesis. Numerical and graphical proof of the Riemann Hypothesis is presented with analytical arguments although more work needs…
A Riemmanian foliated dynamical system of 3-dimension $(\mathrm{RFDS}^{3})$ is a closed Riemannian 3-manifold with additional structures: foliation, dynamical system. In the context of arithmetic topology, it is a geometric/analytic…
Relativistic dynamics with energy and momentum resricted to an anti-de-Sitter space is presented, specifically in the introduction of coordiate operators conjugate to such momenta. Definition of functions of these operators, their…
We present a prototype of behavior of glassy systems driven by quantum dynamics in a quenching protocol by analyzing the random energy model in a transverse field. We calculate several types of dynamical quantum amplitude and find a…
We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space Q. These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental…
We consider a charged particle moving in the plane subject to electromagnetic potentials with non-vanishing radial limits. We analyse the classical and the quantum dynamics for large time in the case the angular part of the (limiting)…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
We study the dynamics of a two-level quantum system interacting with an external electromagnetic field periodic and quasiperiodic in time. The quantum evolution is described exactly by the classical equations of motion of a gyromagnet in a…
We investigate the meaning of the wave function by analyzing the mass and charge density distribution of a quantum system. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus…
We have given some arguments that a two-dimensional Lorentz-invariant Hamiltonian may be relevant to the Riemann hypothesis concerning zero points of the Riemann zeta function. Some eigenfunction of the Hamiltonian corresponding to…
Physical systems are often neither completely closed nor completely open, but instead they are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main…
We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these…
Let $a\in (0,1)$ and let $F_s(a)$ be the periodized zeta function that is defined as $F_s(a) = \sum n^{-s} \exp (2\pi i na)$ for $\Re s >1$, and extended to the complex plane via analytic continuation. Let $s_n = \sigma_n + it_n, \, t_n >0…
A possible connection between quantum computing and Zeta functions of finite field equations is described. Inspired by the 'spectral approach' to the Riemann conjecture, the assumption is that the zeroes of such Zeta functions correspond to…
We consider quantum general relativity in three dimensions with a positive cosmological constant. The Hartle-Hawking wave function is computed as a function of metric data at asymptotic future infinity. The analytic continuation from…