Related papers: Unveiling Symmetries Patterns: A Study of Circular…
Research on synchronization of coupled oscillators has helped explain how uniform behavior emerges in populations of non-uniform systems. But explaining how uniform populations engage in sustainable non-uniform synchronization may prove to…
In this paper, we study the occurrence of patterns in the cycle structures of permutations.
This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\leq j\leq N$) has the natural frequency $\omega_j$ and is described by the Hamiltonian $\frac{1}{2}p_j^2+\frac{1}{2}\omega_j^2x_j^2$. The…
The concept of unique normal form is formulated in terms of a spectral sequence. As an illustration of this technique some results of Baider and Churchill concerning the normal form of the anharmonic oscillator are reproduced. The aim of…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\'enard and generalized Li\'enard type, which physically describe important…
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
The one-dimensional Schr\"{o}dinger equation with the singular harmonic oscillator is investigated. The Hermiticity of the operators related to observable physical quantities is used as a criterion to show that the attractive or repulsive…
We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the…
We study the entanglement Hamiltonian of two disjoint blocks in the harmonic chain on the line and in its ground state. In the regime of large mass, the non vanishing terms are only the on-site and the nearest-neighbour ones. Analytic…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical…
Conventionally while we talk about geometry associated with a simple harmonic oscillator, we draw a circle with a radius equal to the amplitude of Oscillator and imagine a particle moving along the perimeter with a frequency same as that of…
The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different…
We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral…
The quantization of circular strings in an anti-de Sitter background spacetime is performed, obtaining a discrete spectrum for the string mass. A comparison with a four-dimensional homogeneous and isotropic spacetime coupled to a conformal…
We carry out a model-theoretic analysis of the Heisenberg algebra. To this end, a geometric structure is associated to the Heisenberg algebra and is shown to be a Zariski geometry. Furthermore, this Zariski geometry is shown to be…
We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the…
In networks of identical linear oscillators (e.g. pendulums undergoing small vibrations) coupled through both dissipative connectors (e.g. dampers) and restorative connectors (e.g. springs) the relation between asymptotic synchronization…
We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…