Related papers: Unveiling Symmetries Patterns: A Study of Circular…
The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with…
Circular-harmonic spectra are a compact representation of local image features in two dimensions. It is well known that the computational complexity of such transforms is greatly reduced when polar separability is exploited in steerable…
The purpose of this paper is the discussion of a pair of coupled linear oscillators that has recently been proposed as a model of a system of two optical resonators. By means of an algebraic approach we show that the frequencies of the…
We show the existence of a continuum of Hamiltonian structures for the two-dimensional isotropic harmonic oscillator. In particular, a continuum of Hamiltonian structures having noncommutative coordinates is presented. A study of the…
Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative…
Linear time invariant (LTI) systems are widely used for modeling system dynamics in science and engineering problems. Harmonic oscillation of LTI systems are widely used for modeling and analyses of periodic physical phenomenon. This study…
Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution…
The isotropic harmonic oscillator in N dimensions is shown to have an underlying symmetry group O(2,1)X O(N)which implies a unique result for the energy spectrum of the system. Raising and lowering operators analogous to those of the…
In the last decades, a very important breakthrough has been brought in the elementary particle physics by the discovery of the phenomenon of the neutrino oscillations, which has shown neutrino properties beyond the Standard Model. But a…
We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance…
Using only linear interactions and a local parity measurement we show how entanglement can be detected between two harmonic oscillators. The scheme generalizes to measure both linear and non-linear functionals of an arbitrary oscillator…
Three-flavor neutrino oscillations in matter can be described by three effective neutrino masses $\widetilde{m}^{}_i$ (for $i = 1, 2, 3$) and the effective mixing matrix $V^{}_{\alpha i}$ (for $\alpha = e, \mu, \tau$ and $i = 1, 2, 3$).…
We discuss the use of symmetries for analysing the structural identifiability and observability of control systems. Special emphasis is put on the role of discrete symmetries, in contrast to the more commonly studied continuous or Lie…
Coupled oscillator-based networks are an attractive approach for implementing hardware neural networks based on emerging nanotechnologies. However, the readout of the state of a coupled oscillator network is a difficult challenge in…
Any system of coupled oscillators may be characterized by its spectrum of resonance frequencies (or eigenfrequencies), which can be tuned by varying the system's parameters. The relationship between control parameters and the eigenfrequency…
We study a system of four identical globally coupled phase oscillators with biharmonic coupling function. Its dimension and the type of coupling make it the minimal system of Kuramoto-type (both in the sense of the phase space's dimension…
A hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These…
We review here some general properties of antiferromagnetic Heisenberg spin chains, emphasizing and discussing the role of hidden symmetries in the classification of the various phases of the models. We present also some recent results that…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…