Related papers: The finite harmonic oscillator and its associated …
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
An exactly-solvable model of the non-relativistic harmonic oscillator with a position-dependent effective mass is constructed. The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. Such a form of the…
In this manuscript, we develope the theory of harmonic analysis on the Heisenberg group G of high dimension. We investigate the theta functions and the Weil representation related to this Heisenberg group and describe the connection among…
A linear open quantum system consisting of a harmonic oscillator linearly coupled to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in a…
The problem of the quantum harmonic oscillator is investigated in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero divisors. Starting with the commutator of the bicomplex position…
We analyze recent results for a harmonic oscillator in an environment with a pointlike defect. We show that the allowed oscillator frequencies predicted by the authors stem from a misinterpretation of the exact solutions of a conditionally…
We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method. A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients. Truncation…
The dynamics of a system formed by a finite number $N$ of globally coupled bistable oscillators and driven by external forces is studied focusing on a global variable defined as the arithmetic mean of each oscillator variable. Several…
We determine the energy eigenvalues and eigenfunctions of the harmonic oscillator where the coordinates and momenta are assumed to obey the modified commutation relations [x_i,p_j]=i hbar[(1+ beta p^2) delta_{ij} + beta' p_i p_j]. These…
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…
The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
Weyl's formulation of quantum mechanics opened the possibility of studying the dynamics of quantum systems both in infinite-dimensional and finite-dimensional systems. Based on Weyl's approach, generalized by Schwinger, a self-consistent…
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the…
Open quantum-system dynamics can follow exponential decay, non-exponential relaxation, or oscillatory dynamics, depending on the system-environment coupling. We study a lattice with a boundary defect that transitions between these regimes,…
We describe a new construction of an incoherent dictionary, referred to as the oscillator dictionary, which is based on considerations in the representation theory of finite groups. The oscillator dictionary consists of order of p^5 unit…
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic up in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a…
A finite oscillator dictionary which has important applications in sequences designs and the compressive sensing was introduced by Gurevich, Hadani and Sochen. In this paper, we first revisit closed formulae of the finite split oscillator…
We present a brief review of discrete structures in a finite Hilbert space, relevant for the theory of quantum information. Unitary operator bases, mutually unbiased bases, Clifford group and stabilizer states, discrete Wigner function,…