Related papers: Falling Coupled Oscillators & Trigonometric Sums
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
A simple model coupling a one-dimensional beam particle to a one-dimensional harmonic oscillator is used to explore complementarity and entanglement. This model, well-known in the inelastic scattering literature, is presented under three…
A method of numerically evaluating slowly convergent monotone series is described. First, we apply a condensation transformation due to Van Wijngaarden to the original series. This transforms the original monotone series into an alternating…
Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to total synchronization. We are able to develop exact solutions for…
We consider a set of interwoven harmonic oscillators where the acceleration of a given oscillator is determined by the position of its nearest neighbor. We show that this problem of N non-local oscillators with periodic boundary conditions…
We propose a new 4D state sum model, related to the balanced model, which is constructed using the octonions, or equivalently, triality. An effective continuum physical theory constructed from this model coupled to the balanced model would…
The von Neumann interaction between a particle and an apparatus, both of arbitrary mass, has been considered in the measurement of the position of a simple harmonic oscillator acted on by an external force. When the measurement has finite…
The theoretical foundations of a new general approach to the measurement problem of vibrational observables in trapped ion systems is reported. The method rests upon the introduction of a simple vibronic coupling structure appropriately…
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here we show that finite inertia of individual…
Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor.…
For a natural extension of the circular unitary ensemble of order n, we study as n tends to infinity, the asymptotic behavior of the sequence of orthogonal polynomials with respect to the spectral measure. The last term of this sequence is…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
We discuss a sum rule satisfied by the correlation function of two particles with small relative momenta. The sum rule, which results from the completeness condition of the quantum states of the two particles, is first derived and then we…
A simple setup was assembled to study the motion of an object while it falls. The setup was used to determine the instantaneous velocity, terminal velocity and acceleration due to gravity. Also, since the whole project was done within $20…
In this paper we study the finite trigonometric sum $\sum a_l\csc\big(\pi l/n\big)$, where $a_l$ are equal to $\cos(2\pi l \nu/n)$ and where the summation index $l$ and the discrete parameter $\nu$ both run through $1$ to $n-1$. This sum is…
Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is…
In a single finite electronic band the total optical spectral weight or optical sum carries information on the interactions involved between the charge carriers as well as on their band structure. It varies with temperature as well as with…
We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…
We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when…
This paper investigates the properties of trajectories in harmonic oscillator systems equipped with a point, absolutely continuous, or singular measure. As demonstrated in [30], infinite-dimensional linear flows of countable oscillator…