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The dissipative quantum dynamics of an anharmonic oscillator is investigated theoretically in the context of carbon-based nano-mechanical systems. In the short-time limit, it is known that macroscopic superposition states appear for such…
The motion of a vibrating object is determined by the way it is held. This simple observation has long inspired string instrument makers to create new sounds by devising elegant string clamping mechanisms, whereby the distance between the…
Resistive switching is one of the foremost candidates for building novel types of non-volatile random access memories. Any practical implementation of such a memory cell calls for a strong miniaturization, at which point fluctuations start…
Asymptotic disturbance rejection (equivalently tracking) for nonlinear systems has been studied only in qualitative terms (the state is asymptotically stable under bounded disturbances). We show how to prove quantitative performance…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
The concept of nonlinear modes is useful for the dynamical characterization of nonlinear mechanical systems. While efficient and broadly applicable methods are now available for the computation of nonlinear modes, nonlinear modal testing is…
We propose a scheme to enhance quantum entanglement in an optomechanical system by exploiting the so-called Duffing nonlinearity. Our model system consists of two mechanically coupled mechanical resonators, both driven by an optical field.…
An experimental arrangement and a set of experiments are developed to generate empirical evidence of the effect of noise on a rotating, macro-scale cantilever structure. The experiment is a controlled representation of a rotating machinery…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped…
Microresonators are micron-scale optical systems that confine light using total internal reflection. These optical systems have gained interest in the last two decades due to their compact sizes, unprecedented measurement capabilities, and…
Singularities in macroscopic systems at discontinuous phase transitions are replaced in finite systems by sharp but continuous changes. Both the energy differences between metastable and stable phases and the energy barriers separating…
Experiments over the past years have demonstrated that it is possible to bring nanomechanical resonators and superconducting qubits close to the quantum regime and to measure their properties with an accuracy close to the Heisenberg…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
In recent years, a new method for experimental nonlinear modal analysis has been developed, which is based on the extended periodic motion concept. The method is well suited to experimentally obtain amplitude-dependent modal properties…
We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…
The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only…
Vibrational resonance focuses on the resonance behavior of a nonlinear system when it is subjected to both a weak low-frequency characteristic signal and a high-frequency auxiliary signal. A traditional Duffing system has a fixed natural…
We study the dissipative quantum Duffing oscillator in the deep quantum regime with two different approaches: The first is based on the exact Floquet states of the linear oscillator and the nonlinearity is treated perturbatively. It well…