Related papers: Structurally stable subharmonic regime of a driven…
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…
An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Environmental fluctuations -- characteristic of all realistic dynamical systems -- suppress…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of…
Transmon qubits are ubiquitously used in superconducting quantum information processor architectures. Strong drives are required to realize fast, high-fidelity, gates and measurements, including parametrically activated processes. Here, we…
We derive the effective hamiltonian for a charge-Josephson qubit in a circuit with no use of phenomenological arguments, showing how energy renormalizations induced by the environment appear with no need of phenomenological counterterms.…
We revisit quantum dynamics of the damped and driven nonlinear oscillator. In the classical case this system has two stationary solutions (the limit cycles) in the certain parameter region, which is the origin of the celebrated bistability…
The transition from classical to quantum behavior for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative size of $\hbar$ is increased. We show evidence to the contrary in the behavior of…
Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of…
We study quasi periodic and frequency locked states that can occur in a sinusoidally driven linear harmonic oscillator in the special relativistic regime. We show how the shift in natural frequency of the oscillator with increasing…
We address the dynamics of nonclassicality for a quantum system interacting with a noisy fluctuating environment described by a classical stochastic field. As a paradigmatic example, we consider a harmonic oscillator initially prepared in a…
This paper investigates the dynamics of quantum analogs of classical impact oscillators to explore how complex nonlinear behaviors manifest in quantum systems. While classical impact oscillators exhibit chaos and bifurcations, quantum…
We show that nonlinear response of a quantum oscillator displays antiresonant dips and resonant peaks with varying frequency of the driving field. The effect is a consequence of special symmetry and is related to resonant multiphoton mixing…
An rf superconducting quantum interference device (SQUID) consists of a superconducting ring interrupted by a Josephson junction (JJ). When driven by an alternating magnetic field, the induced supercurrents around the ring are determined by…
In this paper, we are concerned with the stabilization of linear port-Hamiltonian systems of arbitrary order $N \in \mathbb{N}$ on a bounded $1$-dimensional spatial domain $(a,b)$. In order to achieve stabilization, we couple the system to…
The oscillatory response of nonlinear systems exhibits characteristic phenomena such as multistability, discontinuous jumps and hysteresis. These can be utilized in applications leading, e.g., to precise frequency measurement, mixing,…
The effect of decaying oscillatory perturbations on autonomous Hamiltonian systems in the plane with a stable equilibrium is investigated. It is assumed that perturbations preserve the equilibrium and satisfy a resonance condition. The…
We examine a strange chaotic attractor and its unstable periodic orbits in case of one degree of freedom nonlinear oscillator with non symmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a…
Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical…