Related papers: Response of the Quantum Ground State to a Parametr…
The evolution of a quantum oscillator, with periodically varying frequency and damping, is studied in the two cases of parametric resonance (PR) producing a limited, or unlimited stretching of the wave function. The different asymptotic…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
A parametrically driven classical harmonic oscillator exhibits resonant instability when driven at twice its natural frequency, with the lowest energy configuration remaining unaffected by the drive. In contrast, the ground state of the…
We investigate the classical problem of motion of a mathematical pendulum with an oscillating pivot. This simple mechanical setting is frequently used as the prime example of a system exhibiting the parametric resonance phenomenon, which…
The competition between parametric resonance (PR) and dissipation is studied in the damped Kronig-Penney model, with time-dependent dissipation rate gamma(t). In the classical case, it is shown that dissipation leaves just a finite number…
A quantum mechanical version of a classical inverted pendulum is analyzed. The stabilization of the classical motion is reflected in the bounded evolution of the quantum mechanical operators in the Heisenberg picture. Interesting links with…
We consider a simple dynamic model of the vibrating screen operating in the parametric resonance (PR) mode. This model was used in the course of designing and setting of such a screen in LPMC. The PR-based screen compares favorably with…
A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold Cesium atoms when driven…
The quantum states of the Kapitza pendulum are described within the effective potential obtained by the method of averaging over the fast oscillations. An analytical estimate of the energy spectrum of stabilized states is given using…
Nonlinear dynamics plays a significant role in interdisciplinary fields spanning biology, engineering, mathematics, and physics. Under small-amplitude approximations, certain nonlinear systems can be effectively described by the linear…
We introduce a simple model for implementing the concepts of quasi-energy and parametric resonances (PRs) in systems with the $\mathcal{PT}$ symmetry, i.e., a pair of coupled and mutually balanced gain and loss elements. The parametric (ac)…
Dynamically stable periodic rotations of a driven pendulum provide a unique mechanism for generating a uniform rotation from bounded excitations. This paper studies the effects of a small ellipticity of the driving, perturbing the classical…
A simple model of a two-mode non-resonant parametric amplifier is studied with special regard to non-classical features such as revivals and squeezing. The methods used apply for an arbitrary pump parameter. Detailed analytical and explicit…
The Kerr parametric oscillator (KPO) has recently attracted considerable attention from the perspective of its applications to quantum information processing, and understanding its properties is an important challenge. Spectroscopic…
Quantum mechanics is considered to arise from an underlying classical structure (``hidden variable theory'', ``sub-quantum mechanics''), where quantum fluctuations follow from a physical noise mechanism. The stability of the hydrogen ground…
This note is concerned with a modified version of the frequency domain physical realizability (PR) condition for linear quantum systems. We consider open quantum systems whose dynamic variables satisfy the canonical commutation relations of…
We study a Schrodinger particle in an infinite spherical well with an oscillating wall. Parametric resonances emerge when the oscillation frequency is equal to the energy difference between two eigenstates of the static cavity. Whereas an…
We explore analytically the quantum dynamics of a point mass pendulum using the Heisenberg equation of motion. Choosing as variables the mean position of the pendulum, a suitably defined generalised variance and a generalised skewness, we…
We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…