Related papers: Quantum states of the Kapitza pendulum
We study quantum mechanics problem described by the Schr\"{o}dinger equation with Kapitza pendulum potential, that is the asymmetric double-well potential on the circle. For the oscillatory states spatially localize around the two stable…
We extend the theory of Kapitza stabilization within the complex domain, i.e. for the case of an imaginary oscillating potential. At a high oscillation frequency, the quasi-energy spectrum is found to be entirely real-valued, however a…
Comparative analysis of three stabilization mechanisms of unstable states of physical systems is presented in this review. These mechanisms are: the quantum Zeno effect, the stabilization of unstable states in an external fast oscillating…
A feasible experimental proposal to realize a non-dispersive quantum pendulum is presented. The proposed setup consists of an ultracold atomic cloud, featuring attractive interatomic interactions, loaded into a tilted ring potential. The…
A numerical study of the quantum double pendulum is conducted. A suitable quantum scaling is found which allows to have as the only parameters the ratios of the lengths and masses of the two pendula and a (quantum) gravity parameter…
Dynamical stabilization processes (homeostasis) are ubiquitous in nature, but energetic resources needed for their existence were not studied systematically. Here we undertake such a study using the famous model of Kapitza's pendulum, which…
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…
A driven pendulum with vertical oscillations of pendulum support (Kapitza pendulum) possesses a number of unusual properties and is a popular object of both analytical and numerical studies. Although some spectacular results can be…
Dynamical stabilization of an inverted pendulum through vertical movement of the pivot is a well-known counterintuitive phenomenon in classical mechanics. This system is also known as Kapitza pendulum and the stability can be explained with…
A generalization of the classical Kapitza pendulum is considered: an inverted planar mathematical pendulum with a vertically vibrating pivot point in a time-periodic horizontal force field. We study the existence of forced oscillations in…
We analyze the quantum properties of a system consisting of two nonlinearly coupled pendula. This non-integrable system exhibits two different symmetries: a permutational symmetry (permutation of the pendula) and another one related to the…
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…
The phenomenon of Parametric Resonance (PR) is very well studied in classical systems with one of the textbook examples being the stabilization of a Kapitza's pendulum in the inverted configuration when the suspension point is oscillated…
As realized by Kapitza long ago, a rigid pendulum can be stabilized upside down by periodically driving its suspension point with tuned amplitude and frequency. While this dynamical stabilization is feasible in a variety of instances in…
We present a pedagogical introduction to Floquet-Magnus theory through the classical example of Kapitza's pendulum - a simple system exhibiting nontrivial dynamical stabilization under rapid periodic driving. By deriving the equations of…
The nodal structure of bound-state wave functions for one-dimensional quantum systems with quartic energy-momentum dispersion and polynomial potentials is analysed by using the semiclassical approximation and variational approach. For…
The planar inverted pendulum with a vibrating pivot point in the presence of an additional horizontal force field is studied. The horizontal force is not assumed to be small or rapidly oscillating. We assume that the pivot point of the…
We present a theoretical analysis of the capacitance of a double quantum dot in the charge and spin qubit configurations probed at high-frequencies. We find that in general the total capacitance of the system consists of two state-dependent…
This paper is devoted to the study of quantum dissipation in cluster decay phenomena in the frame of the Lindblad approach to quantum open systems. The tunneling of a metastable state across a piecewise quadratic potential is envisaged for…
Quantum algorithms for estimating the ground state energy of a quantum system often operate by preparing a classically accessible quantum state and then applying quantum phase estimation. Whether this approach yields quantum advantage…