Oscillatory states of quantum Kapitza pendulum

Quantum states of the Kapitza pendulum

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 approximate model potential. For the lowest states of an inverted pendulum, the spectrum is repeduced by the energies of a harmonic oscillator with perturbation theory corrections. Tunneling effect contribution to the energies of resonance states in the double-well effective potential is estimated. The results of numerical simulations of vibrational and rotational…

The imaginary Kapitza pendulum

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 substantial difference with respect to a real potential emerges, that is the formation of a truly bound state instead of a resonance. The predictions of the Kapitza averaging method and the transition from a complex to an entirely real-valued quasi-energy spectrum at high frequencies are confirmed by numerical simulations of the Schrodinger equation for an oscil…

Dynamical Stability of a Many-body Kapitza Pendulum

We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine-Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the effective Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investiga…

卡皮察摆作为Floquet-马格斯理论的经典前奏

Kapitza's Pendulum as a Classical Prelude to Floquet-Magnus Theory

通过卡皮察摆的经典例子介绍Floquet-马格斯理论，推导运动方程并分析稳定性条件，展示其在经典和量子系统中的应用。

作为量子摆的超流体环

Superfluid rings as quantum pendulums

本研究提出一种基于装载到倾斜环形势阱的吸引相互作用超冷原子云的无色散量子摆实验方案，可调控相互作用切换经典与量子域，揭示量子相位印记驱动的类Kapitza经典稳定化机制，并探讨其作为重力仪的应用潜力。

一种量子力学摆钟

A Quantum Mechanical Pendulum Clock

本研究提出一种仅依赖热资源的量子区域光力学摆钟模型，其擒纵机构由腔中发射器提供、依赖极限环运行，可突破热力学不确定关系提升精度，增加发射器数量可趋近宏观摆钟行为，用于研究量子-经典转变。