耦合振荡器回路中的能流放大

Virtual double-well potential for an underdamped oscillator created by a feedback loop

Virtual potentials are a very elegant, precise and flexible tool to manipulate small systems and explore fundamental questions in stochastic thermodynamics. In particular double-well potentials have applications in information processing, such as the demonstration of Landauer's principle. Nevertheless, virtual double-well potentials had never been implemented in underdamped systems. In this article, we detail how to face the experimental challenge of creating a feedback loop for an underdamped system (exploring its potential energy landscape much faster than its over-damped counterpart), in or…

基于物理相变的弛豫振荡器反馈再生噪声模型

Noise Model of Relaxation Oscillators Due to Feedback Regeneration Based on Physical Phase Change

提出了一种研究弛张振荡器再生噪声尖峰的新方法。在传统的相位噪声模型中，噪声尖峰没有得到令人满意的解释。本文试图将噪声尖峰/跳跃现象视为热力学系统中的相变（例如从气体到液体或铁磁体的磁化）来解释。两者都是由于再生（振荡器中的正反馈以及由于铁磁体中的正反馈导致的自旋对齐）。所用的数学工具是热力学中的配分函数，并将结果映射到热力学系统和弛张振子之间。理论的发展和公式推导出预测的跳跃的幅度，作为一个功能的设计参数，如再生参数或环路增益。公式表明，当再生参数/回路增益接近1时，噪声急剧增加，在相变中温度接近临界温度时，情况大致相同。对使用CMOS的电路（Eldo）进行了模拟，以及对铁磁体（伊辛模型）进行了蒙特卡罗模拟（Metropolis），两者都显示出与公式一致的跳跃行为。在0.13 μ m CMOS工艺制造的弛张振荡器上的测量验证了这种行为，其中当再生参数/环路增益接近1时噪声急剧增加，与理论公式密切匹配。使用该公式，设计人员可以通过其对再生参数/环路增益的影响来量化噪声尖峰的变化，该噪声尖峰依赖于设计参数，例如gm（器件增益）、R、I 0。

Correlation Functions of the Anharmonic Oscillator: Numerical Verification of Two-Loop Corrections to the Large-Order Behavior

Recently, the large-order behavior of correlation functions of the $O(N)$-anharmonic oscillator has been analyzed by us in [L. T. Giorgini et el., Phys. Rev. D 101, 125001 (2020)]. Two-loop corrections about the instanton configurations were obtained for the partition function, and the two-point and four-point functions, and the derivative of the two-point function at zero momentum transfer. Here, we attempt to verify the obtained analytic results against numerical calculations of higher-order coefficients for the $O(1)$, $O(2)$, and $O(3)$ oscillators, and demonstrate the drastic improvement …

Onset of synchronization in networks of second-order Kuramoto oscillators with delayed coupling: Exact results and application to phase-locked loops

We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we show that the model can be related to a network of phase-locked loops widely used in electronic circuits for generating a stable frequency at multiples of an input frequency. We study the model for a generic choice of the natural frequency distribution of the oscillators, to elucidate how a synchronized phase bifurcates from an incoherent phase as the coupl…

Information and thermodynamics: fast and precise approach to Landauer's bound in an underdamped micro-mechanical oscillator

The Landauer principle states that at least $k_B T \ln 2$ of energy is required to erase a 1-bit memory, with $k_B T$ the thermal energy of the system. We study the effects of inertia on this bound using as one-bit memory an underdamped micro-mechanical oscillator confined in a double-well potential created by a feedback loop. The potential barrier is precisely tunable in the few $k_B T$ range. We measure, within the stochastic thermodynamic framework, the work and the heat of the erasure protocol. We demonstrate experimentally and theoretically that, in this underdamped system, the Landauer b…