约瑟夫森结与阵列的非线性混沌行为及研究进展

约瑟夫森结是一种利用超导材料制备的新型量子电子器件,它的一个显著特性是具有高度的非线性,因而会出现明显的混沌行为。约瑟夫森结与阵列的混沌行为具有重要的研究和应用价值,受到了广泛的关注。文中对约瑟夫森结与阵列的非线性混沌行为及研究进展做一些介绍。     

电阻并联约瑟夫森结阵列中的混沌行为

采用数值方法,对存在并联电阻的约瑟夫森结串联阵列进行了研究。首次发现当阵列中结的个数为3时,其中存在明显的混沌行为,并给出了存在混沌行为的参数范围。根据A.A.Chernikov和G.Schmidt的理论,只有当约瑟夫森结的个数大于或者等于4时才能观察到混沌行为;这一发现说明了其理论存在一定的局限性。     

本征约瑟夫森结阵列的PSpice模型及混沌行为研究

建立了电容耦合本征约瑟夫森结阵列在电路仿真软件PSpice中的模型，利用这个模型对恒定电流驱动下的本征约瑟夫森结阵列进行了仿真研究.通过与不存在电容耦合的本征约瑟夫森结的时域波形、频谱、分维和相图等结果的对比，发现了本征约瑟夫森结阵列中的混沌行为.这一发现对于本征约瑟夫森结的理论和应用研究有重要的意义.     

直流偏置的与RLC谐振器耦合的约瑟夫森结动力学行为的数值模拟

用数值模拟方法研究一种直流偏置的与RLC电路耦合的约瑟夫森结的动力学行为.数值模拟发现,选择合适的偏置电流,系统表现出周期三与混沌共存的动力学现象.给出了相应吸引子,吸引域的几何结构.对该系统的动力学研究为约瑟夫森器件稳定工作提供了有价值的参考 关键词： 约瑟夫森结 混沌 吸引子 吸引域 庞加莱截面 李雅谱诺夫指数     

电阻电容分路的约瑟夫森结中阵发性混沌及混沌控制的计算机模拟

通过计算机模拟研究了电阻电容分路的约瑟夫森结中的混沌行为,给出了结电压随阻尼参数及偏置直流电流变化的分岔图,从而展示了混沌产生的方式及混沌出现的参数区间,并基于弱周期扰动理论提出了控制RCSJJ中混沌的方案,模拟结果证明了该方案的有效性.     

约瑟夫森结无穷维电磁系统中的时空行为分析

针对一类含无损传输线的约瑟夫森结无穷维电磁系统,运用行波理论推导了电压正向行波分量的Poincaré映射关系,并在此基础上建立了传输线沿线电压的离散映射模型。通过数值计算描绘了传输线沿线电压的空间振幅变化图和时空行为发展图,分析了系统的时空行为随参数变化的动态演化过程。结果表明在一定参数条件下,约瑟夫森结无穷维电磁系统中存在着周期和时空混沌等丰富的非线性动力学行为。     

rf-偏置约瑟夫森结的混沌控制以及热噪声的影响的研究

本文研究rf-偏置约瑟夫森结的混沌行为的控制,数值分析表明延迟反馈控制法能有效地对该系统嵌埋于混沌吸引子中的不稳定周期轨道进行稳定控制,受控后系统锁相建立,电压标准恢复正常工作,同时还考虑了热噪声对控制的影响,对有效控制的实验温度范围进行了数值估计。     

一类约瑟夫森结混沌系统的谐和共振控制

引入外激和参激两种不同形式的谐和共振激励,探讨了一类约瑟夫森结(Josephson junction)系统的混沌控制问题.利用Melnikov方法研究了异宿混沌的生成和抑制,得到了在一定的控制激励振幅范围内,能确保异宿混沌被控制住,而且推导出控制激励与系统的激励两者之间的相位差和两者频率之间的共振阶数应满足的关系式.从定性的角度说明相位差在异宿混沌的控制中确实有着至关重要的影响,而且,数值方法的研究表明可通过调节相位来控制非自治系统中的稳态混沌.通过分析、比较外激和参激两种不同的共振激励对约瑟夫森结系统的异宿混沌的控制效果,得到对于较小的共振频率,宜采用参激激励,而对于较大的共振频率,宜采用外激激励. 关键词： 混沌控制 谐和共振激励 相位控制 Melnikov方法     

一种通过约瑟夫森结非线性频率响应确定微波耗散的方法

通过对电流偏置超导约瑟夫森结的微波驱动行为的研究,提出了一个确定约瑟夫森结微波耗散的方法.结的微波耗散由它的品质因子描述.微波耗散严重影响约瑟夫森器件如参量放大器、超导量子比特等的性能.对电流偏置的约瑟夫森结势阱采用四阶近似后,可以得到在较强微波驱动下约瑟夫森结非线性微波响应方程.该方程定量描述了非线性共振频率随外加微波功率变化关系:非线性共振频率与结等离子频率的差别依赖于约瑟夫森结的微波品质因子.对电流偏置的约瑟夫森结的微波运动行为进行了数值模拟.模拟结果确证了微波品质因子与非线性共振频率-等离子频率差别的定量关系可以应用于约瑟夫森结中.用这种非线性频率响应方法来确定约瑟夫森结的微波耗散没有严格的温度要求,可在单个电流偏置的结中完成,实验上具有简单可靠性.     

线性延时反馈Josephson结的Hopf分岔和混沌化

考虑线性延时反馈控制下电阻-电容分路的Josephson结,运用非线性动力学理论分析了受控系统平凡解的稳定性.理论分析表明,随着控制参数的改变,系统的稳定平凡解将会通过Hopf分岔失稳,并推导了发生Hopf分岔的临界参数条件.对不同参数条件下受控系统的动力学进行了数值分析.结果显示,系统由Hopf分岔产生的稳定周期解,将进一步通过对称破缺分岔和倍周期分岔通向混沌. 关键词： 约瑟夫森结 线性延时反馈 Hopf分岔 混沌     

Chaotic behavior of a stack of intrinsic Josephson junctions at the transition to branching for overcritical currents

Phase dynamics of a stack of coupled intrinsic Josephson junctions was investigated in the framework of capacitively coupled Josephson junctions with diffusion current model. We study the transition from the current-voltage characteristic specific to Josephson junctions arrays with small dissipation and weak coupling between the junctions to the arrays with strong coupling between the junctions and high dissipation. Low dissipative arrays of Josephson junctions are characterized by the absence of branching for overcritical currents which appears for highly dissipative arrays. Described branching appears due to charging on the superconducting layers and charge traveling waves generation. Arrays of Josephson junctions with intermediate values of coupling and dissipation parameters are characterized by the chaotic behavior, confirmed by positive Lyapunov exponent, and branching on the current voltage characteristic for both sub- and overcritical currents.     

Phase synchronization in an array of driven Josephson junctions

We consider an array of N Josephson junctions connected in parallel and explore the condition for chaotic synchronization. It is found that the outer junctions can be synchronized while they remain uncorrelated to the inner ones when an external biasing is applied. The stability of the solution is found out for the outer junctions in the synchronization manifold. Symmetry considerations lead to a situation wherein the inner junctions can synchronize for certain values of the parameter. In the presence of a phase difference between the applied fields, all the junctions exhibit phase synchronization. It is also found that chaotic motion changes to periodic in the presence of phase differences.     

Synchronization of chaos in resistive-capacitive-inductive shunted Josephson junctions

We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent （MCLE） is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.     

CHAOTIC SOLITON IN COUPLED LONG JOSEPHSON JUNCTIONS

The interaction between soliton and sinusoidal wave in two weakly coupled long Josephson junctions is studied. Theoretical analysis reveals that the soliton may be embedded in Melnikov chaotic attractors and the Fiske-step-modes are implied in the boundedness condition of the system. Comparison between the chaotic soliton oscillators and synchronized soliton oscillators shows that the former possesses greater maximal velocity and energy.     

Superconductivity-induced macroscopic resonant tunneling

We show analytically and by numerical simulations that the conductance through pi-biased chaotic Josephson junctions is enhanced by several orders of magnitude in the short-wavelength regime. We identify the mechanism behind this effect as macroscopic resonant tunneling through a macroscopic number of low-energy quasidegenerate Andreev levels.     

Chaos in Josephson junctions

A detailed analysis of the control space characterization of phase locked states and chaotic attractors in Josephson junctions is presented, based on a model that includes both quadratic damping and cosine interference terms. In addition, some novel features of the nonlinear characteristics of the junction like evolution of basin boundaries, bifurcation structure analysis and scaling behaviour of Lyapunov exponent are discussed.     

Quantum coherence in a superfluid Josephson junction

We report a new kind of experiment in which we take an array of nanoscale apertures that form a superfluid (4)He Josephson junction and apply quantum phase gradients directly along the array. We observe collective coherent behaviors from aperture elements, leading to quantum interference. Connections to superconducting and Bose-Einstein condensate Josephson junctions as well as phase coherence among the superfluid aperture array are discussed.