Universal phenomenon of self-organized criticality in magnetic flux dynamics

Magnetization curves of square arrays of Josephson junctions of two basic types were investigated: superconductor–insulator–superconductor (SIS) and superconductor–normal metal–superconductor (SNS).

Magnetic flux avalanches were observed in SIS arrays. A statistical analysis of flux avalanches showed that their size distribution can be described by a power law with a crossover where the exponent n varies from −1.2 for small avalanches to −3.5 for the large ones. Such a behavior of avalanches is interpreted as the self-organized criticality (SOC) manifestation. In SNS arrays, the flux avalanches were not observed, but a considerable asymmetry of a hysteresis curve was revealed.     

Magnetic moment of square SIS Josephson arrays: Self-organized criticality

The temperature-and magnetic-field dependences of the magnetic moment of square Josephson arrays with SIS-type junctions are studied experimentally. Two temperature regions are observed with different types of magnetization curves. Magnetic flux avalanches are detected in the low-temperature region. Statistical analysis of avalanche amplitudes A shows that their size distribution varies in accordance with the power law P∝Aⁿ with crossover, when exponent n varies from n=?0.7 for small avalanches to n=?6 for large avalanches, while the frequency spectrum varies in accordance with the law 1/f^α. Such behavior is interpreted as a manifestation of self-organized criticality.     

Self-Organization in a Granular Medium by Internal Avalanches

Internal avalanches of grain displacements can be created inside a granular material kept in a bin in two ways: (i) by removing a randomly selected grain at the bottom of the bin; and (ii) by breaking a stable arch of grains clogging a hole at the bottom of the bin. Repeated generation of such avalanches leads the system to a steady state. It is relevant to ask whether this state is a critical state, as in self-organized criticality (SOC). We review here some recent studies of this problem using cellular automata and hard-disc models.     

Criticality in a simple model for brain functioning

We introduce a simple model for a set of interacting idealized neurons. The model presents a self-organized state in which avalanches of all sizes are observed and activity is detected in the whole extension of the simulated system without a typical length scale. The basic elements of the model are endowed with the main features of a neuron function. On this basis it is speculated that the collective system that they form, i.e., the brain, could display self-organized criticality in some situations.     

Continuous Variable Entanglement of Two Mesoscopic Josephson Junctions Induced by a Thermal Radiation Field

The continuous-variable （CV） entanglement between two mesoscopic Josephson junctions is studied and the time-dependent characteristic function in Wigner representation for the Josephson junction subsystem driven by a singlemode thermal field is analytically obtained. It is found that an initial lowest energy state of the junction subsystem can evolve into a two-mode entangled Gaussian state through the interaction with the thermal radiation field. Furthermore, we investigate the influence of the temperature on the entanglement of the junctions and find that the CV entanglement of the two junctions shows the critical behavior with respect to the temperature.     

Subharmonic Shapiro steps and noise in high-T c superconductor Josephson junctions

An experimental investigation is made of the subharmonic Shapiro steps observed on the I-V curves of high-T _c superconductor Josephson junctions and on the bias-voltage dependences of the rf noise and detector response when the junctions are subjected to external submillimeter radiation. Structures of this type are ordinarily described by a nonsinusoidal current-phase relation, which is why subharmonic steps appear. Numerical modeling of the processes occurring in a Josephson junction by means of a simple current-phase relation, as in the case of an SNS junction, gives good agreement with experiment. The width of the characteristic Josephson generation line of the junction was estimated on the basis of the noise dependences and the selective detector response. The width can be explained by taking into account the shot noise of the tunneling component of the conductivity. A model of the conductivity of a high-T _c superconductor Josephson junction, consisting of a tunnel junction with microshorts possessing metallic conductivity, is discussed. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 5, 426–430 (10 September 1998)     

Self-organized criticality and stock market dynamics: an empirical study

The stock market is a complex self-interacting system, characterized by intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically the possibility that the market is in a self-organized critical state (SOC). A wavelet transform method is used in order to separate high activity periods, related to the avalanches found in sandpile models, from quiescent. A statistical analysis of the filtered data shows a power law behaviour in the avalanche size, duration and laminar times. The memory process, implied by the power law distribution of the laminar times, is not consistent with classical conservative models for self-organized criticality. We argue that a “near-SOC” state or a time dependence in the driver, which may be chaotic, can explain this behaviour.     

Self-organized criticality in a nutshell

In order to gain insight into the nature of self-organized criticality (SOC), we present a minimal model exhibiting this phenomenon. In this analytically solvable model, the state of the system is fully described by a single-integer variable. The system organizes in its critical state without external tuning. We derive analytically the probability distribution of durations of disturbances propagating through the system. As required by SOC, this distribution is scale invariant and follows a power law over several orders of magnitude. Our solution also reproduces the exponential tail of the distribution due to finite size effects. Moreover, we show that large avalanches are suppressed when stabilizing the system in its critical state. Interestingly, avalanches are affected in a similar way when driving the system away from the critical state. With this model, we have reduced SOC dynamics to a leveling process as described by Ehrenfest's famous flea model.     

Properties of Josephson junctions in the inhomogeneous magnetic field of a system of ferromagnetic particles

The effect of a system of ferromagnetic particles on the field-dependent critical current of a Josephson junction is experimentally studied for junctions of different geometries. For edge junctions, the effect of commensurability between the periodic magnetic field of the particles and the Josephson vortex lattice is observed. The effect manifests itself in additional maxima of the field-dependent critical current. For overlap junctions, giant (greater than sixfold) variations of the maximum critical current are observed depending on the magnetic state of the particles. The changes in the “Fraunhofer” pattern of the overlaped Josephson junctions are attributed to the formation of Abrikosov vortices due to the effect of uniformly magnetized particles. The effects revealed in the experiments can be used to analyze the inhomogeneous magnetic field of a system of submicron particles and to control the transport properties of Josephson junctions.     

Degenerate ground state in a mesoscopic YBa2Cu3O(7-x) grain boundary Josephson junction

We have measured the current-phase relationship I(varphi) of symmetric 45 degrees YBa2Cu3O7-x grain boundary Josephson junctions. Substantial deviations of the Josephson current from conventional tunnel-junction behavior have been observed: (i) The critical current exhibits, as a function of temperature T, a local minimum at a temperature T*. (ii) At T approximately T*, the first harmonic of I(phi) changes sign. (iii) For T相似文献   

Large-scale simulation of avalanche cluster distribution in sand pile model

The avalanche cluster distribution of the sand pile model of self-organized criticality is studied on the square lattice. A vectorized multispin coding algorithm is developed for this study with three bits per site. The exponents characterizing the size and the lifetime of the avalanches are slightly different from the previous estimates.     

Subharmonic gap structure in superconducting scanning tunneling microscope junctions

We observe a subharmonic gap structure (SGS) and the Josephson effect in superconducting scanning tunneling microscope junctions with resistances below 100 kΩ. The magnitude of the n=2 SGS is shown to scale with the square of the junction normal state conductance, in agreement with theory. We show by analyzing the Josephson effect in these junctions that the superconducting phase dynamics are strongly affected by thermal fluctuations. We estimate the linewidth of the Josephson oscillations due to phase fluctuations, a quantity that may be important in modern theories of the subgap structure. While phase fluctuations may smear the SGS current onsets, we conclude that the sharpness of these onsets in our data is not limited by fluctuations.     

The Relation Between Barrier Structure and Current Uniformity in YBCO Josephson Junctions

Electromagnetic transport measurements were combined with high-resolution electron microscopy observations to study the relation between structure and local critical currents in YBa₂Cu₃O_7–x (YBCO) Josephson junctions. The spatial variation of the critical current J(x) along the length of the boundary for interface engineered Josephson junctions and bicrystal grain boundary Josephson junctions was determined using a phase retrieval algorithm. The current distribution solutions were found to be highly uniform along the length of interface engineered junctions in contrast to solutions for grain boundary junctions. The latter showed significant spatial oscillations in the critical current as well as areas along the boundary that carried no current. Microstructural evaluation of interface engineered junctions fabricated using identical processing parameters to the junctions used for transport measurements suggest that the uniform current distribution is controlled by a highly uniform barrier layer formed between the superconducting electrodes. Microstructural evaluation of grain boundary junctions similar to the junctions used for transport measurements show considerable variations of the grain boundary structure within a single junction.     

Self-organized branching process for a one-dimensional rice-pile model

A self-organized branching process is introduced to describe one-dimensional rice-pile model with stochastic topplings. Although the branching processes are generally expected to describe well high-dimensional systems, our modification highlights some of the peculiarities present in one dimension. We find analytically that the crossover behavior from the trivial one-dimensional BTW behaviour to self-organized criticality is characterised by a power-law distribution of avalanches. The finite-size effects, which are crucial to the crossover, are calculated. Received 21 June 2001 and Received in final form 14 November 2001     

Fluctuations and finite-size effect in the Bak-Sneppen model

The self-organized criticality in the nearest-neighbor version of the Bak-Sneppen model is investigated from the event-by-event fluctuations of the mean fitness. The finite-size effect on the evolution of the critical state is shown, and a scaling solution to the gap equation for an infinite one-dimensional lattice is given numerically for the first time. The mean lifetime of avalanches is presented as a function of the gap from the solution. The critical value of the gap and an exponent are calculated from the solution. Received 10 December 2000 and Received in final form 18 January 2001     

Looking for self-organized critical behavior in avalanches of slightly cohesive powders

We report results from a statistical analysis of avalanches of cohesive powders in a slowly rotated drum. Interparticle adhesion, which diminishes the effect of inertia and whose magnitude strongly fluctuates in a local scale, makes avalanches in slightly cohesive powders eligible for displaying self-organized criticality. However, the results show that avalanche sizes, time interval between avalanches, and maximum stable angle do not follow a power-law distribution. Otherwise, these parameters scale with powder cohesiveness.     

SrTiO3基片上Tl-2212双晶约瑟夫森结的动态特性及噪声影响研究

在SrTiO₃（STO）基片上制作了Tl-2212双晶约瑟夫森结,并对其进行了微波辐照下的I-V特性测试,观察到了夏皮罗台阶,符合约瑟夫森电压-频率关系.利用数值仿真对约瑟夫森结建立了RCSJ模型,仿真结果与实验数据符合较好,利用此模型深入研究了噪声对结动态特性的影响,解释了噪声影响下结的微波感应台阶幅度减小和极小值展宽现象,提出了有效噪声温度为工作温度和外部噪声的等效温度之和. 关键词： RCSJ模型 噪声 Tl-2212双晶约瑟夫森结     

Ferromagnetic 0–<Emphasis Type="BoldItalic">π</Emphasis> Josephson junctions

We present a study on low-T_c superconductor-insulator-ferromagnet-superconductor (SIFS) Josephson junctions. SIFS junctions have gained considerable interest in recent years because they show a number of interesting properties for future classical and quantum computing devices. We optimized the fabrication process of these junctions to achieve a homogeneous current transport, ending up with high-quality samples. Depending on the thickness of the ferromagnetic layer and on temperature, the SIFS junctions are in the ground state with a phase drop of either 0 or π. By using a ferromagnetic layer with variable step-like thickness along the junction, we obtained a so-called 0–π Josephson junction, in which 0 and π ground states compete with each other. At a certain temperature the 0 and π parts of the junction are perfectly symmetric, i.e. the absolute critical current densities are equal. In this case the degenerate ground state corresponds to a vortex of supercurrent circulating clock- or counterclockwise and creating a magnetic flux which carries a fraction of the magnetic flux quantum Φ₀. PACS  74.50.+r; 74.78.Fk; 74.81.-g; 85.25.Cp     

Sound wave interaction with Josephson junction and transformation of the contact coherent binding energy into ultrasonic waves

The problem of ultrasonic wave propagation in narrow Josephson junctions at nonzero temperature has been investigated. Using the derived solution of the nonstationary Fokker-Planck equation, the total current flowing through the narrow Josephson junction is calculated, and the coefficient of the ultrasonic wave passage through the Josephson junction is determined. The singularity of this coefficient is studied in the ultrasound amplification mode associated with the transformation of coherent binding energy of the contact into ultrasonic waves, and the possibility of experimental measurement of the lifetime of the Josephson junction in the metastable state under the conditions of maximum ultrasound amplification by the contact is discussed.     

在一个磁通量子内dc Josephson电流的阶梯效应(Ⅰ)——双结SQUID

如果将由两个相同的Josephson结组成的双结SQUID放置于Q值足够高的谐振腔内,当其Josephson频率ω=2eV₀/h与谐振腔的本征频率ω_r发生谐振时,腔内就被激起一个驻波电磁场,这个场对两个结的反馈作用,将导致双结SQUID的dc Josephson电流在一个磁通量子内随磁场产生多次阶梯效应。理论给出两个结的Josephson电流产生一系列新的干涉作用:如果两个结分别位于反馈场的波峰,则阶跃电流加强;如果其中一个位于波谷,则使SQUID的干涉图形改变π/2位相,且两个结电流产生相干性减小;如果一个在波峰一个在波节,则SQUID退化到单结;如果两个结都在波节,则不出现n≠0的阶梯。 关键词：