Temperature-dependent third cumulant of tunneling noise

Poisson statistics predicts that the shot noise in a tunnel junction has a temperature independent third cumulant e(2)I, determined solely by the mean current I. Experimental data, however, show a puzzling temperature dependence. We demonstrate theoretically that the third cumulant becomes strongly temperature dependent and may even change sign as a result of feedback from the electromagnetic environment. In the limit of a noninvasive (zero-impedance) measurement circuit in thermal equilibrium with the junction, we find that the third cumulant crosses over from e(2)I at low temperatures to -e(2)I at high temperatures.     

Behavior and finite-size effects of the sixth order cumulant in the three-dimensional Ising universality class

The high-order cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics(QCD). This has been calculated to the sixth order in experiments.Corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the three-dimensional Ising model, which is expected to be in the same universality class as QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that at non-zero external magnetic field, when the critical point is approached from the crossover side, the sixth order cumulant has a negative valley. The width of the negative valley narrows with decreasing external field. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finite-size system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising model, we calculated the sixth order cumulant of different sizes of systems. We discuss the finite-size effects on the temperature at which the cumulant changes sign.     

Cumulant approach to the two-dimensional magneto-conductivity problem

The validity of assumptions involved in experimental evaluations of the g-factor of electrons in (100) surface inversion layers of p-silicon from Shubnikov-De Haas oscillations of the surface conductivity by the method of tilted megnetic fields is discussed on the basis of the transport theory of a two-dimensional electron-impurity system. The self-consistent Born approximation is shown to be insufficient to this task, and an alternative cumulant approach is discussed. Contrary to recent work, the cumulant approach is introduced in a simple manner, avoiding the path-integral formalism.     

Noise and full counting statistics of incoherent multiple Andreev reflection

We present a general theory for the full counting statistics of multiple Andreev reflections in incoherent superconducting-normal-superconducting contacts. The theory, based on a stochastic path integral approach, is applied to a superconductor-double-barrier system. It is found that all cumulants of the current show a pronounced subharmonic gap structure at voltages V=2Delta/en. For low voltages V or =3. We show that this low-voltage result holds for a large class of incoherent superconducting-normal-superconducting contacts.     

Path integral computation of phonon anharmonicity

The partition function of an oscillator disturbed by a set of electron particle paths has been computed by a path integral formalism which permits to evaluate at any temperature the relevant cumulant terms in the series expansion. The low temperature cutoffs in the anharmonic cumulant series are determined fulfilling the constraint of the third law of thermodynamics. The general method here proposed has been applied to the semiclassical Su-Schrieffer-Heeger model whose time dependent source current is linear in the oscillator displacement field. We find that this peculiar current induces large electron-phonon anharmonicities on the phonon subsystem. As a signature of anharmonicity the phonon heat capacity shows a peak whose temperature location strongly varies with the strength of the e-ph coupling. Since the electron hopping potential provides a sizeable background in the low and intermediate temperature range, such a peak is partly smeared in the total heat capacity. Low energy oscillators are more sensitive to anharmonic perturbations.Received: 7 January 2004, Published online: 3 August 2004PACS: 71.20.Rv Polymers and organic compounds - 31.15.Kb Path-integral methods - 63.20.Kr Phonon-electron and phonon-phonon interactions     

一种声发射信号方位角自适应监测算法*

四阶累积量可用于声发射信号处理,结合盲波束形成算法可对声发射信号的方位角进行估计。由于四阶累积量的计算量较大,采用迭代计算的思想,提出一种基于四阶累积量的自适应声发射信号方位角监测算法。与改进前的算法相比,自适应算法的计算复杂度和所需存贮空间均显著降低,可用于声发射信号的方位估计和监测。计算机仿真及实测数据分析均验证了算法的有效性。     

Current correlations in quantum spin Hall insulators

We consider a four-terminal setup of a two-dimensional topological insulator (quantum spin Hall insulator) with local tunneling between the upper and lower edges. The edge modes are modeled as helical Luttinger liquids and the electron-electron interactions are taken into account exactly. Using perturbation theory in the tunneling, we derive the cumulant generating function for the interedge current. We show that different possible transport channels give rise to different signatures in the current noise and current cross correlations, which could be exploited in experiments to elucidate the interplay between electron-electron interactions and the helical nature of the edge states.     

Time Ordering and Counting Statistics

The basic quantum mechanical relation between fluctuations of transported charge and current correlators is discussed. It is found that, as a rule, the correlators are to be time-ordered in an unusual way. Instances where the difference with the conventional ordering matters are illustrated by means of a simple scattering model. We apply the results to resolve a discrepancy concerning the third cumulant of charge transport across a tunnel junction.     

典型概率密度背景下四阶累积量波束形成的阵增益

在理论上零均值高斯分布噪声的四阶累积量恒等于零,而实际噪声和混响的概率密度是影响四阶累积量波束形成技术性能的关键问题。本文针对海洋环境噪声与海底混响的瞬时幅度分布,分别推导了四阶累积量波束形成阵增益函数;建立了阵增益与阵元数、海洋环境噪声和海底混响统计特性的四阶矩和二阶矩及输入信噪比的关系;确定了与常规波束形成阵增益之间存在临界信噪比,高于临界信干比时四阶累积量波束形成可以获得比常规波束形成更高的阵增益与分辨率。实验数据处理结果验证了四阶累积量波束形成阵增益和分辨率理论结果的一致性。      

Photon number cumulant expansion and generating function for photon added- and subtracted-two-mode squeezed states

For the first time, we derive the photon number cumulant for two-mode squeezed state and show that its cumulant expansion leads to normalization of two-mode photon subtracted-squeezed states and photon added- squeezed states. We show that the normalization is related to Jacobi polynomial, so the cumulant expansion in turn represents the new generating function of Jacobi polynomial.     

Quantum-limited shot noise and quantum interference in graphene-based Corbino disk

This is a theoretical study of finite voltage effects on the conductance, the shot-noise power and the third, charge-transfer cumulant for graphene-based Corbino disk in the presence of external magnetic fields. Periodic magnetoconductance oscillations, predicted in earlier works, become invisible for relatively small source–drain voltages, as the current decays rapidly with magnetic field. Quantum interference still governs the behaviour of higher charge-transfer cumulants.     

Array gain of fourth-order cumulants beamforming under typical probability density background

The fourth-order cumulant of zero mean Gaussian distribution noise always equals to zero theoretically.In practice the probability density of noise and reverberation is the key problem to performance of the fourth-order cumulant beamforming technique.In this paper,the array gain functions of the fourth-order cumulant beamforming are deducted considering the instantaneous amplitude distribution of the ambient sea noise and bottom reverberation respectively.And the relationships are determined between array gain and the factors including the number of the array elements,the fourth-order and second-order statistical properties of the noise and reverberation,and the input signal-to-noise ratio.It is also verified that there is a critical signal-to-interference ratio and the fourth-order cumulant beamforming can obtain higher gain and resolution than the conventional beamforming method when the ratio is larger than it.The results of experiment data processing demonstrate that the gain and the resolution of the fourth-order cumulant beamforming coincide with the theoretic.     

Critical relaxation of the temperature in a square lattice Ising system

The critical dynamics of an energy-like perturbation in a square Ising spin system is studied by the real space renormalization group approach. The critical exponent is 2.14 in the cumulant expansion and 2.29 in the potential moving approximations.     

Multiparticle interference, Greenberger-Horne-Zeilinger entanglement, and full counting statistics

We investigate the quantum transport in a generalized N-particle Hanbury Brown-Twiss setup enclosing magnetic flux, and demonstrate that the Nth-order cumulant of current cross correlations exhibits Aharonov-Bohm oscillations, while there is no such oscillation in all the lower-order cumulants. The multiparticle interference results from the orbital Greenberger-Horne-Zeilinger entanglement of N indistinguishable particles. For sufficiently strong Aharonov-Bohm oscillations the generalized Bell inequalities may be violated, proving the N-particle quantum nonlocality.     

Full counting statistics of a superconducting beam splitter

We study the statistics of charge transport in a mesoscopic three-terminal device with one superconducting terminal and two normal-metal terminals. We calculate the full distribution of transmitted charges into the two symmetrically biased normal terminals. In a wide parameter range, we find large positive cross correlations between the currents in the two normal arms. We also determine the third cumulant that provides additional information on the statistics not contained in the current noise.     

Frequency scales for current statistics of mesoscopic conductors

We calculate the third cumulant of current in a chaotic cavity with contacts of arbitrary transparency as a function of frequency. Its frequency dependence drastically differs from that of the conventional noise. In addition to a dispersion at the inverse RC time characteristic of charge relaxation, it has a low-frequency dispersion at the inverse dwell time of electrons in the cavity. This effect is suppressed if both contacts have either large or small transparencies.     

Cumulant functions in optical coherence theory

Cumulant functions are introduced to describe the statistical state of a radiation field. These functions are simply related to the optical coherence functions but have some interesting features. It is shown that if the cumulant functions of all orders greater than some numberN ₀ vanish then they also vanish for all orders greater than 2. Thermal field is the only field having this property. This property holds whether the field is described by a classical stochastic process or by a quantum density operator. Further the particular operator ordering used in defining these cumulant functions for the quantized field affects only the second order cumulant function. To describe the statistical state of a vector field such as partially polarized or unpolarized radiation, one would need to introduce cumulant tensors.     

水声信号稀疏重构的高阶累积量波达方向估计

高阶累积量具有高斯噪声抑制和阵元扩展特性,将高阶累积量引入水声信号的方位估计中,提出了离格稀疏贝叶斯学习重构的高阶累积量测向算法。该方法利用高阶累积量对高斯噪声的自然盲性,计算阵列信号四阶累积量来滤除高斯噪声,使阵元在原来的结构上扩展了一倍;并构造出选择矩阵剔除了四阶累积量中的冗余项,能再一次的扩展阵元,得到的新观测模型具有更好的统计性能;最后利用空域稀疏性,推导出四阶累积量下的离格稀疏表示模型,采用贝叶斯学习解算出源信号的最大后验概率,实现了目标方位估计。数值仿真和海试实验数据表明,该方法在相邻声源方位间隔为4°的情况下分辨概率可达到95%以上,在信噪比大于-5 dB时目标方位估计的均方根误差在1°以内,可显著抑制背景噪声干扰,在多声源密集分布条件下也能准确、稳健的对水声目标方位进行估计。      

Critical Binder cumulant of two-dimensional Ising models

The fourth-order cumulant of the magnetization, the Binder cumulant, is determined at the phase transition of Ising models on square and triangular lattices, using Monte Carlo techniques. Its value at criticality depends sensitively on boundary conditions, details of the clusters used in calculating the cumulant, and symmetry of the interactions or, here, lattice structure. Possibilities to identify generic critical cumulants are discussed.