An autocorrelation function is obtained on the base of the recurrence relation formalism, whose continued fraction form corresponds to that of golden ratio. It turns out that this GR autocorrelation is known in science and obeys all necessary conditions, in contrast to the exponential autocorrelation function. Using the Kubo approach it is shown how exponential correlations appear in the linear response theory as a result of non-Hermitian relaxation of the system.
Pólya urn is a stochastic process in which balls are randomly drawn from an urn of red and blue balls, and balls of the same color as the drawn balls are added. The probability of a ball of a certain color being drawn is equal to the percentage of balls of that color in the urn. We introduce arbitrary memory kernels to modify this probability. If the memory kernel decays exponentially, it is a stationary process and is mean-reverting. If the memory kernel decays by a power-law, a phase transition occurs and the asymptotic behavior of the autocorrelation function changes. An auxiliary field var…
Matrix elements of observables in eigenstates of generic Hamiltonians are described by the Srednicki ansatz within the eigenstate thermalization hypothesis (ETH). We study a quantum chaotic spin-fermion model in a one-dimensional lattice, which consists of a spin-1/2 XX chain coupled to a single itinerant fermion. In our study, we focus on translationally invariant observables including the charge and energy current, thereby also connecting the ETH with transport properties. Considering observables with a Hilbert-Schmidt norm of one, we first perform a comprehensive analysis of ETH in the mode…
采用事件驱动的分子动力学模拟方法，通过取向自相关函数研究了致密硬核流体中的糖蜜拖尾现象。在流体-固体相变附近，存在三个区域的对取向自相关函数的弛豫，即动力学，糖蜜（拉伸指数），和扩散功率衰减。糖蜜和扩散功率制度的密度依赖性进行评估，后者比较与理论预测在三维空间。最大的星系团在冻结密度只有几个球体直径的情况下只持续了大约30皮秒（~ 2.8 x 10^{-11}[s]）。通过键取向序参量观察到的最显著的现象是，随着凝固密度的接近，团簇的尺寸急剧增大。
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrela…
The relation between spontaneous and stimulated global brain activity is a fundamental problem in the understanding of brain functions. This question is investigated both theoretically and experimentally within the context of nonequilibrium fluctuation-dissipation relations. We consider the stochastic coarse-grained Wilson-Cowan model in the linear noise approximation and compare analytical results to experimental data from magnetoencephalography (MEG) of human brain. The short time behavior of the autocorrelation function for spontaneous activity is characterized by a double-exponential decay…
