Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems

We derive an exact formula for the scaled cumulant generating function of the time-integrated current associated to an arbitrary ballistically transported conserved charge. Our results rely on the Euler-scale description of interacting, many-body, integrable models out of equilibrium given by the generalized hydrodynamics, and on the large deviation theory. Crucially, our findings extend previous studies by accounting for inhomogeneous and dynamical initial states in interacting systems. We present exact expressions for the first three cumulants of the time-integrated current. Considering the non-interacting limit of our general expression for the scaled cumulant generating function, we further show that for the partitioning protocol initial state our result coincides with previous results of the literature. Given the universality of the generalized hydrodynamics, the expression obtained for the scaled cumulant generating function is applicable to any interacting integrable model obeying the hydrodynamic equations, both classical and quantum.

New perspectives on the Erlang-A queue

The nonstationary Erlang-A queue is a fundamental queueing model that is used to describe the dynamic behavior of large-scale multiserver service systems that may experience customer abandonments, such as call centers, hospitals, and urban mobility systems. In this paper we develop novel approximations to all of its transient and steady state moments, the moment generating function, and the cumulant generating function. We also provide precise bounds for the difference of our approximations and the true model. More importantly, we show that our approximations have explicit stochastic representations as shifted Poisson random variables. Moreover, we are also able to show that our approximations and bounds also hold for nonstationary Erlang-B and Erlang-C queueing models under certain stability conditions.

Multidisciplinary reliability design optimization using an enhanced saddlepoint approximation in the framework of sequential optimization and reliability analysis

For high reliability calculation efficiency and evaluation accuracy, saddlepoint approximation technology has been introduced into design and optimization under uncertainties. When using saddlepoint approximation, there are two prerequisites: all random information is tractable and saddlepoint equations are easy to be solved. However, the above requirements cannot always be met in complex multidisciplinary systems. Random variables sometimes are intractable, or saddlepoint equations are highly nonlinear. To tackle these problems, in this study, an efficient reliability-based multidisciplinary design optimization using the combination method of saddlepoint approximation and third-moment is given. A simplified alternative cumulant generating function can be constructed by saddlepoint approximation and third-moment with the first, second and third moments of a random variable effectively. Then, this cumulant generating function can be utilized to calculate the cumulative distribution function and the probability density function of this random variable approximately. Moreover, to obtain better efficiency, the framework of sequential optimization and reliability analysis is introduced in this study. The corresponding formula of the proposed reliability-based multidisciplinary design optimization is given in detail. Two test problems are solved to show the application of the proposed method.

COUNTING STATISTICS OF NONEQUILIBRIUM TUNNELING PROCESS USING FUNCTIONAL RENORMALIZATION GROUP

We develop a scheme to investigate the flux of nonequilibrium transport based on the full counting statistics and nonequilibrium functional renormalization group method. As an illustrative example, we study the charge transfer in the system of an interacting quantum dot connected to two noninteracting reservoirs via tunneling. Within the lowest approximation in functional renormalization group, we obtain the cumulant generating function analytically.