相关论文: The Memory Function Formalism: A Review
In this work we propose a generalization of the concept of Ruelle operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call generalized Ruelle operator, that generalizes both the Ruelle…
The Mori-Zwanzig projection formalism is widely used in studying systems with many degrees of freedom. We used a system-bath Hamiltonian system to show that the Mori's and Zwanzig's projection procedures are mutual limiting cases of each…
In this paper we discuss a concept of dynamic memory and an application of fractional calculus to describe the dynamic memory. The concept of memory is considered from the standpoint of economic models in the framework of continuous time…
We present a general numerical approach for constructing governing equations for unknown dynamical systems when only data on a subset of the state variables are available. The unknown equations for these observed variables are thus a…
We derive a formula for the electrical conductivity of solids that includes relaxation, dissipation, and quantum coherence. The derivation is based on the Kubo formula, with a Mori memory function approach to include dissipation effects at…
In the first part of this paper we review several formalisms which give alternative ways for describing the light. They are: the formalism `baroque' and the Majorana-Oppenheimer form of electrodynamics, the Sachs' theory of Elementary…
Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the…
We develop the general formalism for the study of neutrino propagation in presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival probabilities and higher…
We introduce the Mori-Zwanzig Mode Decomposition (MZMD), a novel data-driven technique for efficient modal analysis of and reduced-order modeling of large-scale spatio-temporal dynamical systems. MZMD represents an extension of Dynamic Mode…
Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov…
An extended Wigner function formalism is introduced for describing the quantum dynamics of particles with internal degrees of freedom in the presence of spatially inhomogeneous fields. The approach is used for quantitative simulations of…
We introduce in detail our newly developed \textit{ab initio} LDA+Gutzwiller method, in which the Gutzwiller variational approach is naturally incorporated with the density functional theory (DFT) through the "Gutzwiller density functional…
We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…
In the present work we illustrate that classical but nonlinear systems may possess features reminiscent of quantum ones, such as memory, upon suitable external perturbation. As our prototypical example, we use the two-dimensional complex…
In this tutorial presentation, we give a comprehensive introduction into the Gutzwiller variational approach and its merger with the density functional theory. The merits of this method are illustrated by a discussion of results for…
We introduce conservative curved systems over multiply connected domains and study relationships of such systems with related notions of functional model, characteristic function, and transfer function. In contrast to standard theory for…
We develop rigorous estimates and provably convergent approximations for the memory integral in the Mori-Zwanzig (MZ) formulation. The new theory is built upon rigorous mathematical foundations and is presented for both state-space and…
Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…
The Fuzzy transform is ubiquitous in different research fields and applications, such as image and data compression, data mining, knowledge discovery, and the analysis of linguistic expressions. As a generalisation of the Fuzzy transform,…
We continue our study of the statistical properties of particles in equilibrium obeying Smoluchowski dynamics. We show that the system is governed by a kinetic equation of the memory function form and that the memory function is given by…