Related papers: Linear Response Theory: A Modern Analytic-Algebrai…
Linear response theory serves as a fundamental tool in the study of quantum transport, extensively employed to elucidate fundamental mechanisms related to the nature of the particles involved and the underlying symmetries. This framework…
We consider a nonlinear stochastic differential equation driven by an $\alpha$-stable L\'{e}vy process ($1<\alpha<2$). We first obtain some regularity results for the probability density of its invariant measure via establishing the a…
Linear response theory is a fundamental framework studying the macroscopic response of a physical system to an external perturbation. This paper focuses on the rigorous mathematical justification of linear response theory for Langevin…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a…
The formalism of linear response theory can be extended to encompass physical situations where an open quantum system evolves towards a non-equilibrium steady-state. Here, we use the framework put forward by Konopik and Lutz [Phys. Rev.…
Finite-time coherent sets represent minimally mixing objects in general nonlinear dynamics, and are spatially mobile features that are the most predictable in the medium term. When the dynamical system is subjected to small parameter…
The linear response of an isolated, homogeneous granular fluid to small spatial perturbations is studied by methods of non-equilibrium statistical mechanics. The long wavelength linear hydrodynamic equations are obtained, with formally…
A new approach to the analytic theory of difference equations with rational and elliptic coefficients is proposed. It is based on the construction of canonical meromorphic solutions which are analytical along "thick paths". The concept of…
Linear response theory lies at the heart of quantum many-body physics because it builds up connections between the dynamical response to an external probe and correlation functions at equilibrium. Here we consider the dynamical response of…
Linear response theory asserts that sufficiently small external biases produce currents proportional to the applied force and forms the theoretical foundation of nonequilibrium transport. Here we demonstrate that linear response can break…
We introduce a linear-scaling real-space methodology to compute time-resolved electrical responses of materials driven far from equilibrium, with energy relaxation and disorder treated on equal footing. Applying this approach to gapped…
The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and a scattering theory of nonlinear response has yet to be fully…
We consider simple examples illustrating some new features of the linear response theory developed by Ruelle for dissipative and chaotic systems [{\em J. of Stat. Phys.} {\bf 95} (1999) 393]. In this theory the concepts of linear response,…
We start from the QED Lagrangian to describe a charged many-particle system coupled to the radiation field. A covariant density matrix approach to kinetic theory of QED plasmas, subjected to a strong external electro-magnetic field has…
The time-dependent Ginzburg-Landau approach is used to investigate nonlinear response of a strongly type-II superconductor. The dissipation takes a form of the flux flow which is quantitatively studied beyond linear response. Thermal…
Nonlinear systems of the reaction-diffusion type, including Gierer-Meinhardt models of autocatalysis, are studied by using Lie algebras coming from the prolongation structure. The consequences of this analytical approach, as the…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…
Understanding how nonequilibrium systems respond to perturbations is a central challenge in physics. In this work, we establish mutual linearity in nonequilibrium overdamped Langevin systems. This theory provides a framework for controlling…
We consider the problem of impulse response estimation of stable linear single-input single-output systems. It is a well-studied problem where flexible non-parametric models recently offered a leap in performance compared to the classical…