Related papers: Linear Response Theory: A Modern Analytic-Algebrai…
The response of a nonlinear stochastic system driven by an external sinusoidal time dependent force is studied by a variety of numerical and analytical approximations. The validity of linear response theory is put to a critical test by…
In this paper we present a formulation of the nonlinear stochastic differential equation which allows for systematic approximations. The method is not restricted to the asymptotic, i.e., stationary, regime but can be applied to derive…
This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a…
Generalizing response theory of open systems far from equilibrium is a central quest of nonequilibrium statistical physics. Using stochastic thermodynamics, we develop an algebraic method to study the response of nonequilibrium steady state…
A system of equations of the reaction-diffusion type is studied in the framework of both the direct and the inverse prolongation structure. We find that this system allows an incomplete prolongation Lie algebra, which is used to find the…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
We present a readily computable semi-analytic Layer Response Theory (LRT) for analysis of cohesive energetics involving two-dimensional layers such as BN or graphene. The theory approximates the Random Phase Approximation (RPA) correlation…
Within a Lagrangian formalism we derive the time-dependent Gutzwiller approximation for general multi-band Hubbard models. Our approach explicitly incorporates the coupling between time-dependent variational parameters and a time-dependent…
Controlling nonlinear systems, especially when data are being used to offset uncertainties in the model, is hard. A natural approach when dealing with the challenges of nonlinear control is to reduce the system to a linear one via change of…
Adaptive tracking control for rigid body dynamics is of critical importance in control and robotics, particularly for addressing uncertainties or variations in system model parameters. However, most existing adaptive control methods are…
We introduce a response theory for open quantum systems within nonequilibrium steady-states subject to a Hamiltonian perturbation. Working in the weak system-bath coupling regime, our results are derived within the…
Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion…
The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous…
The discovery of linear embedding is the key to the synthesis of linear control techniques for nonlinear systems. In recent years, while Koopman operator theory has become a prominent approach for learning these linear embeddings through…
We study nonlinear response in weakly coupled nonequilibrium $\phi^4$ theory in the context of both classical transport theory and real time quantum field theory, based on a generalized Kubo formula which we derive. A novel connection…
Linear response theory has developed into a formidable set of tools for studying the forced behaviour of a large variety of systems - including out of equilibrium ones. In this paper we provide a new angle on the problem, by studying under…
This article has one single purpose: introduce a new and simple, yet highly insightful approach to capture, fully and quantitatively, the dynamics of the circular flow of income in economies. The proposed approach relies mostly on basic…
Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…
We collect recent results on deriving useful response relations also for nonequilibrium systems. The approach is based on dynamical ensembles, determined by an action on trajectory space. (Anti)Symmetry under time-reversal separates two…
The conceptually new approach based on the logarithmic norm to design of robust adaptive state-feedback controller for linear time-varying (LTV) systems under system's modeling uncertainty and nonlinear external disturbance is proposed.…