Related papers: Nonlinear response theory for Markov processes: Si…
This paper describes a robust linear time-invariant output-feedback control strategy to reduce turbulent fluctuations, and therefore skin-friction drag, in wall-bounded turbulent fluid flows, that nonetheless gives performance guarantees in…
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…
The solution to nonlinear Fokker-Planck equation is constructed in terms of the minimal Markov semigroup generated by the equation. The semigroup is obtained by a purely functional analytical method via Hille-Yosida theorem. The existence…
It is an interesting open problem to achieve adaptive prescribed-time control for strict-feedback systems with unknown and fast or even abrupt time-varying parameters. In this paper we present a solution with the aid of several design and…
Laser frequency stabilization is conventionally analyzed using continuous-time control theory, which accurately models analog feedback but is insufficient for digital implementations where quantization, sampling, and stochastic noise shape…
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov stability of the front against fully…
In recent years, the investigation of nonlinear electromagnetic responses has received significant attention due to its potential for elucidating the quantum properties of matter. Although remarkable progress has been achieved in developing…
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local…
Nonlinear density response theory is revisited focusing on the harmonically perturbed finite temperature uniform electron gas. Within the non-interacting limit, brute force quantum kinetic theory calculations for the quadratic, cubic,…
A microscopic approach to the proton-neutron nuclear response is formulated in the finite-temperature relativistic nuclear field theory framework. The approach is based on the meson-nucleon Lagrangian of quantum hadrodynamics and advances…
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under…
We present a physically inspired generalization of equilibrium response formulae, the fluctuation-dissipation theorem, to Markov jump processes possibly describing interacting particle systems out-of-equilibrium. Here, the time-dependent…
This paper proposes a novel formulation of frequency response for nonlinear systems in the Koopman operator framework. This framework is a promising direction for the analysis and synthesis of systems with nonlinear dynamics based on…
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a time and path-dependent…
This paper studies multi-agent systems with nonlinear consensus protocols, i.e., only nonlinear measurements of the states are available to agents. The solutions of these systems are understood in Filippov sense since the possible…
In a recent paper (A.E. Glazounov and A.K. Tagantsev, Phys.Rev. Lett. 85, 2192 (2000)) it has been proposed a phenomenological model of the dynamic non-linear response in relaxor ferroelectrics based on the averaging of the…
We present a rigorous statistical-mechanics theory of nonlinear many mode laser systems. An important example is the passively mode-locked laser that promotes pulse operation when a saturable absorber is placed in the cavity. It was shown…
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…