相关论文: Lyapunov Potential Description for Laser Dynamics
In the context of mechanical Lagrangian dynamics, we prove a new Lyapunov instability criterion for a non strict local minimum equilibrium point of a smooth potential where the sufficient condition for instability is the existence of a…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
A model to simulate the phenomenon of random lasing is presented. It couples Maxwell's equations with the rate equations of electronic population in a disordered system. Finite difference time domain methods are used to obtain the field…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
The mode dynamics of a random laser is investigated in experiment and theory. The laser consists of a ZnCdO/ZnO multiple quantum well with air-holes that provide the necessary feedback. Time-resolved measurements reveal multimode spectra…
Consider a non-autonomous continuous-time linear system in which the time-dependent matrix determining the dynamics is piecewise constant and takes finitely many values $A_1, \dotsc, A_N$. This paper studies the equality cases between the…
Oscillations and noise are ubiquitous in physical and biological systems. When oscillations arise from a deterministic limit cycle, entrainment and synchronization may be analyzed in terms of the asymptotic phase function. In the presence…
The phase description is a powerful tool for analyzing noisy limit cycle oscillators. The method, however, has found only limited applications so far, because the present theory is applicable only to the Gaussian noise while noise in the…
We compute the full Lyapunov spectra for a hard-disk fluid under temperature gradient and shear. The system is thermalized by deterministic and time-reversible scattering at the boundary. This thermostating mechanism allows for energy…
The sensitivity of trajectories over finite time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M_{ij} of the stability matrix M. For globally…
A system plus environment conservative model is used to characterize the nonlinear dynamics when the time averaged energy for the system particle starts to decay. The system particle dynamics is regular for low values of the $N$ environment…
With a scalar potential and a bivector potential, the vector field associated with the drift of a diffusion is decomposed into a generalized gradient field, a field perpendicular to the gradient, and a divergence-free field. We give such…
Optical tweezers setup is often used to probe the motion of individual tracer particle, which promotes the study of relaxation dynamics of a generic process confined in a harmonic potential. We uncover the dependence of ensemble- and…
Control of the potential energy and free evolution lie at the heart of levitodynamics as key requirements for sensing, wave function expansion, and mechanical squeezing protocols. Here, we experimentally demonstrate full control over the…
We present an analysis of the power fluctuations in the statistical steady state of a passively mode locked laser. We use statistical light-mode theory to map this problem to that of fluctuations in a reference equilibrium statistical…
We study the linearized Vlasov-Poisson equation in the gravitational case around steady states that are decreasing and continuous functions of the energy. We identify the absolutely continuous spectrum and give criteria for the existence of…
We propose a semi-classical approach based on the Vlasov equation to describe the time-dependent electronic dynamics in a bulk simple metal under an ultrashort intense laser pulse. We include in the effective potential not only the ionic…
We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long time…
There are conflicting reports in the literature regarding the finite-size scaling of the Liouvillian gap and dynamical fluctuations at discontinuous phase transitions, with various studies reporting either exponential or power-law behavior.…