Related papers: Exact dynamical decay rate for the almost Mathieu …
We consider a thermodynamically correct framework for electro-energy-reaction-diffusion systems, which feature a monotone entropy functional while conserving the total charge and the total energy. For these systems, we construct a relative…
For analytic quasi-periodic Schr\"odinger cocycles, You and Zhang [9] proved that the Lyapunov exponent is H\"older continuous for weak Liouville frequency. In this paper, we prove that the H\"older continuity also holds if the analytic…
Constraints are found on the spatial variation of finite-time Lyapunov exponents of two and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of…
Studying the subexponential convergence towards equilibrium of a strong Markov process, we exhibit an intermediate Lyapunov condition equivalent to the control of some moment of a hitting time. This provides a link, similar (although more…
We investigate the sensitivity of a disordered system with diffractive scatterers to a weak external perturbation. Specifically, we calculate the fidelity M(t) (also called the Loschmidt echo) characterizing a return probability after a…
The mass spectra of $D_s$ meson is obtained in the framework of relativistic independent quark model using Martin like potential for the quark confinement. The predicted excited states are in good agreement with the experimental results as…
We consider decay of metastable states of forced vibrations of a quantum oscillator close to bifurcation points, where dissipation becomes effectively strong. We show that decay occurs via quantum activation over an effective barrier. The…
We show that in the classical interaction picture the echo-dynamics, namely the composition of perturbed forward and unperturbed backward hamiltonian evolution, can be treated as a time-dependent hamiltonian system. For strongly chaotic…
In this paper we derive a quantitative dichotomy for the top Lyapunov exponent of a class of non-dissipative SDEs on a compact manifold in the small noise limit. Specifically, we prove that in this class, either the Lyapunov exponent is…
In this paper, a continuous finite-time-convergent differentiator is presented based on a strong Lyapunov function. The continuous differentiator can reduce chattering phenomenon sufficiently than normal sliding mode differentiator, and the…
We exploit the analogy between dynamics of inertial particle pair separation in a random-in-time flow and the Anderson model of a quantum particle on the line in a spatially random real-valued potential. Thereby we get an exact formula for…
In this paper, we consider a Diophantine quasi-periodic time-dependent analytic perturbation of a convex integrable Hamiltonian system, and we prove a result of stability of the action variables for an exponentially long interval of time.…
This paper investigates the initial boundary value problem of a finitely degenerate semilinear pseudo-parabolic equation associated with H\"{o}rmander's operator. Based on the global existence of solutions in previous literature, the…
We study decay rates for the energy of solutions of the damped wave equation on the torus. We consider dampings invariant in one direction and bounded above and below by multiples of $x^{\beta}$ near the boundary of the support and show…
We prove that the quasi-periodic Schr\"{o}dinger operator with a finitely differentiable potential has purely absolutely continuous spectrum for all phases if the frequency is Diophantine and the potential is sufficiently small in the…
We prove that infinitely differentiable almost reducible quasi-periodic cocycles, under a Diophantine condition on the frequency vector, are almost reducible to a sequence of real constant cocycles with a sequence of real conjugations, up…
Dissipative hyperbolic systems of \textit{regularity-loss} have been recently received increasing attention. Usually, extra higher regularity is assumed to obtain the optimal decay estimates, in comparison with that for the global-in-time…
Recently, it was observed that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In particular, under mild assumptions on the…
Using results from our companion article [arXiv:1112.4824v2] on a Schauder approach to existence of solutions to a degenerate-parabolic partial differential equation, we solve three intertwined problems, motivated by probability theory and…
In this paper we prove an inequality for individual and uniform Diophantine exponents in the case of simultaneous approximation. This inequality is better than Jarnik's for small values of the uniform exponent.