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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…

Analysis of PDEs · Mathematics 2025-08-08 Michael Kniely

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…

Mathematical Physics · Physics 2018-07-17 Licheng Fang , Daxiong Piao

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…

Chaotic Dynamics · Physics 2009-10-31 Jean-Luc Thiffeault , Allen H. Boozer

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…

Probability · Mathematics 2021-08-03 Armand Bernou

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…

Disordered Systems and Neural Networks · Physics 2009-11-07 Y. Adamov , I. V. Gornyi , A. D. Mirlin

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…

High Energy Physics - Phenomenology · Physics 2016-06-01 Manan Shah , Bhavin Patel , P C Vinodkumar

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…

Mesoscale and Nanoscale Physics · Physics 2007-05-23 M. I. Dykman

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…

Chaotic Dynamics · Physics 2009-11-10 Gregor Veble , Tomaz Prosen

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…

Probability · Mathematics 2024-06-04 Jacob Bedrossian , Chi-Hao Wu

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…

Systems and Control · Computer Science 2013-06-21 Xinhua Wang , Hai Lin

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…

Chaotic Dynamics · Physics 2007-05-23 Peter Horvai

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.…

Dynamical Systems · Mathematics 2015-06-23 Abed Bounemoura

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…

Mathematical Physics · Physics 2025-07-01 Xiang-kun Shao , Xue-song Li , Nan-jing Huang , Donal O'Regan

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…

Analysis of PDEs · Mathematics 2020-07-06 Kiril Datchev , Perry Kleinhenz

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…

Dynamical Systems · Mathematics 2021-03-30 Ao Cai

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…

Dynamical Systems · Mathematics 2025-08-26 Maxime Chatal , Claire Chavaudret , L. Hakan Eliasson

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…

Analysis of PDEs · Mathematics 2015-10-30 Jiang Xu , Shuichi Kawashima

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…

Classical Analysis and ODEs · Mathematics 2015-05-22 James Bremer , Vladimir Rokhlin

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…

Probability · Mathematics 2016-04-08 Paul M. N. Feehan , Camelia Pop

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.

Number Theory · Mathematics 2010-09-07 Oleg N. German