Related papers: Analytic Lyapunov exponents in a classical nonline…
We continue our study of the parabolic Anderson equation $\partial u/\partial t = \kappa\Delta u + \gamma\xi u$ for the space-time field $u\colon\,\Z^d\times [0,\infty)\to\R$, where $\kappa \in [0,\infty)$ is the diffusion constant,…
We are concerned with solvability of nonlinear systems involving a discrete singular $\phi$-Laplacian operator of type \begin{equation*} u \mapsto \Delta\left[\phi(\Delta u(n-1))\right] \qquad (n\in \{1, \dots, T\}), \end{equation*}…
We consider the fourth order problem $\Delta^{2}u=\lambda f(u)$ on a general bounded domain $\Omega$ in $R^{n}$ with the Navier boundary condition $u=\Delta u=0$ on $\partial \Omega$. Here, $\lambda$ is a positive parameter and $…
Using a temporally weighted norm we first establish a result on the global existence and uniqueness of solutions for Caputo fractional stochastic differential equations of order $\alpha\in(\frac{1}{2},1)$ whose coefficients satisfy a…
Statistical behavior of a classical $\phi ^{4}$ Hamiltonian lattice is investigated from microscopic dynamics. The largest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the system. It is…
We study semilinear elliptic equations \begin{equation*} \begin{cases} -\Delta u = f(u) & \text{in } \Omega, \\ \partial_\nu u = 0 & \text{on } \partial\Omega, \end{cases} \end{equation*} with homogeneous Neumann boundary conditions in…
The Fermi-Pasta-Ulam (FPU) one-dimensional Hamiltonian includes a quartic term which guarantees ergodicity of the system in the thermodynamic limit. Consistently, the Boltzmann factor $P(\epsilon) \sim e^{-\beta \epsilon}$ describes its…
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…
We present some analytic results aiming at explaining the lack of thermalization observed by Fermi Pasta and Ulam in their celebrated numerical experiment. In particular we focus on results which persist as the number $N$ of particles tends…
This study investigates the intricate relationship between dissipative processes of open quantum systems and the non-Hermitian quantum field theory of relativistic fermionic systems. By examining the influence of dissipative effects on…
For a three-dimensional theory with a coupling $\phi \epsilon ^{\mu \nu \lambda} v_\mu F_{\nu \lambda}$, where $v_\mu$ is an external constant background, we compute the interaction potential within the structure of the gauge-invariant but…
In this work, we derive the Newman-Penrose formalism of Maxwell's equations using two approaches: differential forms and intrinsic derivatives. Denoting $(k_{AF})^\mu$ as $k^\mu$, with $k^\mu=(k^t,k^r,0,0)$ in spherically symmetric…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
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…
This paper studies Laplace's equation $-\Delta\,u=0$ in an exterior region $U\varsubsetneq{\mathbb R}^N$, when $N\geq3$, subject to the nonlinear boundary condition $\frac{\partial…
In this paper, we investigated the Pauli equation in a two-dimensional noncommutative phase-space by considering a constant magnetic field perpendicular to the plane. We mapped the noncommutative problem to the equivalent commutative one…
By means of expressing volumes in phase space in terms of traces of quantum operators, a relationship between the Hamiltonian poles and the Lyapunov exponents in a non Hermitian quantum dynamics, is presented. We illustrate the formalism by…
This paper is devoted to the study of the existence of positive solutions for a problem related to a higher order fractional differential equation involving a nonlinear term depending on a fractional differential operator,…
We calculate the Lyapunov exponents in a classical molecular dynamics framework. The system is composed of few hundreds particles interacting either through Yukawa (Nuclear) or Slater-Kirkwood (Atomic) forces. The forces are chosen to give…
A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments…