相关论文: Streched exponential in non-linear stochastic file…
We show that at a second order phase transition, of \phi^4 like system, a necessary condition for streched exponential decay of the time structure factor is obeyed. Using the ideas presented in this proof a crude estimate of the decay of…
We consider non-linear stochastic field equations such as the KPZ equation for deposition and the noise driven Navier-Stokes equation for hydrodynamics. We focus on the Fourier transform of the time dependent two point field correlation,…
We study the deviations from the exponential decay law, both in quantum field theory (QFT) and quantum mechanics (QM), for an unstable particle which can decay in (at least) two decay channels. After a review of general properties of…
We consider the exactly soluble Edwards-Wilkinson Model in one dimension and demonstrate explicitly, that it is possible to construct a field, that does not depend explicitly on time, such that the corresponding time dependent correlation…
In this paper we analyze a nonlinear abstract evolution equation with an infinite number of time-dependent time delays and a Lipschitz continuous nonlinear term. By using a fixed point argument we prove the existence of a mild solution.…
We consider the two-species totally asymmetric simple exclusion process on $\mathbb{Z}$ with a translation-invariant stationary measure as the initial condition. We establish the asymptotic decoupling of the marginal height profiles along…
This paper develops further and systematically the asymptotic expansion theory that was initiated by Foias and Saut in [11]. We study the long-time dynamics of a large class of dissipative systems of nonlinear ordinary differential…
We study the dynamic structure factor of fluctuating elastic thin sheets subject to conservative (athermal) random forcing. In Steinbock, Katzav & Boudaoud, Phys. Rev. Research 4, 033096 (2022), the static structure factor of such a sheet…
The classical model of q-damped oscillator is introduced and solved in terms of Jackson q-exponential function for three different cases, under-damped, over-damped and the critical one. It is shown that in all three cases solution is…
In this paper, we analyze a semilinear damped second order evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. The nonlinear term satisfies a local Lipschitz continuity assumption. Under…
The truncated two-point function of the ferromagnetic Ising model on $\mathbb Z^d$ ($d\ge3$) in its pure phases is proven to decay exponentially fast throughout the ordered regime ($\beta>\beta_c$ and $h=0$). Together with the previously…
For the Ising model defined on $a\mathbb{Z}^2$ at critical temperature with external field $a^{15/8}h$, we give a simple and elementary proof that its truncated two-point function decays exponentially. The proof combines the high…
In this paper, we derive suitable optimal $L^p-L^q$ decay estimates, $1\leq p\leq q\leq \infty$, for the solutions to the $\sigma$-evolution equation, $\sigma>1$, with structural damping and power nonlinearity $|u|^{1+\alpha}$ or…
Stretched exponential relaxation ($\exp{-(t/\tau)}^{\beta_K}$) is observed in a large variety of systems but has not been explained so far. Studying random walks on percolation clusters in curved spaces whose dimensions range from 2 to 7,…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
We consider the Fisher-KPP equation with a non-local interaction term. Hamel and Ryzhik showed that in solutions of this equation, the front location at a large time $t$ is $\sqrt 2 t +o(t)$. We study the asymptotics of the second order…
Thin growing tissues (such as plant leaves) can be modelled by a bounded domain $S\subset R^2$ endowed with a Riemannian metric $g$, which models the internal strains caused by the differential growth of the tissue. The elastic energy is…
We compute the critical exponents for nonextensive $\lambda\phi^{3}$ scalar field theory for all loop orders and $|q - 1| < 1$. We apply the results for both nonextensive percolation and Lee-Yang edge singularity problems. The corresponding…
In this article we define and quantize a truncated form of the nonassociative and noncommutative Snyder phi^4 field theory using the functional method in momentum space. More precisely, the action is approximated by expanding up to the…
We provide conditions for the existence of measurable solutions to the equation $\xi(T\omega)=f(\omega,\xi(\omega))$, where $T:\Omega \rightarrow\Omega$ is an automorphism of the probability space $\Omega$ and $f(\omega,\cdot)$ is a…