arXiv subjects

Kevin Peralta-Martinez

Publications and source records attributed to Kevin Peralta-Martinez.

2 recordsLinked to original sources

arXiv2026

Survival probability of random networks

In this work we study in detail all phases of the time evolution of a delta-like excitation in Erdös-Renyi (ER) random networks by means of the survival probability (SP): The initial decay of the SP (both, the fast decay followed by the power-law decay), the correlation hole regime (the regime between the minimum value of the SP and its saturation value), and the saturation of the SP. Specifically, we found that (i) the power-law decay of the SP and the time-averaged SP are proportional to $t^{-D_{2}}$ and $t^{-\widetilde{D}_{2}}$, respectively (where $D_2$ and $\widetilde{D}_2$ are the correlation dimension of the eigenstates of the randomly weighted adjacency matrices of the ER random networks and the correlation dimension associated with the initial state, respectively) and (ii) the relative depth of the correlation hole of the SP scales with the average degree $\langle k\rangle\approx np$ (here, $n$ and $p$ are the size and the connection probability of the ER random networks). In addition, we show that the eigenstates of the randomly weighted adjacency matrices of ER networks display clear multifractal properties.

cond-mat.stat-mech↗

arXiv2023

Leaking from the phase space of the Riemann-Liouville fractional standard map

In this work we characterize the escape of orbits from the phase space of the Riemann-Liouville (RL) fractional standard map (fSM). The RL-fSM, given in action-angle variables, is derived from the equation of motion of the kicked rotor when the second order derivative is substituted by a RL derivative of fractional order $α$. Thus, the RL-fSM is parameterized by $K$ and $α\in(1,2]$ which control the strength of nonlinearity and the fractional order of the RL derivative, respectively. Indeed, for $α=2$ and given initial conditions, the RL-fSM reproduces Chirikov's standard map. By computing the survival probability $P_{\text{S}}(n)$ and the frequency of escape $P_{\text{E}}(n)$, for a hole of hight $h$ placed in the action axis, we observe two scenarios: When the phase space is ergodic, both scattering functions are scale invariant with the typical escape time $n_{\text{typ}}=\exp\langle \ln n \rangle \propto (h/K)^2$. In contrast, when the phase space is not ergodic, the scattering functions show a clear non-universal and parameter-dependent behavior.

nlin.CD↗