Speaker
Description
In this work we study the problem of a random walk
in a finite-size randomly inhomogeneous one-dimensional medium by using a Fock space approach.
We map the master equation of the walker into a Schr\"odinger-like equation
and we describe the evolution of the random walk in a Fock space in which the
system states are assigned to the sites of a regular one-dimensional lattice.
This formalism allows to evaluate the
probability $P(i,t)$ of finding
the walker in a given point $i$ at a given time $t$.
Unlike previous applications of a Fock space for random walks displaying
anomalous diffusion \cite{nicolau_jpa,araujo_jsm}, here
we set in each point $i$ of the domain
the probability $r_i \in [0,1]$ for the walker to stay
and the symmetric probabilities $(1-r_i)/2$ to jump on the left
or on the right, respectively, into the nearest neighbor site.
Moreover, probabilities $r_i$ are assumed to be random and drawn
from a Beta distribution $B(a,b)$ in each $i$-site of the domain.
If $b < 1$, then a crossover from standard to sub-diffusion is observed.
We show that the walker distribution converges
to a stretched-exponential in the case of subdiffusion and the
functional relation between the anomalous exponent and the
statistical features of $r_i$ distributed according to $B(a,b)$
is also provided.
\begin{thebibliography}{99.}
\bibitem{nicolau_jpa}N. S. Nicolau, H. A. Araújo, E. P. Raposo et al:
J. Phys. A: Math. Theor. \textbf{54}, 325006 (2021)
\bibitem{araujo_jsm} H. A. Araújo, M. O. Lukin, E. P. Raposo et al:
J. Stat. Mech. \textbf{2020}, 083202 (2020)
\end{thebibliography}
