### 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}