Quantum random walk: Effect of quenching
Sanchari Goswami, Parongama Sen · Physical Review A · 2012
We study the effect of quenching on a discrete quantum random walk by removing a detector placed at a position ${x}_{D}$ abruptly at time ${t}_{R}$ from its path. The results show that this may lead to an enhancement of the occurrence probability at ${x}_{D}$ provided the time of removal ${t}_{R}<{t}_{R}^{\mathrm{lim}}$, where ${t}_{R}^{\mathrm{lim}}$ scales as ${x}_{D}{}^{2}$. The ratio of the occurrence probabilities for a quenched walker (${t}_{R}\ensuremath{ e}0$) and free walker (${t}_{R}=0$) shows that it scales as $1/{t}_{R}$ at large values of ${t}_{R}$ independent of ${x}_{D}$. On the other hand, if ${t}_{R}$ is fixed, this ratio varies as ${x}_{D}^{2}$ for small ${x}_{D}$. The results are compared to the classical case. We also calculate the correlations as functions of both time and position.