Quantum random walk : effect of quenching

TL;DR

This paper investigates how abrupt removal of a detector affects a discrete quantum random walk, revealing conditions under which the walker's probability distribution is enhanced and analyzing the scaling behavior of these effects.

Contribution

It introduces the study of quenching effects on quantum random walks, showing how detector removal influences probability distributions and correlations, with scaling laws derived.

Findings

Probability at detector position can be enhanced by quenching if removal time is below a critical limit.

The ratio of quenched to free walk probabilities scales as 1/t_R at large t_R.

The probability ratio scales as x_D^2 for small x_D when t_R is fixed.

Abstract

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 $t_R < t_{R}^{lim}$ where $t_{R}^{lim}$ scales as $x_D{^2}$. The ratio of the occurrence probabilities for a quenched walker ($t_R \neq 0$) 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.