Trapping of Continuous-Time Quantum walks on Erdos-Renyi graphs

TL;DR

This paper investigates how continuous-time quantum walks on Erdős-Rényi graphs are affected by traps, revealing unique decay behaviors and the influence of graph connectivity and dilution on survival probabilities.

Contribution

It provides a detailed analysis of quantum walk trapping dynamics on Erdős-Rényi graphs, highlighting non-monotonic decay rates and stationary states influenced by trap concentration and graph dilution.

Findings

Survival probability decays exponentially with a rate depending non-monotonically on graph connectivity.

At very low or high dilution, stationary states dominate, leading to finite survival probability.

Quantum walks exhibit qualitatively different trapping behavior compared to classical walks.

Abstract

We consider the coherent exciton transport, modeled by continuous-time quantum walks, on Erd\"{o}s-R\'{e}ny graphs in the presence of a random distribution of traps. The role of trap concentration and of the substrate dilution is deepened showing that, at long times and for intermediate degree of dilution, the survival probability typically decays exponentially with a (average) decay rate which depends non monotonically on the graph connectivity; when the degree of dilution is either very low or very high, stationary states, not affected by traps, get more likely giving rise to a survival probability decaying to a finite value. Both these features constitute a qualitative difference with respect to the behavior found for classical walks.