Continuous-Time Quantum Walks and Trapping

TL;DR

This paper explores how continuous-time quantum walks differ from classical random walks in trapping scenarios, revealing that quantum effects lead to distinct survival probabilities depending on trap configurations, unlike classical exponential decay.

Contribution

It demonstrates the formal connection between classical CTRWs and quantum CTQWs and analyzes how trap arrangements influence quantum survival probabilities.

Findings

Quantum walks show non-exponential decay in survival probability.

Trap configuration significantly affects quantum transport behavior.

Classical decay remains exponential regardless of trap arrangement.

Abstract

Recent findings suggest that processes such as the electronic energy transfer through the photosynthetic antenna display quantal features, aspects known from the dynamics of charge carriers along polymer backbones. Hence, in modeling energy transfer one has to leave the classical, master-equation-type formalism and advance towards an increasingly quantum-mechanical picture, while still retaining a local description of the complex network of molecules involved in the transport, say through a tight-binding approach. Interestingly, the continuous time random walk (CTRW) picture, widely employed in describing transport in random environments, can be mathematically reformulated to yield a quantum-mechanical Hamiltonian of tight-binding type; the procedure uses the mathematical analogies between time-evolution operators in statistical and in quantum mechanics: The result are continuous-time quantum walks (CTQWs). However, beyond these formal analogies, CTRWs and CTQWs display vastly different physical properties. In particular, here we focus on trapping processes on a ring and show, both analytically and numerically, that distinct configurations of traps (ranging from periodical to random) yield strongly different behaviours for the quantal mean survival probability, while classically (under ordered conditions) we always find an exponential decay at long times.