2009/03/19 by Elena Agliari, ELENA AGLIARI, Oliver Muelken +3 · 1 citation
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Energy transfer #Exponential function #Formalism (music) #Hamiltonian (control theory) #Quantum #Quantum many-body systems #Quantum walk #Random walk #Spectroscopy and Quantum Chemical Studies #Stochastic process #Trapping #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1142/s0218127410025715
8 pages, 6 figures; to be published in International Journal of Bifurcation and Chaos
arxiv created 2009/03/19 · openalex publication_date 2010/02/01 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Recent findings suggest that processes such as the excitonic 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 behaviors for the quantal mean survival probability, while classically (under ordered conditions) we always find an exponential decay at long times.