Enhanced Quantum Transport in Multiplex Networks

Quantum transport through disordered structures is inhibited by (Anderson) localization effects. The disorder can be either topological as in random networks or energetical as in the original Anderson model. In both cases the eigenstates of the Hamiltonian associated with the network become localized. We show how to overcome localization by network multiplexing. Here, multiple layers of random networks with the same number of nodes are stacked in such a way that in the perpendicular directions regular one-dimensional networks are formed. Depending on the ratio of the coupling within the layer and perpendicular to it, transport gets either enhanced or diminished. In particular, if the couplings are of the same order, transport gets enhanced and localization effects can be overcome. We exemplify our results by two examples: multiplexes of random networks and of one-dimensional Anderson models.Comment: 4 pages, 3 figures, fixed reference

Inefficient quantum walks on networks: the role of the density of states

We show by general arguments that networks whose density of states contains few highly degenerate eigenvalues result in inefficient performances of continuous-time quantum walks (CTQW) over these networks, while systems whose eigenvalues all have the same degeneracy lead to very efficient transport. We exemplify our results by considering CTQW and, for comparison, its classical counterpart, continuous-time random walks, over simple structures, whose eigenvalues and eigenstates can be calculated analytically. Extensions to more complicated, hyper-branched networks are discussed.Comment: 6 pages, 4 figure

Continuous time quantum walks in phase space

We formulate continuous time quantum walks (CTQW) in a discrete quantum mechanical phase space. We define and calculate the Wigner function (WF) and its marginal distributions for CTQWs on circles of arbitrary length $N$. The WF of the CTQW shows characteristic features in phase space. Revivals of the probability distributions found for continuous and for discrete quantum carpets do manifest themselves as characteristic patterns in phase space.Comment: slightly revised version to be published in PRA, 6 pages, 6 color figures (high quality postscript figures are available upon request

Directed excitation transfer in vibrating chains by external fields

We study the coherent dynamics of excitations on vibrating chains. By applying an external field and matching the field strength with the oscillation frequency of the chain it is possible to obtain an (average) transport of an initial Gaussian wave packet. We distinguish between a uniform oscillation of all nodes of the chain and the chain being in its lowest eigenmode. Both cases can lead to directed transport.Comment: 7 pages, 10 figures (some of the figures are in png-format, high-quality pdf-files available upon request

Environment-assisted quantum transport and trapping in dimers

We study the dynamics and trapping of excitations for a dimer with an energy off-set $\Delta$ coupled to an external environment. Using a Lindblad quantum master equation approach, we calculate the survival probability $\Pi(t)$ of the excitation and define different lifetimes $\tau_s$ of the excitation, corresponding to the duration of the decay of $\Pi(t)$ in between two predefined values. We show that it is not possible to always enhance the overall decay to the trap. However, it is possible, even for not too small environmental couplings and for values of $\Delta$ of the order ${\cal O}(1)$, to decrease certain lifetimes $\tau_s$, leading to faster decay of $\Pi(t)$ in these time intervals: There is an optimal environmental coupling, leading to a maximal decay for fixed $\Delta$.Comment: 5 pages, 4 figure

Spacetime structures of continuous time quantum walks

The propagation by continuous time quantum walks (CTQWs) on one-dimensional lattices shows structures in the transition probabilities between different sites reminiscent of quantum carpets. For a system with periodic boundary conditions, we calculate the transition probabilities for a CTQW by diagonalizing the transfer matrix and by a Bloch function ansatz. Remarkably, the results obtained for the Bloch function ansatz can be related to results from (discrete) generalized coined quantum walks. Furthermore, we show that here the first revival time turns out to be larger than for quantum carpets.Comment: 5 pages, 4 figures; accepted for publication in PR

Coherent dynamics on hierarchical systems

We study the coherent transport modeled by continuous-time quantum walks, focussing on hierarchical structures. For these we use Husimi cacti, lattices dual to the dendrimers. We find that the transport depends strongly on the initial site of the excitation. For systems of sizes $N\le21$, we find that processes which start at central sites are nearly recurrent. Furthermore, we compare the classical limiting probability distribution to the long time average of the quantum mechanical transition probability which shows characteristic patterns. We succeed in finding a good lower bound for the (space) average of the quantum mechanical probability to be still or again at the initial site.Comment: 7 pages, 5 figure

Energy transfer properties and absorption spectra of the FMO complex: from exact PIMC calculations to TCL master equations

We investigate the excitonic energy transfer (EET) in the Fenna-Matthews-Olsen complex and obtain the linear absorption spectrum (at 300 K) by a phenomenological time-convolutionless (TCL) master equation which is validated by utilizing Path Integral Monte Carlo (PIMC) simulations. By applying Marcus' theory for choosing the proper Lindblad operators for the long-time incoherent hopping process and using local non-Markovian dephasing rates, our model shows very good agreement with the PIMC results for EET. It also correctly reproduces the linear absorption spectrum that is found in experiment, without using any fitting parameters.Comment: Added citations and small typographic correction

Geometrical aspects of quantum walks on random two-dimensional structures

We study the transport properties of continuous-time quantum walks (CTQW) over finite two-dimensional structures with a given number of randomly placed bonds and with different aspect ratios (AR). Here, we focus on the transport from, say, the left side to the right side of the structure where absorbing sites are placed. We do so by analyzing the long-time average of the survival probability of CTQW. We compare the results to the classical continuous-time random walk case (CTRW). For small AR (landscape configurations) we observe only small differences between the quantum and the classical transport properties, i.e., roughly the same number of bonds is needed to facilitate the transport. However, with increasing AR (portrait configurations) a much larger number of bonds is needed in the CTQW case than in the CTRW case. While for CTRW the number of bonds needed decreases when going from small AR to large AR, for CTRW this number is large for small AR, has a minimum for the square configuration, and increases again for increasing AR. We corroborate our findings for large AR by showing that the corresponding quantum eigenstates are strongly localized in situations in which the transport is facilitated in the CTRW case.Comment: 7 pages, 4 figure

Universal Behavior of Quantum Walks with Long-Range Steps

Quantum walks with long-range steps $R^{-\gamma}$ ($R$ being the distance between sites) on a discrete line behave in similar ways for all $\gamma\geq2$. This is in contrast to classical random walks, which for $\gamma >3$ belong to a different universality class than for $\gamma \leq 3$. We show that the average probabilities to be at the initial site after time $t$ as well as the mean square displacements are of the same functional form for quantum walks with $\gamma=2$, 4, and with nearest neighbor steps. We interpolate this result to arbitrary $\gamma\geq2$.Comment: 4 pages, 3 figure