Quantum transport on generalized scale-free networks

Maciel, Cássio Macêdo; Mendes, Carlos F. O.; Strunz, Walter T.; Galiceanu, Mircea

doi:10.1103/physreva.102.032219

Cited by 8 publications

(23 citation statements)

References 90 publications

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“…For CTRWs we find the equipartition value 1/ N . In the quantum CTQW case, however, does not converge to a constant value, but it shows an oscillatory pattern around the long time asymptotic average value 57 : It is known 59 , 61 that the long time average transition probability depends only on the eigenvalue density 59 , 61 , 62 : where is the most degenerate eigenvalue.…”

Section: Methodsmentioning

confidence: 99%

“…For the considered networks the number of branches is very small, namely three for all nodes of fullerenes, two or three for graphene sheets or nanotubes, and ranging between two and five for graphite. Thus, the number of branches is not as low as in rings, for which we have only two, or as high as in scale-free networks 59 , for which one can consider highly connected nodes. All our networks are composed of connected rings of size six, i.e.…”

Section: Introductionmentioning

confidence: 97%

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Quantum transport on honeycomb networks

Batalha

Volta²,

Strunz

et al. 2022

Sci Rep

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We study the transport properties on honeycomb networks motivated by graphene structures by using the continuous-time quantum walk (CTQW) model. For various relevant topologies we consider the average return probability and its long-time average as measures for the transport efficiency. These quantities are fully determined by the eigenvalues and the eigenvectors of the connectivity matrix of the network. For all networks derived from graphene structures we notice a nontrivial interplay between good spreading and localization effects. Flat graphene with similar number of hexagons along both directions shows a decrease in transport efficiency compared to more one-dimensional structures. This loss can be overcome by increasing the number of layers, thus creating a graphite network, but it gets less efficient when rolling up the sheets so that a nanotube structure is considered. We found peculiar results for honeycomb networks constructed from square graphene, i.e. the same number of hexagons along both directions of the graphene sheet. For these kind of networks we encounter significant differences between networks with an even or odd number of hexagons along one of the axes.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Quantum transport on honeycomb networks

Batalha

Volta²,

Strunz

et al. 2022

Sci Rep

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“…There is a strong connection between classical or quantum transport and the underlying topology of the network [81]. The CTQW model has been applied to various variants of regular or irregular networks [79][80][81][82][83][84][85][86][87][88][89][90][91]. We extend these studies by considering quantum transport on a new class of complex irregular networks: the multilayer scalefree networks and we study in detail the influence of the number of layers L and their underlying topology on the transport.…”

Section: Introductionmentioning

confidence: 99%

“…d), with d being the average diameter of a layer, on the transport. Our chosen generalized scale-free network model [83,92] is a mixture of linear and starlike segments, with their topology being controlled by the exponent γ of the power-law degree distribution. Low values of γ provide networks with a predominant starlike topology, while for large γ-values we encounter networks with longer linear chains.…”

Section: Introductionmentioning

confidence: 99%

Quantum transport on multilayer generalized scale-free networks

Galiceanu,

Strunz

2024

Phys. Scr.

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We study single-particle quantum transport on multilayer generalized scale-free networks using the continuous-time quantum walk model. Our focus is directed at the average return probability and its long-time average value as measures for the transport eﬃciency. In the continuous-time model these quantities are completely determined by all the eigenvalues and eigenvectors of the connectivity matrix. For all multilayer networks a nontrivial interplay between good spreading and localization eﬀects is observed. The spreading is enhanced by increasing the number of layers L or the power-law exponent γ of the degree distribution. For our choice of the parameters, namely L (1 ≤ L ≤ 50) or γ (1 ≤ γ ≤ 4), the quantum eﬃciency is increased by at least one order of magnitude. The topological transition between networks without loops, which corresponds to a single scale-free network layer (L = 1), and networks with loops (L = 2) is the most impactful. Another important change occurs when L gets higher than the average diameter d of the layers, namely a new scaling behavior for random walks and lower ﬂuctuations around the long-time average value for quantum walks. The quantum transport is more sensitive to changes of the minimum allowed degree, Kmin, than to the maximum allowed degree, Kmax. The same quantum eﬃciency is found by varying at least one of the parameters: L, γ, Kmin, or Kmax, although the network’s topology is diﬀerent. The quantum eﬃciency of all multilayer scale-free networks shows a universal behavior for any size of the layers, more precise, is inversely proportional to the number of layers.

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“…In the past decade, the chiral quantum walk has attracted lots of attentions [22][23][24][25][26]. Research has shown that chirality can lead to novel physical phenomena [16,27], inspiring further exploration both theoretically [19,[28][29][30][31][32][33][34][35] and experiments [36][37][38]. In the presence of chirality, asymmetric and non-reciprocal transports were experimentally demonstrated in quantum circuits [22], quantum optics [23], and optical waveguides [26].…”

Section: Introductionmentioning

confidence: 99%

Controlled transport in chiral quantum walks on graphs

Cai

2023

New J. Phys.

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We investigate novel transport properties of chiral continuous-time quantum walks (CTQWs) on graphs. By employing a gauge transformation, we demonstrate that CTQWs on chiral chains are equivalent to those on non-chiral chains, but with additional momenta from initial wave packets. This explains the novel transport phenomenon numerically studied in [New J. Phys. 23, 083005(2021)]. Building on this, we delve deeper into the analysis of chiral CTQWs on the Y-junction graph, introducing phases to account for the chirality. The phase plays a key role in controlling both asymmetric transport and directed complete transport among the chains in the Y-junction graph. We systematically analyze these features through a comprehensive examination of the chiral continuous-time quantum walk (CTQW) on a Y-junction graph. Our analysis shows that the CTQW on Y-junction graph can be modeled as a combination of three wave functions, each of which evolves independently on three effective open chains. By constructing a lattice scattering theory, we calculate the phase shift of a wave packet after it interacts with the potential-shifted boundary. Our results demonstrate that the interplay of these phase shifts leads to the observed enhancement and suppression of quantum transport. The explicit condition for directed complete transport or 100% efficiency is analytically derived. Our theory has applications in building quantum versions of binary tree search algorithms.

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Quantum transport on generalized scale-free networks

Cited by 8 publications

References 90 publications

Quantum transport on honeycomb networks

Quantum transport on honeycomb networks

Quantum transport on multilayer generalized scale-free networks

Controlled transport in chiral quantum walks on graphs

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