Quantum walks and trapping on regular hyperbranched fractals

Volta, A.

doi:10.1088/1751-8113/42/22/225003

Cited by 13 publications

(14 citation statements)

References 34 publications

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“…Volta investigated so-called regular hyperbranched fractals, see Fig. 36, for which the eigenvalue spectra of the connectivity matrices can be calculated recursively [111]. As shown previously [112], the eigenvalues of the (g + 1)st generation can be obtained from the eigenvalues of the gth generation by solving…”

Section: Hyperbranched Fractalsmentioning

confidence: 98%

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Continuous-time quantum walks: Models for coherent transport on complex networks

2011

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This paper reviews recent advances in continuous-time quantum walks (CTQW) and their application to transport in various systems. The introduction gives a brief survey of the historical background of CTQW. After a short outline of the theoretical ideas behind CTQW and of its relation to classical continuous-time random walks (CTRW) in Sec. 2, implications for the efficiency of the transport are presented in Sec. 3. The fourth section gives an overview of different types of networks on which CTQW have been studied so far. Extensions of CTQW to systems with long-range interactions and with static disorder are discussed in section V. Systems with traps, i.e., systems in which the walker's probability to remain inside the system is not conserved, are presented in section IV. Relations to similar approaches to the transport are studied in section VII. The paper closes with an outlook on possible future directions.

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Section: Hyperbranched Fractalsmentioning

confidence: 98%

“…Placing now a trap node at the center of the fractal, Volta is able to calculate the (complex) spectrum of the Hamiltonian including the trap [111]. It turns out that only the nondegenerate eigenvalues depend on the trapping strength Γ.…”

Section: Hyperbranched Fractalsmentioning

confidence: 99%

Continuous-time quantum walks: Models for coherent transport on complex networks

2011

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“…Second, from a more formal point of view, excitonic trapping process has also been studied in various complex networks including for example hyperbranched fractals 25 , Sierpinsky fractals 26 , cycle graphs with longrange interactions 27 , chains and rings [28][29][30] , and random networks 31 . These works, intimately connected to graph theory, exploit the formal resemblance between the excitonic delocalization occuring in nature and the continuous time quantum walk (CTQW) 32 .…”

Section: Introductionmentioning

confidence: 99%

Continuous-time quantum walk on an extended star graph: Disorder-enhanced trapping process

Yalouz

Pouthier

2020

Phys. Rev. E

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Using a tight binding model, we investigate the dynamics of an exciton on a disordered extended star graph whose central site acts as an energetic trap. Our results highlight the beneficial role of the disorder to improve the excitonic absorption at the core of the graph. In this context, we evidence the existence of an optimal disorder allowing to strongly minimize the absorption time. Numerical proofs are given to demonstrate that this enhancement originates from a disorder-induced restructuring process that positively affects the system eigenstates. In a complementary way, we also evidence the existence of an optimal value of absorption rate allowing to reduce even more the aborption time when the disorder is optimal. The resulting super optimized trapping process is interpreted as the positive interplay between the action of the disorder and the arising of the so-called superradiance transition.

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“…The trapping problem has been studied in a large variety of networks with a special emphasis on the comparison between CTQW and classical random walk. Examples among many are hyperbranched fractals [34], Sierpinsky fractals [35], cycle graphs with long-range interactions [36], chains and rings [37][38][39], and random networks [40].…”

Section: Introductionmentioning

confidence: 99%

Continuous-time quantum walk on an extended star graph: Trapping and superradiance transition

Yalouz

Pouthier

2018

Phys. Rev. E

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A tight-binding model is introduced for describing the dynamics of an exciton on an extended star graph whose central node is occupied by a trap. On this graph, the exciton dynamics is governed by two kinds of eigenstates: many eigenstates are associated with degenerate real eigenvalues insensitive to the trap, whereas three decaying eigenstates characterized by complex energies contribute to the trapping process. It is shown that the excitonic population absorbed by the trap depends on the size of the graph, only. By contrast, both the size parameters and the absorption rate control the dynamics of the trapping. When these parameters are judiciously chosen, the efficiency of the transfer is optimized resulting in the minimization of the absorption time. Analysis of the eigenstates reveals that such a feature arises around the superradiance transition. Moreover, depending on the size of the network, two situations are highlighted where the transport efficiency is either superoptimized or suboptimized.

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Quantum walks and trapping on regular hyperbranched fractals

Cited by 13 publications

References 34 publications

Continuous-time quantum walks: Models for coherent transport on complex networks

Continuous-time quantum walks: Models for coherent transport on complex networks

Continuous-time quantum walk on an extended star graph: Disorder-enhanced trapping process

Continuous-time quantum walk on an extended star graph: Trapping and superradiance transition

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