Continuous-time quantum walks on multilayer dendrimer networks

Galiceanu, Mircea; Strunz, Walter T.

doi:10.1103/physreve.94.022307

Cited by 16 publications

(24 citation statements)

References 42 publications

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“…Remarkably, our theoretical findings are well supported by mechanical experiments performed on different types of polymers. We expect our findings to be important not only to polymer physics or related areas of research, but also to the research of complex real networks 56 , of classical and quantum transport on complex networks 72 – 75 , of the coherent transfer of excitons 76 – 78 or of the fluorescence depolarization under quasiresonant Förster energy transfer 35 , 79 .…”

Section: Discussionmentioning

confidence: 87%

Relaxation dynamics of generalized scale-free polymer networks

Jurjiu

Júnior

Galiceanu

2018

Sci Rep

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We focus on treelike generalized scale-free polymer networks, whose geometries depend on a parameter, γ, that controls their connectivity and on two modularity parameters: the minimum allowed degree, Kmin, and the maximum allowed degree, Kmax. We monitor the influence of these parameters on the static and dynamic properties of the achieved generalized scale-free polymer networks. The relaxation dynamics is studied in the framework of generalized Gaussian structures model by employing the Rouse-type approach. The dynamical quantities on which we focus are the average monomer displacement under external forces and the mechanical relaxation moduli (storage and loss modulus), while for the static and structure properties of these networks we concentrate on the eigenvalue spectrum, diameter, and degree correlations. Depending on the values of network’s parameters we were able to switch between distinct hyperbranched structures: networks with more linearlike segments or with a predominant star or dendrimerlike topology. We have observed a stronger influence on Kmin than on Kmax. In the intermediate time (frequency) domain, all physical quantities obey power-laws for polymer networks with γ = 2.5 and Kmin = 2 and we prove additionally that for networks with γ ≥ 2.5 new regions with constant slope emerge by a proper choice of Kmin. Remarkably, we show that for certain values of the parameter set one may obtain self-similar networks.

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Section: Discussionmentioning

confidence: 87%

Relaxation dynamics of generalized scale-free polymer networks

Jurjiu

Júnior

Galiceanu

2018

Sci Rep

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“…In this paper, we extend the previous works [39,40,41,42,43,44,45,46,47,48] devoted to the study of the dynamics of polymers with complex architectures by considering another class of polymer systems, the “multilayer networks” or “networks of the networks” [49,50,51,52]. The multilayer structure on which we focus is built by connecting to each other identical layer.…”

Section: Introductionmentioning

confidence: 89%

Dynamics of a Complex Multilayer Polymer Network: Mechanical Relaxation and Energy Transfer

2018

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Abstract:In this paper, we focus on the mechanical relaxation of a multilayer polymer network built by connecting identical layers that have, as underlying topologies, the dual Sierpinski gasket and the regular dendrimer. Additionally, we analyze the dynamics of dipolar energy transfer over a system of chromophores arranged in the form of a multilayer network. Both dynamical processes are studied in the framework of the generalized Gaussian structure (GSS) model. We develop a method whereby the whole eigenvalue spectrum of the connectivity matrix of the multilayer network can be determined iteratively, thereby rendering possible the analysis of the dynamics of networks consisting of a large number of layers. This fact allows us to study in detail the crossover from layer-like behavior to chain-like behavior. Remarkably, we highlight the existence of two bulk-like behaviors. The theoretical findings with respect to the decomposition of the intermediate domain of the relaxation quantities, as well as the chain-like behavior, are well supported by experimental results.

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“…The (10) describes that what kind of graphs suitable for performing optimal spatial search by CTQW. The Laplacian eigenvalues and eigenvectors need to be calculated for the associated graph.…”

Section: Review Of Spatial Search By Ctqwmentioning

confidence: 99%

“…One of these algorithm, called continuous time quantum walk(CTQW), is proposed by Farhi and Gutmann to solve the decision problem [6]. The CTQW can be applied in lots of situations [7][8][9][10][11]13] and it is an universal quantum algorithm [14]. By using CTQW, Childs and Goldstone presented quantum spacial algorithm on periodic lattice [15].…”

Section: Introductionmentioning

confidence: 99%

Spatial search for a general multi-vertex state on graph by continuous-time quantum walks

Li,

Chen,

Ruan

et al. 2018

Preprint

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In this work, we consider the spatial search for a general marked state on graphs by continuous time quantum walks. As a simplest case, we compute the amplitude expression of the search for the multi-vertex uniform superposition state on hypercube, and find that the spatial search algorithm is optimal for the two-vertex uniform state. However, on general graphs, a common formula can't be obtained for searching a general non-uniform superposition state. Fortunately, a Laplacian spectrum condition which determines whether the associated graph could be appropriate for performing the optimal spatial search is presented. The condition implies that if the proportion of the maximum and the non-zero minimum Laplacian eigenvalues is less or equal to 1+1/ √ 2, then the spatial search is optimal for any general state. At last, we apply this condition to three kind graphs, the induced complete graph, the strongly regular graph and the regular complete multi-partite graphs. By the condition, one can conclude that these graphs will become suitable for optimal search with properly setting their graph parameters.

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Continuous-time quantum walks on multilayer dendrimer networks

Cited by 16 publications

References 42 publications

Relaxation dynamics of generalized scale-free polymer networks

Relaxation dynamics of generalized scale-free polymer networks

Dynamics of a Complex Multilayer Polymer Network: Mechanical Relaxation and Energy Transfer

Spatial search for a general multi-vertex state on graph by continuous-time quantum walks

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