Quantum transport on small-world networks: A continuous-time quantum walk approach

Mülken, Oliver; Pernice, Volker; Blumen, A.

doi:10.1103/physreve.76.051125

Cited by 81 publications

(113 citation statements)

References 33 publications

Supporting

Mentioning

107

Contrasting

Unclassified

Order By: Relevance

“…In fact, both quantities have been already used to characterize the eigenfunctions of the adjacency matrices of random network models (see some examples in Refs. [31,36,39,42,48,[53][54][55][56][57][66][67][68][69]). …”

Section: B Entropic Eigenfunction Localization Lengthmentioning

confidence: 99%

Universality in the spectral and eigenfunction properties of random networks

et al. 2015

View full text Add to dashboard Cite

By the use of extensive numerical simulations we show that the nearest-neighbor energy level spacing distribution P (s) and the entropic eigenfunction localization length of the adjacency matrices of Erdős-Rényi (ER) fully random networks are universal for fixed average degree ξ ≡ αN (α and N being the average network connectivity and the network size, respectively). We also demonstrate that Brody distribution characterizes well P (s) in the transition from α = 0, when the vertices in the network are isolated, to α = 1, when the network is fully connected. Moreover, we explore the validity of our findings when relaxing the randomness of our network model and show that, in contrast to standard ER networks, ER networks with diagonal disorder also show universality. Finally, we also discuss the spectral and eigenfunction properties of small-world networks.

show abstract

Section: B Entropic Eigenfunction Localization Lengthmentioning

confidence: 99%

Universality in the spectral and eigenfunction properties of random networks

et al. 2015

View full text Add to dashboard Cite

show abstract

“…In order to take the ensemble averaging into account, we introduce as the ensemble averaged participation ratio [23]. …”

Section: B Participation Ratio and Eigenstatesmentioning

confidence: 99%

Geometrical aspects of quantum walks on random two-dimensional structures

2013

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…Monitoring the hitting time in this way is a discrete-time analog for the hitting time defined for continuous-time quantum walks, which is defined through the survival time of an excitation in the system where the Hamiltonian includes a trapping site [29][30][31]. …”

Section: Discussionmentioning

confidence: 99%

Generalized Kac lemma for recurrence time in iterated open quantum systems

2016

View full text Add to dashboard Cite

We consider recurrence to the initial state after repeated actions of a quantum channel. After each iteration a projective measurement is applied to check recurrence. The corresponding return time is known to be an integer for the special case of unital channels, including unitary channels. We prove that for a more general class of quantum channels the expected return time can be given as the inverse of the weight of the initial state in the steady state. This statement is a generalization of the Kac lemma for classical Markov chains.

show abstract

Quantum transport on small-world networks: A continuous-time quantum walk approach

Cited by 81 publications

References 33 publications

Universality in the spectral and eigenfunction properties of random networks

Universality in the spectral and eigenfunction properties of random networks

Geometrical aspects of quantum walks on random two-dimensional structures

Generalized Kac lemma for recurrence time in iterated open quantum systems

Contact Info

Product

Resources

About