Transport properties of continuous-time quantum walks on Sierpinski fractals

Darázs, Zoltán; Anishchenko, Anastasiia; Kiss, T.; Blumen, A.; Mülken, Oliver

doi:10.1103/physreve.90.032113

Cited by 35 publications

(41 citation statements)

References 43 publications

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“…However, for α=0 the stationary states are resilient to percolations and the trapping effect is preserved. We note that in the framework of continuous-time quantum walks similar effects have been found in [51][52][53][54].…”

Section: Discussionsupporting

confidence: 75%

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Percolation assisted excitation transport in discrete-time quantum walks

2016

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Coherent transport of excitations along chains of coupled quantum systems represents an interesting problem with a number of applications ranging from quantum optics to solar cell technology. A convenient tool for studying such processes are quantum walks. They allow us to determine all the process features in a quantitative way. We study the survival probability and the transport efficiency on a simple, highly symmetric graph represented by a ring. The propagation of excitation is modeled by a discrete-time (coined) quantum walk. For a two-state quantum walk, where the excitation (walker) has to leave its actual position to the neighboring sites, the survival probability decays exponentially and the transport efficiency is unity. The decay rate of the survival probability can be estimated using the leading eigenvalue of the evolution operator. However, if the excitation is allowed to stay at its present position, i.e. the propagation is modeled by a lazy quantum walk, then part of the wave-packet can be trapped in the vicinity of the origin and never reaches the sink. In such a case, the survival probability does not vanish and the excitation transport is not efficient. The dependency of the transport efficiency on the initial state is determined. Nevertheless, we show that for some lazy quantum walks dynamical, percolations of the ring eliminate the trapping effect and efficient excitation transport can be achieved. OPEN ACCESS RECEIVED

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Section: Discussionsupporting

confidence: 75%

“…In [39] the authors have found edgestate enhanced transport along the cut between the source and the absorption center in a two-dimensional quantum walk. For continuous-time quantum walks the effects of trapping, scaling and percolation on transport have been discussed in [51][52][53][54].…”

Section: Introductionmentioning

confidence: 99%

Percolation assisted excitation transport in discrete-time quantum walks

2016

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“…Their relatively simple geometry (e. g. if compared with stochastically generated fractals) facilitates quantitative or qualitative connections between structural and transport properties. Random walks were already intensively studied in fractal lattices with the geometry of SCs, with finite or infinite ramification, and in randomized versions of the SCs [7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Scaling relations in the diffusive infiltration in fractals

Reis

2016

Phys. Rev. E

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In a recent work on fluid infiltration in a Hele-Shaw cell with the pore-block geometry of Sierpinski carpets (SCs), the area filled by the invading fluid was shown to scale as F ∼ t n , with n < 1/2, thus providing a macroscopic realization of anomalous diffusion [Filipovitch et al, Water Resour. Res. 52 5167 (2016)]. The results agree with simulations of a diffusion equation with constant pressure at one of the borders of those fractals, but the exponent n is very different from the anomalous exponent ν = 1/D W of single particle diffusion in the same fractals (D W is the random walk dimension). Here we use a scaling approach to show that those exponents are related as n = ν (D F − D B ), where D F and D B are the fractal dimensions of the bulk and of the border from which diffusing particles come, respectively. This relation is supported by accurate numerical estimates in two SCs and in two generalized Menger sponges (MSs), in which we performed simulations of single particle random walks (RWs) with a rigid impermeable border and of a diffusive infiltration model in which that border is permanently filled with diffusing particles. This study includes one MS whose external border is also fractal. The exponent relation is also consistent with the recent simulational and experimental results on fluid infiltration in SCs, and explains the approximate quadratic dependence of n on D F in these fractals. We also show that the mean-square displacement of single particle RWs has log-periodic oscillations, whose periods are similar for fractals with the same scaling factor in the generator (even with different embedding dimensions), which is consistent with the discrete scale invariance scenario. The roughness of a diffusion front defined in the infiltration problem also shows this type of oscillation, which is enhanced in fractals with narrow channels between large lacunas.

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“…(20) can be understood as follows. At t = 0, the system is prepared in a factorized state |Ψ (0) = [c 0 | +c 1 |χ + ]⊗|Ψ …”

Section: Discussionmentioning

confidence: 99%

“…Examples include the element distinctness problem [13], the spatial search problem [14], and the hitting problem [15,16]. Consequently, CTQW and excitonmediated quantum walk have been studied in a large variety of networks such as binary and glued trees [16,17], Apollonian networks [18,19], fractal networks [20,21], sequentially growing networks [22] and star graphs [23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

The excitonic qubit coupled with a phonon bath on a star graph: anomalous decoherence and coherence revivals

Yalouz

Falvo

Pouthier

2017

Quantum Inf Process

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Based on the operatorial formulation of perturbation theory, the dynamical properties of a Frenkel exciton coupled with a thermal phonon bath on a star graph are studied. Within this method, the dynamics is governed by an effective Hamiltonian which accounts for exciton-phonon entanglement. The exciton is dressed by a virtual phonon cloud, whereas the phonons are dressed by virtual excitonic transitions. Special attention is paid to the description of the coherence of a qubit state initially located on the central node of the graph. Within the nonadiabatic weak coupling limit, it is shown that several timescales govern the coherence dynamics. In the short time limit, the coherence behaves as if the exciton was insensitive to the phonon bath. Then, quantum decoherence takes place, this decoherence being enhanced by the size of the graph and by temperature. However, the coherence does not vanish in the long time limit. Instead, it exhibits incomplete revivals that occur periodically at specific revival times and it shows almost exact recurrences that take place at particular super-revival times, a singular behavior that has been corroborated by performing exact quantum calculations.

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Transport properties of continuous-time quantum walks on Sierpinski fractals

Cited by 35 publications

References 43 publications

Percolation assisted excitation transport in discrete-time quantum walks

Percolation assisted excitation transport in discrete-time quantum walks

Scaling relations in the diffusive infiltration in fractals

The excitonic qubit coupled with a phonon bath on a star graph: anomalous decoherence and coherence revivals

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