Generalized Open Quantum Walks on Apollonian Networks

Pawela, Łukasz; Gawron, Piotr; Miszczak, Jarosław Adam; Sadowski, Przemysław

doi:10.1371/journal.pone.0130967

Cited by 19 publications

(24 citation statements)

References 38 publications

(51 reference statements)

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“…trajectories. Quantum-mechanical counterpart of the (mean-)FPT is an ill-defined and the context-sensitive concept [43][44][45][46]. Since it is linked with the deterministic classical trajectories, there is not a straightforward quantum mechanical definition.…”

Section: The First Passage Timementioning

confidence: 99%

Dynamical stability of the weakly nonharmonic propeller-shaped planar Brownian rotator

2020

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Dynamical stability is a prerequisite for control and functioning of desired nano-machines. We utilize the Caldeira-Leggett master equation to investigate dynamical stability of molecular cogwheels modeled as a rigid, propeller-shaped planar rotator. In order to match certain expected realistic physical situations, we consider a weakly nonharmonic external potential for the rotator.Two methods for investigating stability are used. First, we employ a quantum-mechanical counterpart of the so-called "first passage time" method. Second, we investigate time dependence of the standard deviation of the rotator for both the angle and angular momentum quantum observables.A perturbation-like procedure is introduced and implemented in order to provide the closed set of differential equations for the moments. Extensive analysis is performed for different combinations of the values of system parameters. The two methods are, in a sense, mutually complementary.Appropriate for the short time behavior, the first passage time exhibits a numerically-relevant dependence only on the damping factor as well as on the rotator size. On the other hand, the standard deviations for both the angle and angular momentum observables exhibit strong dependence on the parameter values for both short and long time intervals. Contrary to our expectations, the time decrease of the standard deviations is found for certain parameter regimes. In addition, for certain parameter regimes nonmonotonic dependence on the rotator size is observed for the standard deviations and for the damping of the oscillation amplitude. Hence non-fulfillment of the classical expectation that the size of the rotator can be reduced to the inertia of the rotator. In effect, the task of designing the desired protocols for the proper control of the molecular rotations becomes an optimization problem that

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Section: The First Passage Timementioning

confidence: 99%

Dynamical stability of the weakly nonharmonic propeller-shaped planar Brownian rotator

2020

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“…There was a lot effort put into studying this approach. We should mention here various asymptotic results for this model [10,11], hitting times studies [12] and potential applications of this model in quantum modeling of biological structures [13] Another model which deserves mention is the quantum stochastic walk [14]. This approach is based on the Gorini-Kossakowski-Sudarshan-Lindblad [15,16] master equation.…”

Section: Quantum Walks Summarymentioning

confidence: 99%

Quantum Walks on Hypergraphs

et al. 2019

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“…In a series of recent papers [1][2][3][4][5][6] various aspects of open quantum walks have been discussed. This is a novel and very promising approach to the quantum walks.…”

Section: Introductionmentioning

confidence: 99%

Central limit theorem for reducible and irreducible open quantum walks

Sadowski

Pawela

2016

Quantum Inf Process

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In this work we aim at proving central limit theorems for open quantum walks on Z d . We study the case when there are various classes of vertices in the network. In particular, we investigate two ways of distributing the vertex classes in the network. First, we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a transition invariant distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.

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Generalized Open Quantum Walks on Apollonian Networks

Cited by 19 publications

References 38 publications

Dynamical stability of the weakly nonharmonic propeller-shaped planar Brownian rotator

Dynamical stability of the weakly nonharmonic propeller-shaped planar Brownian rotator

Quantum Walks on Hypergraphs

Central limit theorem for reducible and irreducible open quantum walks

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