arXiv subjects

A. R. C. Buarque

Publications and source records attributed to A. R. C. Buarque.

15 recordsLinked to original sources

arXiv2026

Nonlinearity-Inhomogeneity Competition in Discrete-Time Quantum Walks

We investigate the interplay between nonlinearity and inhomogeneities in discrete-time quantum walks on one-dimensional lattices. Nonlinear effects are introduced through a Kerr-like, intensity-dependent local phase, while spatial and temporal inhomogeneities are implemented via random variations of the quantum gate operations. By analyzing typical quantities, such as the return probability and the participation function, we identify distinct quantum walking regimes as the nonlinear parameter $χ$ and the quantum gate parameter $θ$ are varied. Spatial inhomogeneities weaken nonlinear self-trapping and constrict the region of robust localization. In this process, partially localized regimes emerge, characterized by the coexistence of a confined core and dispersive wave-packet components. In contrast, temporal inhomogeneities act as time-dependent perturbations that continuously disrupt the phase coherence required for self-trapped excitation, thereby enhancing dispersive emission and promoting delocalization. By using $χ$ versus $θ$ diagrams, we display a comprehensive characterization of how inhomogeneities modify the stability and extent of prevailing dynamical regimes, elucidating the competition between nonlinearity and inhomogeneities in discrete-time quantum walks.

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arXiv2025

Noise correlations behind superdiffusive quantum walks

We study how discrete-time quantum walks behave under short-range correlated noise. By considering noise as a source of inhomogeneity of quantum gates, we introduce a primitive relaxation in the assumption of uncorrelated stochastic noise: binary pair correlations manifesting in the random distribution. Using different quantum gates, we examined the transport properties for both spatial and temporal noise regimes. For spatial inhomogeneities, we unveil noise correlations driving quantum walks from the well-known exponentially localized regime to superdiffusive spreading. This scenario displays an intriguing performance in which the superdiffusive exponent is almost invariant to the degree of inhomogeneity. The time-asymptotic regime and the finite-size scaling also unveil an emergent superdiffusive behavior for quantum walks undergoing temporal noise correlation, replacing the diffusive regime exhibited when noise is random and uncorrelated. However, some quantum gates are insensitive to correlations, contrasting with the spatial noise scenario. Numerical and analytical results provide valuable insights into the underlying mechanism of superdiffusive quantum walks, including those arising from deterministic aperiodic inhomogeneities.

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arXiv2025

Boomerang quantum walks

In this study, we investigate the emergence of the quantum boomerang effect in discrete-time quantum walks (DTQWs) subjected to random phase disorder. Our analysis shows that this effect can arise solely from the intrinsic momentum dynamics of the DTQW, without requiring external bias or asymmetry. We explore the evolution of the mean position of the quantum walker, denoted as $\overline{X}(t)$, under various initial conditions of the walker and quantum coin operators. The results indicate a significant dependence of the observed phenomena on the choice of initial state, enabling the selective induction of the quantum boomerang effect in both or only one portion of the wavepacket associated with specific internal states. By varying the quantum coin parameter $θ$, we find that the maximum mean position follows a power-law decay near the Pauli-Z coin, characterized by $X_{\text{Max}} \sim θ^{-2}$. Additionally, we identify a scaling behavior $X_{\text{Max}} \sim W^{-2}$, which is consistent with the localization length observed in disordered quantum systems. Such a selective nature of the boomerang effect related to internal states reveals valuable insights for controlling quantum transport, which could lead to applications in quantum state management, spatial separation of quantum information carriers, and targeted information retrieval.

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arXiv2023

Managing rogue quantum amplitudes: a control perspective in quantum walks

We investigate the emergence of rogue quantum amplitudes in discrete-time quantum walks (DTQWs) influenced by phase disorder. Our study reveals the statistics of occupation probability amplitudes in space and time, uncovering optimal disorder regimes that favor rogue wave events. Through numerical simulations, we demonstrate that the probability of rogue waves increases with quantum coins close to the Pauli-Z choice, regardless the disorder degree. Conversely, for coins near Pauli-X rogue events are scarce, except under weak disorder. A monotonic threshold is observed between rare- and high-probability rogue wave regimes, depending on the quantum coin. We provide a comprehensive analysis of the coin-disorder interplay to rogue wave events. Our findings shed light on the possible control of extreme quantum amplitudes through quantum coins in disordered DTQWs.

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arXiv2023

Discrete-time quantum walk dispersion control through long-range correlations

We investigate the evolution dynamics of inhomogeneous discrete-time one-dimensional quantum walks displaying long-range correlations in both space and time. The associated quantum coin operators are built to exhibit a random inhomogeneity distribution of long-range correlations embedded in the time evolution protocol through a fractional Brownian motion with spectrum following a power-law behavior, $S(k)\sim 1/k^ν$. The power-law correlated disorder encoded in the phases of the quantum coin is shown to give rise to a wide variety of spreading patterns of the qubit states, from localized to subdiffusive, diffusive, and superdiffusive (including ballistic) behavior, depending on the relative strength of the parameters driving the correlation degree. Dispersion control is then possible in one-dimensional discrete-time quantum walks by suitably tunning the long-range correlation properties assigned to the inhomogeneous quantum coin operator.

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arXiv2022

Nonlinear flip-flop quantum walks through potential barriers

The dynamics of nonlinear flip-flop quantum walk with amplitude-dependent phase shifts with pertubing potential barrier is investigated. Through the adjustment between uniform local perturbations and a Kerrlike nonlinearity of the medium we find a rich set of dynamic profiles. We will show the existence of different Hadamard quantum walking regimes, including those with mobile soliton-like structures or self-trapped states. The latter is predominant for perturbations with amplitudes that tend to $φ\rightarrow π/2$. In this system, the qubit shows an unusual behavior as we increase the amplitudes of the potential barriers, and displays a monotonic decrease in the self-trapping $φ_c$ with respect to the nonlinear parameter. A chaotic-like regime becomes predominant for intermediate nonlinearity values. Furthermore, we show that by changing the quantum coins ($θ$) a non-trivial dynamic arises, where coins close to Pauli-X drives the system to a regime with predominant soliton-like structures, while the chaotic behavior are restricted to a narrow region in the $χ$-$φ$ plane. We believe that is possible to implement and observe the proprieties of this model in a integrated photonic system.

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arXiv2022

Rogue waves in quantum lattices with correlated disorder

We investigate the outbreak of anomalous quantum wavefunction amplitudes in a one-dimensional tight-binding lattice featuring correlated diagonal disorder. Such rogue-wave-like behavior is fostered by a competition between localization and mobility. The effective correlation length of the disorder is ultimately responsible for bringing the local disorder strength to a minimum, fuelling the occurrence of extreme events of much higher amplitudes, specially when compared to the case of uncorrelated disorder. Our findings are valid for a class of discrete one-dimensional systems and reveal profound aspects of the role of randomness in rogue-wave generation.

cond-mat.dis-nn↗

arXiv2022

Nonlinear three-state quantum walks

The dynamics of a three-state quantum walk with amplitude-dependent phase shifts is investigated. We consider two representative inputs whose linear evolution is known to display either full dispersion of the wave packet or intrinsic localization on the initial position. The nonlinear counterpart presents much more involved dynamics featuring self-trapping, solitonic pulses, radiation, and chaotic-like behavior. We show that nonlinearity leads to a metastable self-trapped wavepacket component that radiates in the long-time regime with the survival probability $\propto t^{-1/2}$. A sudden dynamical transition from such metastable state to the point when the radiation process is triggered is found for a set of parameters.

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arXiv2022

Rogue waves in discrete-time quantum walks

Rogue waves are rapid and unpredictable events of exceptional amplitude reported in various fields, such as oceanography and optics, with much of the interest being targeted towards their physical origins and likelihood of occurrence. Here, we use the all-round framework of discrete-time quantum walks to study the onset of those events due to a random phase modulation, unveiling its long-tailed statistics, distribution profile, and dependence upon the degree of randomness. We find that those rogue waves belong the Gumbel family of extreme value distributions.

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arXiv2021

Universal dynamical scaling laws in three-state quantum walks

We perform a finite-time scaling analysis over the detrapping point of a three-state quantum walk on the line. The coin operator is parameterized by $ρ$ that controls the wavepacket spreading velocity. The input state prepared at the origin is set as symmetric linear combination of two eigenstates of the coin operator with a characteristic mixing angle $θ$, one of them being the component that results in full spreading occurring at $θ_c(ρ)$ for which no fraction of the wavepacket remains trapped near the initial position. We show that relevant quantities such as the survival probability and the participation ratio assume single parameter scaling forms at the vicinity of the detrapping angle $θ_c$. In particular, we show that the participation ratio grows linearly in time with a logarithmic correction, thus shedding light on previous reports of sublinear behavior.

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arXiv2020

Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics

The sensitivity of quantum systems to external disturbances is a fundamental problem for the implementation of functional quantum devices, quantum information and computation. Based on remarkable experimental progress in optics and ultra-cold gases, we study the consequences of a short-time (instantaneous) noise while an intensity-dependent phase acquisition is associated with a qubit propagating on $N$-cycle. By employing quantum coherence measures, we report emerging unstable regimes in which hitherto unknown quantum walks arise, such as self-focusing and breathing dynamics. Our results unveil appropriate settings which favor the stable regime, with the asymptotic distribution surviving for weak nonlinearities and disappearing in the thermodynamic limit with $1/N$. The diagram showing the threshold between different regimes reveals the quantum gates close to Pauli-Z as more noise-tolerant. As we move towards the Pauli-X quantum gate, such aptness dramatically decreases and the threshold to self-focusing regime becomes almost unavoidable. Quantum gates close to Hadamard exhibit an unusual aspect, in which an increment of the nonlinear strength can remove the dynamics from self-focusing regime.

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arXiv2020

Bloch-like super-oscillations and unidirectional motion of phase driven quantum walkers

We study the dynamics of a quantum walker simultaneously subjected to time-independent and -dependent phases. Such dynamics emulates a charged quantum particle in a lattice subjected to a superposition of static and harmonic electric fields. With proper settings, we investigate the possibility to induce Bloch-like super-oscillations, resulting from a close tuning of the frequency of the harmonic phase $ω$ and that associated with the regular Bloch-like oscillations $ω_B$ . By exploring the frequency spectra of the wavepacket centroid, we are able to distinguish the regimes on which regular and super-Bloch oscillations are predominant. Furthermore, we show that under exact resonant conditions $ω=ω_B$ unidirectional motion is established with the wavepacket average velocity being a function of the quantum walk coin operator parameter, the relative strengths of the static and harmonic terms, as well as the own phase of the harmonic phase. We show that the average drift velocity can be well described within a continuous-time analogous model.

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arXiv2019

Self-trapped quantum walks

We study the existence and charaterization of self-trapping phenomena in discrete-time quantum walks. By considering a Kerr-like nonlinearity, we associate an acquisition of the intensity-dependent phase to the walker while it propagates on the lattice. Adjusting the nonlinear parameter ($χ$) and the quantum gates ($θ$), we will show the existence of different quantum walking regimes, including those with travelling soliton-like structures or localized by self-trapping. This latter scenario is absent for quantum gates close enough to Pauli-X. It appears for intermediate configurations and becomes predominant as quantum gates get closer to Pauli-Z. By using $χ$ versus $θ$ diagrams, we will show that the threshold between quantum walks with delocalized or localized regimes exhibit an unusual aspect, in which an increment on the nonlinear strength can induce the system from localized to a delocalized regime.

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arXiv2019

Aperiodic space-inhomogeneous quantum walks: localization properties, energy spectra and enhancement of entanglement

We study the localization properties, energy spectra and coin-position entanglement of the aperiodic discrete-time quantum walks. The aperiodicity is described by spatially dependent quantum coins distributed on the lattice, whose distribution is neither periodic (Bloch-like) nor random (Anderson-like). Within transport properties we identified delocalized/localized quantum walks mediated by a proper adjusting of aperiodic parameter. Both scenarios are studied by exploring typical quantities (inverse participation ratio and survival probability), as well as the energy spectra of an associated effective Hamiltonian. By using the energy spectra analysis, we show that the early stage the inhomogeneity leads to vanishing gap between two main bands, which justifies the the delocalized character observed for $ν<0.5$. With increase of $ν$ arises gaps and flat-bands on the energy spectra, which corroborates the suppresion of transport detected for $ν>0.5$. For $ν$ high enough we observe an energy spectra which resembles that described by the 1d Anderson model. Within coin-position entanglement, we show many settings in which an enhancement in the ability to entangle is observed. This behavior brings new informations about the role played by aperiodicity on the coin-poisition entanglement for static inhomogeneous systems, reported before as almost always reducing the entanglement when comparing with the homogeneous case. We extend the analysis in order to show that systems with static inhomogeneity are able to exhibit asymptotic limit of entanglement.

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arXiv2017

Unidirectional quantum walk of two correlated particles: Separating bound-pair and unbound wavepacket components

We study the unidirectional transport of two-particle quantum wavepackets in a regular one-dimensional lattice. We show that the bound-pair state component behaves differently from unbound states when subjected to an external pulsed electric field. Thus, strongly entangled particles exhibit a quite distinct dynamics when compared to a single particle system. With respect to centroid motion, our numerical results are corroborated with an analytical expression obtained using a semi-classical approach. The wavefunction profile reveals that the particle-particle interaction induces the splitting of the initial wavepacket into two branches that propagate with specific directions and drift velocities. With a proper external field tunning, the wavepacket components can perform an unidirectional transport on the same or opposite directions. The amplitude of each mode is related to the degree of entanglement betweem particles, which presents a non-monotonic dependence on the interaction strength.

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