arXiv subjects

Caio B. Naves

Publications and source records attributed to Caio B. Naves.

7 recordsLinked to original sources

arXiv2026

Algebraic structure of Fock-state lattices

We analyze Fock-state lattices (FSLs) from an algebraic viewpoint. Starting from a Lie algebra, we associate a FSL constructed from the action of its generators: diagonal (Cartan) generators define the lattice sites, while off-diagonal (root) generators determine the lattice bonds. This construction reveals that identifying an underlying algebraic structure provides direct physical insight into FSLs, including their dimensionality, connectivity, symmetry constraints, and possible transport and revival phenomena. By examining several common Lie algebras, we identify not only their associated FSLs but also the corresponding Lie phase spaces, thereby establishing a systematic connection between FSL dynamics and phase-space geometry. In many cases, both the phase space and the FSL exhibit nontrivial curvature, opening possibilities for exploring quantum dynamics in curved synthetic spaces. We further address whether every integrable Hamiltonian admits an underlying Lie algebra that reproduces the same FSL structure. We show that this is not generally the case, particularly for Hamiltonians that are nonlinear in the generators, and that for systems combining different types of degrees of freedom the appropriate underlying structure may instead be a Lie superalgebra.

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arXiv2026

Discrete-time quantum walks in synthetic dimensions

In this work we introduce discrete-time quantum walks in state space, more precisely on Fock-state lattices. Fock-state lattices provide a natural and clean setting for implementing lattice models, particularly in quantum optical systems. Thus, contrary to the common setting where the walker resides in real space or phase space, here the walk takes place in a synthetic space. We present a general formalism based on Lie algebras and their properties. For each Lie algebra one can associate both a phase space and a Fock-state lattice, and by understanding how these spaces are related, together with the action of generalized displacement operators, we construct the discrete unitary operator that generates the walk. In this framework the displacement operators replace the usual nearest-neighbor shifts and lead to state-dependent tunneling on the lattice. By considering several examples we demonstrate ballistic spreading and other characteristic features of discrete-time quantum walks, such as coin-walker entanglement and symmetry-induced interference patterns. We also show that different algebraic structures can give rise to qualitatively different dynamics, including anomalous behavior such as super-ballistic spreading as well as localization effects.

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arXiv2026

When level repulsion fails: non-normality and chaos in open quantum systems

For Hamiltonian systems, level statistics provide a faithful diagnostic of quantum chaos. By analogy, the statistics of the Lindbladian spectrum are often used in open quantum systems, and the Grobe-Haake-Sommers conjecture proposes that systems with chaotic classical counterparts should exhibit level repulsion in the Lindbladian spectrum. Here we point out an important flaw in this analogy: Hamiltonian and Lindbladian spectra behave differently and have distinct physical interpretations, and one should therefore not expect the latter to provide a reliable diagnostic. For Lindbladians, the late-time dynamics are not determined by the bulk of the eigenvalues but only by those eigenvalues -- and their corresponding eigenvectors -- with small real parts. Combined with the strong non-normality typical of Lindbladians, this allows situations in which the level statistics can be tuned almost arbitrarily without affecting the dynamics on either short or long time scales. We explicitly demonstrate this phenomenon and provide examples in which Ginibre level repulsion arises while the system dynamics at no time show signatures of chaos. We further relate this mechanism to the emergence of a non-Hermitian skin effect in Liouville space, linking boundary-induced eigenvector localization to the observed spectral instability. Our results show that level statistics cannot universally serve as a reliable diagnostic of quantum chaos in open quantum systems and highlight the need for alternative diagnostics that remain robust in strongly non-normal regimes.

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arXiv2025

Liouville Fock state lattices and potential simulators

We introduce Liouville Fock state lattices (LFSLs) as a framework for visualizing open quantum systems through matrix representations of the Lindblad master equation (LME). By vectorizing the LME, the state evolves in a doubled Hilbert space, naturally forming a synthetic lattice. Unlike the unitary evolution of pure states, LFSL states exhibit nontrivial dynamics due to the non-Hermitian Liouvillian, featuring population drifts, sources, and sinks--paralleling stochastic classical lattices. We explore these "classical simulators" in both the Fock representation and alternative positive semidefinite representations, which more closely resemble classical probability distributions. We further demonstrate how infinite steady state manifolds can derive from frustration in the LFSL.

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arXiv2023

Quantum walks with spatiotemporal fractal disorder

We investigate the transport and entanglement properties exhibited by quantum walks with coin operators concatenated in a space-time fractal structure. Inspired by recent developments in photonics, we choose the paradigmatic Sierpinski gasket. The 0-1 pattern of the fractal is mapped into an alternation of the generalized Hadamard-Fourier operators. In fulfilling the blank space on the analysis of the impact of disorder in quantum walk properties -- specifically, fractal deterministic disorder --, our results show a robust effect of entanglement enhancement as well as an interesting novel road to superdiffusive spreading with a tunable scaling exponent attaining effective ballistic diffusion. Namely, with this fractal approach it is possible to obtain an increase in quantum entanglement without jeopardizing spreading. Alongside those features, we analyze further properties such as the degree of interference and visibility. The present model corresponds to a new application of fractals in an experimentally feasible setting, namely the building block for the construction of photonic patterned structures.

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arXiv2022

Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator

We study a 2-D disordered time-discrete quantum walk based on 1-D `generalized elephant quantum walk' where an entangling coin operator is assumed and which paves the way to a new set of properties. We show that considering a given disorder in one direction, it is possible to control the degree of spreading and entanglement in the other direction. This observation helps assert that the random quantum walks of this ilk serve as a controllable decoherence channel with the degree of randomness being the tunable parameter and highlight the role of dimensionality in quantum systems regarding information and transport.

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arXiv2022

Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states

Recently, it was introduced a generalization of a nonstandard step operator named the elephant quantum walk (EQW). With proper statistical distribution for the steps, that generalized EQW (gEQW) can be tuned to exhibit a myriad of dynamical scaling behavior ranging from standard diffusion to %and superdiffusion to ballistic and hyperballistic spreading. In this work, we study the influence of the statistics of the step size and the delocalization of the initial states on the entanglement entropy of the coin. Our results show that the gEQW generates maximally entangled states for almost all initial coin states and coin operators considering initially localized walkers and for the delocalized ones, taking the proper limit, the same condition is guaranteed. Differently from all the previous protocols that produce highly entangled states via QWs, this model is not upper-bounded by ballistic spreading and hence opens novel prospects for applications of dynamically disordered QWs as a robust maximal entanglement generator in programmable setups that ranges from slower-than-ballistic to faster-than ballistic.

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