arXiv subjects

Sergio Lerma-Hernandez

Publications and source records attributed to Sergio Lerma-Hernandez.

5 recordsLinked to original sources

arXiv2026

Dynamical witnesses and universal behavior across chaos and non-ergodicity in the tilted Bose-Hubbard model

Quantum chaos in isolated quantum systems is intimately linked to thermalization and the rapid relaxation of observables. Although the spectral properties of the chaotic phase in the tilted Bose-Hubbard model have been well characterized, the corresponding dynamical signatures across the transition to regularity remain less explored . In this work, we investigate this transition by analyzing the time evolution of the survival probability, the single-site entanglement entropy, and the half-chain imbalance. Our results reveal a clear hierarchy in the sensitivity of these observables: the relaxation value of the entanglement entropy varies smoothly as a function of the Hamiltonian parameters across the chaos-regular transition, while the imbalance exhibits a more pronounced distinction. Most notably, the survival probability emerges as the most robust indicator of the transition between chaos and regularity. When appropriately scaled, all three observables converge onto a common behavior as a function of the Hamiltonian parameters for different numbers of sites and bosons,enabling a universal characterization of the transition between chaotic and regular dynamics.

quant-ph↗

arXiv2025

Diagnosing Thermalization via Participation Ratio in Disordered Bosonic Chains

We study thermalization in a disordered one-dimensional interacting bosonic system described by the Aubry-Andre model using full exact diagonalization. We find a broad chaotic energy window where the system's eigenstates satisfy the Eigenstate Thermalization Hypothesis (ETH), demonstrated by the smooth energy dependence of observables like entanglement entropy and local particle number, whose fluctuations decrease with system size. Dynamically, we investigate the equilibration of initial Fock states and find that thermalization is not universal. The key finding is a direct and nontrivial correlation between an initial state's delocalization in the energy eigenbasis quantified by the Participation Ratio (PR) and its subsequent equilibration. States with a high PR consistently evolve toward the microcanonical ensemble prediction, whereas those exhibiting a low PR display deviations whose magnitude inversely correlates with the PR value. This connection is quantitatively confirmed by the trace distance, providing a powerful, experimentally relevant diagnostic for predicting which initial states will reach thermal equilibrium.

quant-ph↗

arXiv2023

Persistent revivals in a system of trapped bosonic atoms

Dynamical signatures of quantum chaos are observed in the survival probability of different initial states, in a system of cold atoms trapped in a linear chain with site noise and open boundary conditions. It is shown that chaos is present in the region of small disorder, at intermediate energies. The study is performed with different number of sites and atoms: 7,8 and 9, but focusing on the case where the particle density is one. States of the occupation basis with energies in the chaotic region are evolved at long times. Remarkable differences in the behaviour of the survival probability are found for states with different energy-eigenbasis participation ratio (PR). Whereas those with large PR clearly exhibit the characteristic random-matrix correlation hole before equilibration, those with small PR present a marginal or even no correlation hole which is replaced by revivals lasting up to the stage of equilibration, suggesting a connection with the quantum scarring phenomenon.

quant-ph↗

arXiv2020

Quantum chaos in a system with high degree of symmetries

We study dynamical signatures of quantum chaos in one of the most relevant models in many-body quantum mechanics, the Bose-Hubbard model, whose high degree of symmetries yields a large number of invariant subspaces and degenerate energy levels. While the standard procedure to reveal signatures of quantum chaos requires classifying the energy levels according to their symmetries, we show that this classification is not necessary to obtain manifestation of spectral correlations in the temporal evolution of the survival probability. Our findings exhibit the survival probability as a powerful tool to detect the presence of quantum chaos, avoiding the experimental and theoretical challenges associated with the determination of a complete set of energy eigenstates and their symmetry classification.

quant-ph↗

arXiv2019

Integrable model of a $p$-wave bosonic superfluid

We present an exactly-solvable $p$-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the $p + ip$ Richardson-Gaudin fermionic model, such as a third order quantum phase transition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair Bose superfluid, and the exact eigenstate at the quantum critical point is a pair condensate analogous to the fermionic Moore-Read state.

cond-mat.quant-gas↗