We study the dynamics of a three-mode bosonic system with mode-changing interactions. For large mode occupations the short-time dynamics is well described by classical mean-field equations allowing us to study chaotic dynamics in the classical system and its signatures in the corresponding quantum dynamics. By introducing a symmetry-breaking term we tune the classical dynamics from integrable to strongly chaotic, which we demonstrate by calculating Poincar\'e sections and Lyapunov exponents. The corresponding quantum system features level statistics that change from Poissonian in the integrable to Wigner-Dyson in the chaotic case. We investigate the behavior of out-of-time-ordered correlators (OTOCs), specifically the squared commutator, for initial states located in regular and chaotic regions of the classical mixed phase space and find marked differences between the two cases. The short-time behavior is well captured by semi-classical truncated Wigner simulations directly relating these features to properties of the underlying classical mean-field dynamics. We discuss a possible experimental realization of this model system in a Bose-Einstein condensate of rubidium atoms, which allows reversing the sign of the Hamiltonian required for measuring OTOCs.
We study the dynamics of a three-mode bosonic system with mode-changing interactions. For large mode occupations the short-time dynamics is well described by classical mean-field equations allowing us to study chaotic dynamics in the classical system and its signatures in the corresponding quantum dynamics. By introducing a symmetry-breaking term we tune the classical dynamics from integrable to strongly chaotic, which we demonstrate by calculating Poincar'e sections and Lyapunov exponents. The corresponding quantum system features level statistics that change from Poissonian in the integrable to Wigner-Dyson in the chaotic case. We investigate the behavior of out-of-time-ordered correlators (OTOCs), specifically the squared commutator, for initial states located in regular and chaotic regions of the classical mixed phase space and find marked differences between the two cases. The short-time behavior is well captured by semi-classical truncated Wigner simulations directly relating these features to properties of the underlying classical mean-field dynamics. We discuss a possible experimental realization of this model system in a Bose-Einstein condensate of rubidium atoms, which allows reversing the sign of the Hamiltonian required for measuring OTOCs.
In this work, we show, that relative oscillations in asymptotic times of microcanonical Out-of-Time-Order correlators (OTOCs) are suppressed by chaos with the size of the sys- tem. Therefore they can serve as an indicator of quantum chaos in quantum systems. We demonstrate this phenomenon on numerical results of the Out-of-Time-Order correlators from a model with hamiltonian based on the u(3) algebra. Firstly we prove, that this model can be used not only for the description of molecular vibrations, but also Bose- Einstein condensate. Then we employ several methods for the analysis of both quantum and classical chaos, namely spectral statistics such as Nearest Neighbour Spacing Distri- bution and Brody distribution, Inverse Participation Ratio, Poincaré sections, Lyapunov exponent, and the chaotic fraction of classical phase space. We compare these results with relative oscillations of microcanonical Out-of-Time-Order correlators and show, that their suppression corresponds with the chaoticity of the quantum system and the fraction of chaotic regions of the classical phase space. 1
Abstract We study the dissipative Bose-Hubbard model on a small ring of sites in the presence of a chiral drive and explore its long-time dynamical structure using the mean-field equations and by simulating the quantum master equation. Remarkably, for large enough drivings, we find that the system admits, in a wide range of parameters, a chaotic attractor at the mean-field level, which manifests as a complex Wigner function on the quantum level. The latter is shown to have the largest weight around the approximate region of phase space occupied by the chaotic attractor. We demonstrate that this behavior could be revealed via measurement of various bosonic correlation functions. In particular, we employ open system methods to calculate the out-of-time-ordered correlator, whose exponential growth signifies a positive quantum Lyapunov exponent in our system. This can open a pathway to the study of chaotic dynamics in interacting systems of photons.
We investigate both the classical and quantum dynamics of a spin-1 Bose–Einstein condensate (BEC) system subject to periodic driving of quadratic Zeeman splitting. Without driving, the system is integrable. Here, we found that increasing the driving strength will drive the system to chaos. Classically, we demonstrate chaotic dynamics by examining the Poincaré section and Lyapunov exponent. While in the quantum regime, the level statistic and Husimi distribution are studied, and they also clearly indicate the onset of quantum chaos. The dynamics of atom number and out-of-time-ordered correlator (OTOC) are also studied. In the integrable region, the variance of atom number and OTOC both remain very small during the time evolution; while in the chaos region, a quick increase is observed in the early time. This work presents a quantum many-body system showing chaotic behavior and can be readily realized in experiment.
We investigate the quantum-classical correspondence in open quantum many-body systems using the SU(3) Bose-Hubbard trimer as a minimal model. Combining exact diagonalization with semiclassical Langevin dynamics, we establish a direct connection between classical trajectories characterized by fixed-point attractors, limit cycles, or chaos and the spectral and structural properties of the quantum steady state. We show that classical dynamical behavior, as quantified by the sign of the Lyapunov exponent, governs the level statistics of the steady-state density matrix: non-positive exponents associated with regular dynamics yield Poissonian statistics, while positive exponents arising from chaotic dynamics lead to Wigner-Dyson statistics. Strong symmetries constrain the system to lower-dimensional manifolds, suppressing chaos and enforcing localization, while weak symmetries preserve the global structure of the phase space and allow chaotic behavior to persist. To characterize phase-space localization, we introduce the phase-space inverse participation ratio IPR, which defines an effective dimension D of the Husimi distribution's support. We find that the entropy scales as S∝lnND, consistently capturing the classical nature of the underlying dynamics. This semiclassical framework, based on stochastic mixtures of coherent states, successfully reproduces not only observable averages but also finer features such as spectral correlations and localization properties. Our results demonstrate that dissipative quantum chaos is imprinted in the steady-state density matrix, much like in closed systems, and that the interplay between dynamical regimes and symmetry constraints can be systematically probed using spectral and phase-space diagnostics. These tools offer a robust foundation for studying ergodicity, localization, and non-equilibrium phases of open quantum systems.
We studied signatures of quantum chaos in dynamics of Rydberg-dressed bosonic atoms held in a one-dimensional triple-well potential. Long-range nearest-neighbor and next-nearest-neighbor interactions, induced by laser dressing atoms to strongly interacting Rydberg states, drastically affect mean-field and quantum many-body dynamics. By analyzing the mean-field dynamics, classical chaos regions with positive and large Lyapunov exponents were identified as a function of the potential well tilting and dressed interactions. In the quantum regime, it was found that level statistics of the eigen-energies gain a Wigner–Dyson distribution when the Lyapunov exponents are large, giving rise to signatures of strong quantum chaos. We found that both the time-averaged entanglement entropy and survival probability of the initial state have distinctively large values in the quantum chaos regime. We further showed that population variances could be used as an indicator of the emergence of quantum chaos. This might provide a way to directly probe quantum chaotic dynamics through analyzing population dynamics in individual potential wells.
The out-of-time-order correlator (OTOC) is studied for a bosonic quantum lattice model. We gain its classical analog through the replacement of both commutators appearing in the quantum correlator by a corresponding Poisson bracket. The evaluation of the Poisson bracket is then performed in a complex-valued description of the Hamiltonian dynamics and, for the initial choice of quantum operators to be site-specific annihilators, turns out to be given by the expectation value of the absolute square of a specific element of the complex-valued monodromy matrix. The growth rate of this expectation value is compared to a typical chaos indicator, the mean finite-time Lyapunov exponent (FTLE). In both cases the numerical phase-space average is weighted by a Wigner function corresponding to a multimode coherent state. For a three-well Bose-Hubbard model in the Mott insulator regime, it is found that although, on the level of single trajectories, FTLE and classical OTOC show similar long-time behavior, after averaging, they exhibit a marked difference [which for purely chaotic initial conditions is close to ln(sqrt[2])], rooting in the different order the logarithm and the average are taken. This observation is an example of the relevance of the fluctuations of the FTLE to correctly explain the quantitative difference between OTOC growth rate and FTLE in a prototypical many-body system.