Abstract We investigate the dynamics of quantum correlations in bipartite systems initially prepared in a squeezed state, comparing closed-system unitary evolution under the Schrödinger equation with open-system dynamics governed by the Caldeira-Leggett master equation in the high-temperature, weak-coupling regime, all within the Bohmian mechanics framework. Quantum nonlocality is quantified via the sensitivity of the Bohmian velocity of one particle to the position of the other. Our results show that in both distinct (local) and common bath scenarios, nonlocal correlations initially grow from zero, reach a peak, and then decay. In the case of local baths, the decay is smooth and monotonic; although the peak value increases with temperature, its temporal width (measured via the full width at half maximum) decreases, indicating a shorter duration of nonlocal correlations. For a common bath, the initial growth and decay are followed by revivals and oscillations, whose amplitude and timing vary with temperature. These non-monotonic behaviors arise despite the Markovian nature of the underlying dynamics and reflect the nontrivial role of system-bath correlations. We also analyze how both temperature and the squeezing decay parameter affect the structure of Bohmian trajectories and the evolution of nonlocal correlations. This trajectory-based, velocity-sensitivity measure offers an intuitive and quantitative understanding of entanglement degradation, decoherence, and their characteristic time scales. Our findings emphasize how the structure of the environment critically shapes the observable dynamics of quantum correlations, even in Markovian regimes.
Abstract We investigate the dynamics of quantum correlations in bipartite systems initially prepared in a squeezed state, comparing closed-system unitary evolution under the Schrödinger equation with open-system dynamics governed by the Caldeira-Leggett master equation in the high-temperature, weak-coupling regime, all within the Bohmian mechanics framework. Quantum nonlocality is quantified via the sensitivity of the Bohmian velocity of one particle to the position of the other. Our results show that in both distinct (local) and common bath scenarios, nonlocal correlations initially grow from zero, reach a peak, and then decay. In the case of local baths, the decay is smooth and monotonic; although the peak value increases with temperature, its temporal width (measured via the full width at half maximum) decreases, indicating a shorter duration of nonlocal correlations. For a common bath, the initial growth and decay are followed by revivals and oscillations, whose amplitude and timing vary with temperature. These non-monotonic behaviors arise despite the Markovian nature of the underlying dynamics and reflect the nontrivial role of system-bath correlations. We also analyze how both temperature and the squeezing decay parameter affect the structure of Bohmian trajectories and the evolution of nonlocal correlations. This trajectory-based, velocity-sensitivity measure offers an intuitive and quantitative understanding of entanglement degradation, decoherence, and their characteristic time scales. Our findings emphasize how the structure of the environment critically shapes the observable dynamics of quantum correlations, even in Markovian regimes.
The dynamics of an open quantum system in the high-temperature regime of the Caldeira-Leggett model using a Bohmian language is investigated. By expressing the density matrix in polar form, generalized continuity and Hamilton-Jacobi equations are obtained. Thermal effects appear explicitly in the former, while they influence the latter only indirectly through an effective potential. Remarkably, the effective potential does not vanish in the classical limit and cannot, in general, be decomposed into simple additive quantum and thermal contributions. Instead, it retains a nontrivial structure leading to a residual temperature dependence in the resulting dynamics. As a consequence, the resulting temperature-dependent-classical trajectories remain deterministic even in the presence of a thermal environment. This behavior contrasts with the stochastic dynamics observed in the Langevin description and reflects the ensemble-based nature of the present approach. To further explore the quantum-to-classical transition, a scaled version of the Caldeira-Leggett equation is introduced by scaling both the density matrix and Planck constant through a quantumness parameter. This parameter takes the value one in the fully quantum regime and smoothly approaches zero in the classical limit. Applications to Gaussian states demonstrate a gradual suppression of coherence and interference, governed jointly by thermal effects and the transition parameter.
Quantum non-Markovianity is crucially related to the study of dynamical maps, which are usually derived for initially factorized system-bath states. We demonstrate that linear response theory also provides a way to derive dynamical maps but for initially correlated (and, in general, entangled) states. Importantly, these maps are always time-translational invariant and allow for a much simpler quantification of non-Markovianity compared to previous approaches. We apply our theory to the Caldeira-Leggett model, for which our quantifier is valid beyond linear response and can be expressed analytically. We find that a classical Brownian particle coupled to an Ohmic bath can already exhibit non-Markovian behavior, a phenomenon related to the initial state preparation procedure. Furthermore, for a peaked spectral density, we show that there is no monotonic relation between our quantifier and the system-bath coupling strength, the sharpness of the peak or the resonance frequency in the bath.
Quantum dots are nanometer-scale semiconductor particles that exhibit size-dependent quantum mechanical properties. In this work, we investigate the dynamics of quantum correlations, quantified by the concurrence and the quantum coherence, in a bipartite system of coupled double quantum dots. The analysis is carried out within both Markovian and non-Markovian regimes, and further extended to different noisy quantum channels, including amplitude damping, phase flip, and phase damping. Our results show that environmental memory plays a crucial role in the preservation of quantum correlations, leading to oscillatory behavior and partial revivals in the non-Markovian regime, in contrast to the monotonic decay observed under Markovian dynamics. Moreover, distinct decoherence mechanisms induce qualitatively different effects: dissipative channels rapidly suppress correlations, while phase-based channels lead to either redistribution or gradual degradation. A key finding is that quantum coherence exhibits a higher robustness compared to entanglement under all considered conditions, highlighting its relevance as a reliable quantum resource in noisy environments. These results provide valuable insights into the control and protection of quantum correlations in realistic solid-state systems.
Abstract Our work explores the time evolution of entanglement, local quantum uncertainty, and correlated coherence within a system modeled by two coupled double quantum dots. The dynamics is described using a time-fractional Schrödinger equation, which is treated here as a phenomenological effective framework introducing temporal nonlocality and memory-like effects, rather than as a first-principles open-system reduction. We vary the fractional parameter τ , the tunneling amplitudes δ A and δ B , and the inter-dot Coulomb interaction strength V , in order to investigate how these key parameters govern the generation, stabilization, and decay of quantum resources within the system. The obtained results reveal that, for both initial states (separable and partially entangled), fractional dynamics with a small τ rapidly generates entanglement reaching maximal values LN ≈ 1 together with strong non-classical correlations quantified by the local quantum uncertainty. Conversely, when τ is closer to unity, entanglement builds up more slowly but the memory-like effects allow quantum resources to remain significant for a longer time, with the negativity remaining above ≈ 0.6 . We also find that higher Coulomb-interaction frequencies V accelerate the build-up of correlations and stabilize coherence, while a strong tunneling asymmetry degrades entanglement and coherence despite the initial benefits of increasing quantum resources. We find that the standard unitary Schrödinger evolution is recovered analytically at τ = 1 , where the Mittag–Leffler functions reduce to ordinary exponentials, while decreasing τ progressively introduces fractional-time nonlocal (memory-like) effects.
In this work, we investigate the non-Markovian features of the Adapted Caldeira-Leggett model, a computationally efficient framework recently proposed to capture the essential physics of the standard Caldeira-Leggett model. While this effective model has been previously validated for decoherence and einselection, its ability to reproduce memory effects remains to be explored. By exploiting the model's capability to explicitly track both system and environment degrees of freedom, we provide a detailed characterization of non-Markovianity through the lens of information backflow. We evaluate the buildup of system-environment correlations and the corresponding modifications of the environmental state, assessing a quantitative upper bound for the revival of distinguishability in the reduced dynamics. Our results, obtained by comparing different distinguishability quantifiers such as trace distance and the square root of the Jensen-Shannon divergence, show that while correlations are primarily sensitive to coupling strength, environmental state changes are more heavily influenced by temperature. Our analysis substantiates the physical interpretation of the distinguishability-based approach to non-Markovianity, and confirms this variant of the Caldeira-Leggett model as a reliable tool for exploring the microscopic origins of different fundamental phenomena in quantum mechanics.
In this paper, we explore the dynamics of nonlocal correlations in a two-qubit system, that is, first prepared in a Gisin state and then interacts with a bosonic non-Markovian environment. We employ uncertainty-induced nonlocality (UIN) and the Horodecki measure (Bell function) to characterize the degree of nonclassical correlations and quantum nonlocality in the system, taking into account the influence of the non-Markovian reservoir. The dynamics of the UIN and the Bell nonlocality are next examined using the various parameters that define the non-Markovian reservoir and the initial Gisin state. Our results show that the amount of nonlocal correlations and the degree of violation of Bell’s inequality can be modulated by varying the physical parameters characterizing the non-Markovian reservoir and the initial Gisin state. We also show that in some specific cases, the system exhibits nonclassical correlations while the evolved Gisin state does not violate Bell’s inequality. Our results also confirm that UIN is robust than Bell’s nonlocality in the presence of decoherence induced by the interaction with the non-Markovian reservoir.