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 This thesis has two parts, in the first, the Caldeira-Leggett model is introduced; its derivation and general consequences are explored following a paper by Caldeira and Leggett[1]. An operator-formalism shortcut through some of the more mathematically cumbersome parts of the derivation of the model is also developed. The correlation of the force resulting from reservoir-interaction is examined in the high- and low-temperature limits, and the Langevin equation is shown to emerge in the classical limit.Abstract The second part introduces decoherence through a thought experiment that demonstrates the destructive effect of random phase shifts on interference terms, and then follows another paper by Caldeira and Leggett[2] in applying their model further to study the phenomenon of dissipative decoherence. The time-evolution of the interference terms in a superposition of Gaussian wave packets in a harmonic oscillator potential is studied when interacting with a heat bath, and they are shown to vanish at a rate much faster than the relaxation of the system.
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.
Focusing on the real-time dynamics of the reduced density matrix of the multidimensional Caldeira-Leggett model, several techniques are adopted in this paper to reduce the spatial and temporal dimensionality, combined into an efficient algorithm. From a spatial perspective, an equivalent formulation of the Dyson series is presented. With the aid of a low-rank approximation, the spatial dimensionality of open quantum system simulations is halved. From a temporal perspective, the frozen Gaussian approximation is used to approximate both the evolution operator and the interaction operator in the multidimensional Caldeira-Leggett model. This reduces the high-dimensional integrals to one- and two-dimensional integrals independent of the truncation level of the Dyson series. Through these techniques, we design an efficient algorithm whose validity is verified through several numerical experiments, including a two-dimensional double slit simulation.