Experimental progress in atomic, molecular, and optical platforms in the last decade has stimulated strong and broad interest in the quantum coherent dynamics of many long-range interacting particles. The prominent collective character of these systems enables novel non-equilibrium phenomena with no counterpart in conventional quantum systems with local interactions. Much of the theory work in this area either focussed on the impact of variable-range interaction tails on the physics of local interactions or relied on mean-field-like descriptions based on the opposite limit of all-to-all infinite-range interactions. In this Report, we present a systematic and organic review of recent advances in the field. Working with prototypical interacting quantum spin lattices without disorder, our presentation hinges upon a versatile theoretical formalism that interpolates between the few-body mean-field physics and the many-body physics of quasi-local interactions. Such a formalism allows us to connect these two regimes, providing both a formal quantitative tool and basic physical intuition. We leverage this unifying framework to review several findings of the last decade, including the peculiar non-ballistic spreading of quantum correlations, counter-intuitive slowdown of entanglement dynamics, suppression of thermalization and equilibration, anomalous scaling of defects upon traversing criticality, dynamical phase transitions, and genuinely non-equilibrium phases stabilized by periodic driving. The style of this Report is on the pedagogical side, which makes it accessible to readers without previous experience in the subject matter.
Experimental progress in atomic, molecular, and optical platforms in the last decade has stimulated strong and broad interest in the quantum coherent dynamics of many long-range interacting particles. The prominent collective character of these systems enables novel non-equilibrium phenomena with no counterpart in conventional quantum systems with local interactions. Much of the theory work in this area either focussed on the impact of variable-range interaction tails on the physics of local interactions or relied on mean-field-like descriptions based on the opposite limit of all-to-all infinite-range interactions. In this Report, we present a systematic and organic review of recent advances in the field. Working with prototypical interacting quantum spin lattices without disorder, our presentation hinges upon a versatile theoretical formalism that interpolates between the few-body mean-field physics and the many-body physics of quasi-local interactions. Such a formalism allows us to connect these two regimes, providing both a formal quantitative tool and basic physical intuition. We leverage this unifying framework to review several findings of the last decade, including the peculiar non-ballistic spreading of quantum correlations, counter-intuitive slowdown of entanglement dynamics, suppression of thermalization and equilibration, anomalous scaling of defects upon traversing criticality, dynamical phase transitions, and genuinely non-equilibrium phases stabilized by periodic driving. The style of this Report is on the pedagogical side, which makes it accessible to readers without previous experience in the subject matter.
Many-body systems with long-range power-law decaying potentials among their microscopic components are known to fall outside the traditional framework of complex systems. While some peculiarities in their behavior had emerged since the very early days of statistical mechanics, the possibility of engineering such systems in experimental setups based on molecular and optical systems has stimulated an im- pressive theoretical activity in the last decades, unveiling a plethora of new physical phenomena. In particular, depending on the exact form of the couplings, long-range- interacting systems may avoid thermalization, remaining trapped in long-lived metastable phases, or exhibit new equilibrium phases at thermal equilibrium. The study of such novel phases, emerging both in the equilibrium behavior and in the dynamics, is the subject of the present thesis. In particular, in Part I the equilibrium behavior of long-range XY model and long-range Villain model are studied, while in the second part the quantum dynamics of long-range spin chains, both isolated and subjected to periodic driving, is investigated.
Recent advances in theoretical physics have increasingly focused on the dynamics of quantum systems with many interacting degrees of freedom, while ultracold atom platforms now enable the realization of diverse theoretical models with precise control over system parameters and advanced monitoring techniques. A prominent example is cavity quantum electrodynamics (CQED), where large atomic or molecular ensembles are coupled to high-finesse optical cavities, enabling strong interaction with confined electromagnetic modes and leading to phenomena such as the superradiant phase transition, in which atoms and photons form a coherent state. Most theoretical studies of CQED have concentrated on regimes of spatially uniform atom–cavity coupling, where collective behavior allows a description in terms of the classical dynamics of a few macroscopic variables. However, experimental capabilities now permit exploration beyond this limit, though theoretical progress is hindered by the exponential computational complexity of simulating large quantum systems, particularly when environmental coupling is included. This thesis addresses such challenges by developing efficient approaches, within the Keldysh formalism of non-equilibrium quantum field theory, to study systems with strongly disordered interactions coupled to external reservoirs. Two representative models are considered: a disordered spin–boson model describing light–matter interactions with quenched disorder, relevant to recent CQED experiments in confocal cavities, and a fermion–phonon system governed by the Yukawa–Sachdev–Ye–Kitaev (Yukawa-SYK) model. Both systems are quantum critical, exhibiting a continuum of low-energy modes above their stationary states, yet disorder produces qualitatively distinct dynamical behaviors: in the spin–boson system it induces slow, glassy relaxation, whereas in the Yukawa-SYK model it leads to rapid thermalization. These contrasting outcomes reveal the non-trivial role of disorder in quantum many-body systems and motivate further investigation into its effects on non-equilibrium quantum dynamics.
This thesis investigates quantum-many body systems out of equilibrium in a variety of physically relevant and intriguing settings. It provides an overview of the recent developments in this field and based on the author’s recent review illuminates many interesting connections and summarises open questions. In this general framework, the various results of the author are embedded. While they often rely on advanced mathematics, great care is taken to present them in an intuitive way and most technical material is discussed separately in appendices. In the context of equilibration, work created as part of this thesis is able to capture the Gaussification of correlated initial states for a large class of free models. This allows to significantly extend equilibration results of free models, which are of crucial importance, as they provide reasonable relaxation time scales and immediately connect to our physical intuition in terms of ballistic spreading. Building on two surprising connections between static and dynamic features of Hamiltonians, which in general are hard to obtain, the results of this thesis further greatly contribute to the recent debate on the true nature of quantum many- body localisation. For those interacting models, we derive the localised structure of eigenstates from a dynamical suppression of information propagation on the low-energy sector. Further, we show how a non-degenerate spectrum, indicating the presence of interactions, and the existence of an approximately local constant of motion are sufficient to show information propagation, if arbitrary energies are allowed. In the context of quantum phase transitions, we continue such connections between static and dynamic features. We specifically investigate the Mott-superfluid transition of the Bose-Hubbard model and ask to what extent it has a universal dynamical signature. In a joint experimental, numerical and analytical effort, complex behaviour of these dynamics is uncovered, thus challenging the common believe that the Kibble-Zurek mechanism is sufficient to fully capture such transitions. We embed such experimental investigation in the recent debate on quantum simulators, which give the exciting perspective of solving notoriously and even provably hard problems efficiently in the laboratory. For such devices, we argue that the final read-out of the results is an important out- standing problem to be solved. We approach this issue in the case of a continuous quantum field, in which the notion of reconstructing the quantum state is even conceptually unclear. Based on tensor network methods, we demonstrate that in an experiment of ultra-cold atoms in a continuous setup, states can nevertheless efficiently be obtained. Thus, this thesis constitutes not only an important review of the field of quantum many-body systems out of equilibrium, but, using advanced mathematical and numerical tools, has significantly contributed to our understanding of various important out- standing questions in interacting many-body systems.
Ultracold atomic and molecular systems provide a useful platform for understanding quantum many-body physics. Recent progresses in AMO experiments enable access to systems exhibiting long-range interactions, opening a window for exploring the interplay between long-range interactions and dissipation. In this thesis, I develop theoretical approaches to study non-equilibrium dynamics in systems where such interplay is crucial.I first focus on a system of KRb molecules, where dipolar interactions and fast chemical reactions coexist. Using a classical kinetic theory and Monte Carlo methods, I study the evaporative cooling in a quasi-two-dimensional trap, and develop a protocol to reach quantum degeneracy. I also study the case where molecules are loaded into an optical lattice, and show that the strong dissipation induces a quantum Zeno effect, which suppresses the molecule loss. The analysis requires including multiple bands to explain recent experimental measurements, and can be used to determine the molecular filling fraction.I also investigate a system of radiating atoms, which experience long-range elastic and dissipative interactions. I explore the collective behavior of atoms and the role of atomic motion. The model is validated by comparison with a recent light scattering experiment using Sr atoms. I also show that incoherently pumped dipoles can undergo a dynamical phase transition to synchronization, and study its signature in the quantum regime.
During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many-body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low-temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role.
Rydberg atoms, characterized by their strong and long-range dipole-dipole interactions, provide a versatile platform for exploring intriguing collective and many-body effects. Recently, the experimental realization of these effects in dense ensembles and reconfigurable atomic arrays has attracted significant interest, particularly for applications in quantum simulations and non-equilibrium physics. This review focuses on such recent development, discussing the theoretical foundations of the interactions between Rydberg atoms and the ensuing many-body physics, while providing a critical survey of experimental techniques for their precise manipulation and observation. We further discuss recent breakthroughs in leveraging Rydberg collective effects to probe novel many-body phases and non-equilibrium dynamics of these systems. By synthesizing theoretical insights with experimental milestones, we provide a comprehensive perspective on this rapidly evolving field and its transformative potential for future quantum technologies.