Understanding fluctuation phenomena plays a dominant role in the development of many-body physics. The time evolution of entanglement is essential to a broad range of subjects in many-body physics, ranging from exotic quantum matter to quantum thermalization. Stemming from various dynamical processes of information, fluctuations in entanglement evolution differ conceptually from out-of-equilibrium fluctuations of traditional physical quantities. Their studies remain elusive. Here we uncover an emergent random structure in the evolution of the many-body wavefunction in two classes of integrable-either interacting or noninteracting-lattice models. It gives rise to out-of-equilibrium entanglement fluctuations which fall into the paradigm of mesoscopic fluctuations of wave interference origin. Specifically, the entanglement entropy variance obeys a universal scaling law in each class, and the full distribution displays a sub-Gaussian upper and a sub-Gamma lower tail. These statistics are independent of both the system's microscopic details and the choice of entanglement probes, and broaden the class of mesoscopic universalities. They have practical implications for controlling entanglement in mesoscopic devices.
Understanding fluctuation phenomena plays a dominant role in the development of many-body physics. The time evolution of entanglement is essential to a broad range of subjects in many-body physics, ranging from exotic quantum matter to quantum thermalization. Stemming from various dynamical processes of information, fluctuations in entanglement evolution differ conceptually from out-of-equilibrium fluctuations of traditional physical quantities. Their studies remain elusive. Here we uncover an emergent random structure in the evolution of the many-body wavefunction in two classes of integrable-either interacting or noninteracting-lattice models. It gives rise to out-of-equilibrium entanglement fluctuations which fall into the paradigm of mesoscopic fluctuations of wave interference origin. Specifically, the entanglement entropy variance obeys a universal scaling law in each class, and the full distribution displays a sub-Gaussian upper and a sub-Gamma lower tail. These statistics are independent of both the system's microscopic details and the choice of entanglement probes, and broaden the class of mesoscopic universalities. They have practical implications for controlling entanglement in mesoscopic devices.
Entanglement fluctuations associated with the Schrödinger evolution of wave functions offer a unique perspective on various fundamental issues ranging from quantum thermalization to state preparation in quantum devices. Very recently, a subset of the present authors showed that, in a class of free-fermion lattice models and interacting spin chains, entanglement dynamics enters into a new regime at long time, with entanglement probes displaying persistent temporal fluctuations, whose statistics falls into the seemingly disparate paradigm of mesoscopic fluctuations in condensed-matter physics. This motivates us to revisit here entanglement dynamics of a canonical bosonic model in many-body physics, i.e., a coupled harmonic oscillator chain. We find that when the system is driven out of equilibrium, the long-time entanglement dynamics exhibits strictly the same statistical behaviors as those of free-fermion models. Specifically, irrespective of entanglement probes and microscopic parameters, the statistical distribution of entanglement fluctuations is flanked by asymmetric tails: sub-Gaussian for upward fluctuations and sub-Gamma for downward; moreover, the variance exhibits a crossover from the scaling ∼ 1 / L to ∼ L A 3 / L 2 as the subsystem size L A increases ( L the total system size). This insensitivity to the particle statistics, dubbed boson-fermion universality, is contrary to the common wisdom that statistical phenomena of a many-body nature depend strongly on particle statistics. Together with our previous work, the present study indicates rich fluctuation phenomena in long-time entanglement dynamics that await in-depth exploration.
Out-of-equilibrium quantum many-body systems stand at the forefront of modern theoretical physics, addressing fundamental questions on thermalization, transport, and universal phenomena. These fields, already well established in condensed matter, statistical physics, quantum optics, and quantum information theory, are progressively gaining even greater relevance with the rapid development of quantum technologies and simulation, which inherently operate in dynamical regimes. In recent years, the traditional paradigm of unitary quantum evolution has been expanded to include measurements, opening new directions in out-of-equilibrium physics. At the core of these advances lie measurement-induced phase transitions (MIPTs), which have emerged as a new class of dynamical critical phenomena characterizing the general behavior of monitored quantum dynamics. When external monitoring intertwines with unitary evolution, many-body quantum correlations change their structure, giving rise to distinct entanglement phases of matter. This discovery has sparked enormous interest in MIPTs, leading to significant advances in open quantum systems, entanglement theory, and more broadly quantum complexity. Despite much progress, a full understanding of monitored many-body dynamics is far from complete, leaving several open questions on the nature of MIPTs, their experimental observability, and the possibilities offered by measurements to enhance control over synthetic quantum matter. These issues persist due to the intrinsic complexity of the problem and the lack of efficient tools to study it, mainly caused by the stochastic character of monitored evolution. This thesis addresses these challenges by expanding the investigation of measurement-induced phenomena in new settings and introducing innovative probes of entanglement and many-body quantum complexity for MIPTs. A core question we investigate is the role of symmetries, non-ergodicity, and especially integrability in measurement-induced criticality, which dramatically affect the non-equilibrium phases. We further explore how these phenomena extend beyond bipartite quantum correlations to multipartite entanglement and quantum non-stabilizerness, highlighting the non-trivial interplay between measurements and complexity notions rooted in quantum information theory. Finally, we focus on the compelling problem of decoherence, modeling how noise spoils entanglement structures. These findings, supported by advanced numerical simulations and theoretical analysis, deepen the current understanding of entanglement, complexity, and integrability in monitored quantum many-body systems, offering new perspectives on their rich behavior. In parallel, we address the experimental problem of dissipation in MIPTs, which is of key relevance for practical implementations. We anticipate the present investigation to foster future research on the nature of monitored dynamical critical phenomena and, more broadly, the applications of measurements in quantum state evolution.
Quantum many-body systems exhibit highly complex interactions that give rise to emergent collective phenomena beyond the behavior of individual particles. One of the most intriguing challenges in modern quantum physics is understanding how isolated quantum systems evolve toward thermal equilibrium despite following fundamentally reversible quantum dynamics. Quantum entanglement has emerged as a central mechanism governing information propagation, thermalization, and the development of statistical equilibrium in isolated many-body systems. Simultaneously, recent advances in quantum information science have enabled researchers to investigate the relationship between entanglement dynamics, information scrambling, and emergent quantum behavior using computational and analytical approaches. This study proposes a Quantum Information Analytics Framework for investigating thermalization processes in isolated many-body quantum systems through the integration of entanglement dynamics, quantum information measures, statistical mechanics, and computational modeling. The proposed framework evaluates system evolution using multiple performance indicators, including entanglement entropy, information propagation, thermal equilibrium, quantum coherence, and computational stability. The findings indicate that quantum entanglement plays a fundamental role in driving thermalization while preserving the underlying unitary evolution of isolated quantum systems. The proposed analytical framework contributes to a deeper understanding of emergent quantum dynamics and provides valuable insights for quantum computing, quantum simulation, condensed matter physics, and next-generation quantum information technologies.
We present an exact expression for the entanglement entropy generated at a quantum point contact between noninteracting electronic leads in terms of the full counting statistics of charge fluctuations, which we illustrate with examples from both equilibrium and nonequilibrium transport. The formula is also applicable to ground-state entanglement entropy in systems described by noninteracting fermions in any dimension, which in one dimension include the critical spin-1/2 XX and Ising models where conformal field theory predictions for the entanglement entropy are reproduced from the full counting statistics. These results may play an important role in experimental measurements of entanglement entropy in mesoscopic structures and cold atoms in optical lattices.
Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behavior and for its possible application in near-term quantum technologies. However, understanding these fluctuations is extremely challenging due, to a large extent, to a lack of efficient important sampling methods for quantum systems. Here, we devise a unified framework-based on population-dynamics methods-for the evaluation of the full probability distribution of generic time-integrated observables in Markovian quantum jump processes. These include quantities carrying information about genuine quantum features, such as quantum superposition or entanglement, not accessible with existing numerical techniques. The algorithm we propose provides dynamical free-energy and entropy functionals which, akin to their equilibrium counterpart, permit one to unveil intriguing phase-transition behavior in quantum trajectories. We discuss some applications and further disclose coexistence and hysteresis, between a highly entangled phase and a low entangled one, in large fluctuations of a strongly interacting few-body system.
Mesoscopic physics and nanoelectronics concentrate on systems with dimensions somewhere between atomic and everyday macroscopic scale. Modern technology enables construction of submicron nanostructures where modeling based on classical physics has proven inadequate. It is possible to design electric circuits where dynamics of single electrons and photons are controlled using state-of-the-art experimental methods. For quantitative understanding of these systems it is necessary to resort to a quantum-mechanical description. Quantum phenomena, such as tunneling and a wave-like interference of particles, are essential ingredients of physics in mesoscopic systems. Field of mesoscopic physics contains a rich variety of topics ranging from fundamental condensed matter physics to quantum information processing and possible future technological applications. \n \nThis thesis presents theoretical studies of mesoscopic quantum phenomena in nanostructures and small electronic devices. We have focused on effects of environment fluctuations and investigated connections between fluctuations and transport phenomena. Decoherence in quantum bits (qubits) and quantum state engineering in superconducting circuits are also studied. The theoretical analysis in each case requires an open-system treatment. \n \nEffects of current fluctuations on quantum probe systems have been studied in detail. We have calculated transitions induced by current noise and discussed how these could be used for characterization of fluctuations. We have also shown that electric fluctuations play a key role in radiation and photon heat transport in nanostructures. Motivated by recent advances in mesoscopic electron-photon systems, we have studied a response of a coupled resonator-qubit system, squeezing of quantum fluctuations in small superconducting circuits and investigated decoherence in Josephson flux qubits.