Exploring Thermalization Phenomena: Insights into Closed and Open Quantum Systems [HBNI Th271]

Abstract

The industrial revolution catalyzed the development of classical thermodynamics, emerg- ing from the furnaces of mines and factories. Subsequently, statistical mechanics refined and shaped its principles. At the dawn of the twenty-first century, the quantum revolution began molding the established laws of classical thermodynamics, integrating them with quantum mechanics to form the framework of quantum thermodynamics—governing the thermodynamic behavior of microscopic quantum systems. In the era of technological miniaturization, understanding the thermalization of microscopic systems in the quantum regime has become a central focus of quantum thermodynamics. This thesis explores the phenomenon of quantum thermalization in both closed and open quantum systems. Thermalization of a closed quantum system has been a nontrivial problem since the early days of quantum mechanics. In generic isolated quantum systems, nonequilibrium dy- namics is expected to result in thermalization, indicating the emergence of statistical me- chanics from quantum dynamics. However, what feature of a quantum many-body sys- tem facilitates quantum thermalization is still not well understood. Recent experimental advancements have shown that entanglement may act as a thermalizing agent, not uni- versally but particularly [Science 353, 794-800 (2016)]. Here, we theoretically show that the thermal averages of an observable in an isolated quantum many-body system with a large number of degrees of freedom emerge from the entangled energy eigenstates of the system. In particular, we show that the expectation values of an observable in entangled energy eigenstates and its marginals are respectively equivalent to the microcanonical and canonical averages of the observable. Collisional models are a category of microscopic framework designed to study open quan- tum systems. The framework involves a system sequentially interacting with a bath com- prised of identically prepared units or ancillas. Here, we explore the thermalization of open quantum systems via a broader process known as quantum homogenization. In this regard, quantum homogenization is a process where the system state approaches the identically prepared state of bath unit in the asymptotic limit. Here, we study the ho- mogenization process for a single qubit in the non-Markovian collisional model frame- work generated via additional ancilla-ancilla interaction. With partial swap operation as both system-ancilla and ancilla-ancilla unitary, we demonstrate that homogenization is achieved irrespective of the initial states of the system or bath units. This is reminiscent of the Markovian scenario, where partial swap is the unique operation for a universal quantum homogenizer [Phys. Rev. A 65, 042105 (2002)]. On the other hand, we ob- serve that the rate of thermalization or more generally homogenization is slower than its Markovian counter part. Interestingly, a different choice of ancilla-ancilla unitary speeds up the homogenization process but loses the universality, being dependent on the initial states of the bath units. To aim at making thermalization even faster, we derive a completely positive post- Markovian master equation from a microscopic Markovian collisional model framework, incorporating bath memory effects via a probabilistic single-shot measurement approach. This phenomenological master equation is both analytically solvable and numerically tractable. Afterward, we investigate thermalization using the derived equation, reveal- ing that the post-Markovian dynamics accelerates the thermalization process, exceeding rates observed within the Markovian framework. The findings provide theoretical insights into quantum statistical mechanics and have practical implications for optimizing quantum technologies, such as heat engines and quantum sensors, by enhancing their performance through thermalization dynamics. This work bridges the understanding of fundamental quantum processes with their applications in emerging quantum technologies.