Our joint theoretical-experimental effort aims at better understanding of the interplay between the emergence of classical behavior (decoherence) in complex closed quantum systems and more conventional quantum transitions in which the long-range order is established (e.g., formation of a supercondcuting state). Analytical and numerical methods that we have recently developed will allow us to address these fundamental issues in several classes of realistic systems with disorder. The theoretical effort will be combined with the study of one-dimensional (1D) and two-dimensional (2D) arrays of nanoscale Josephson junctions by dc transport and microwave measurements at ultra-low temperatures. These arrays, specifically designed for the testing of theoretical ideas, will allow us to explore the emergence of a large-scale physics near the superconductor-insulator (S-I) transition and the dynamics of localized and delocalized Cooper pair states over a wide energy range. Special attention will be paid to the so-called “bad metal” phase frequently observed in the experiments with Josephson arrays and metal films. The emergence of this enigmatic phase signals an intricate interplay between the quantum S-I transition and the quantum-classical transition. The study of both 1D and 2D arrays will address the effects of disorder on the quantum phase transitions and the emergence of ergodic behavior in almost integrable quantum systems. The quantum phase transitions in 1D arrays share many common features with a wide spectrum of physical phenomena, from quark confinement to ferromagnetism. We will explore the spectrum of their bound states which reflects exotic quantum symmetries that emerge near the critical point. The results of our research will have far reaching consequences for the understanding of Nature and will have important implications for physics and quantum computation.
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