Non-ergodic phenomena in many-body quantum systems

The assumption of ergodicity is the cornerstone of conventional thermodynamics, connecting the equilibrium properties of macroscopic systems to the chaotic nature of the underlying microscopic dynamics, which eventuates in thermalization and the scrambling of information contained in any generic initial condition. The modern understanding of ergodicity in a quantum mechanical framework is encapsulated in the so-called eigenstate thermalization hypothesis, which asserts that thermalization of an isolated quantum system is a manifestation of the random-like character of individual eigenstates in the bulk of the spectrum of the system's Hamiltonian. In this work, we consider two major exceptions to the rule of generic thermalization in interacting many-body quantum systems: many-body localization, and quantum spin glasses. In the first part, we debate the possibility of localization in a system endowed with a non-Abelian symmetry. We show that, in line with proposed theoretical arguments, such a system is probably delocalized in the thermodynamic limit, but the ergodization length scale is anomalously large, explaining the non-ergodic behavior observed in previous experimental and numerical works. A crucial feature of this system is the quasi-tensor-network nature of its eigenstates, which is dictated by the presence of nontrivial symmetry multiplets. As a consequence, ergodicity may only be restored by extensively large cascades of resonating spins, explaining the system's resistance to delocalization. In the second part, we study the effects of non-ergodic behavior in glassy systems in relation to the possibility of speeding up classical algorithms via quantum resources, namely tunneling across tall free energy barriers. First, we define a pseudo-tunneling event in classical diffusion Monte Carlo (DMC) and characterize the corresponding tunneling rate. Our findings suggest that DMC is very efficient at tunneling in stoquastic problems even in the presence of frustrated couplings, asymptotically outperforming incoherent quantum tunneling. We also analyze in detail the impact of importance sampling, finding that it does not alter the scaling. Next, we study the so-called population transfer (PT) algorithm applied to the problem of energy matching in combinatorial problems. After summarizing some known results on a simpler model, we take the quantum random energy model as a testbed for a thorough, model-agnostic numerical characterization of the algorithm, including parameter setting and quality assessment. From the accessible system sizes, we observe no meaningful asymptotic speedup, but argue in favor of a better performance in more realistic energy landscapes

Traffic and Related Self-Driven Many-Particle Systems

Since the subject of traffic dynamics has captured the interest of physicists, many astonishing effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by so-called ``phantom traffic jams'', although they all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction of the traffic volume cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize in lanes, while similar systems are ``freezing by heating''? Why do self-organizing systems tend to reach an optimal state? Why do panicking pedestrians produce dangerous deadlocks? All these questions have been answered by applying and extending methods from statistical physics and non-linear dynamics to self-driven many-particle systems. This review article on traffic introduces (i) empirically data, facts, and observations, (ii) the main approaches to pedestrian, highway, and city traffic, (iii) microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts like a general modelling framework for self-driven many-particle systems, including spin systems. Subjects such as the optimization of traffic flows and relations to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are discussed as well.Comment: A shortened version of this article will appear in Reviews of Modern Physics, an extended one as a book. The 63 figures were omitted because of storage capacity. For related work see http://www.helbing.org

Evolution: From Big Bang to Nanorobots

The present volume is the fourth issue of the Yearbook series entitled ‘Evolution’. The title of the present volume is ‘From Big Bang to Nanorobots’. In this way we demonstrate that all phases of evolution and Big History are covered in the articles of the present Yearbook. Several articles also present the forecasts about future development. The main objective of our Yearbook as well as of the previous issues is the creation of a unified interdisciplinary field of research in which the scientists specializing in different disciplines could work within the framework of unified or similar paradigms, using the common terminology and searching for common rules, tendencies and regularities. At the same time for the formation of such an integrated field one should use all available opportunities: theories, laws and methods. In the present volume, a number of such approaches are used

Evolution: From Big Bang to Nanorobots

The present volume is the fourth issue of the Yearbook series entitled ‘Evolution’. The title of the present volume is ‘From Big Bang to Nanorobots’. In this way we demonstrate that all phases of evolution and Big History are covered in the articles of the present Yearbook. Several articles also present the forecasts about future development. The main objective of our Yearbook as well as of the previous issues is the creation of a unified interdisciplinary field of research in which the scientists specializing in different disciplines could work within the framework of unified or similar paradigms, using the common terminology and searching for common rules, tendencies and regularities. At the same time for the formation of such an integrated field one should use all available opportunities: theories, laws and methods. In the present volume, a number of such approaches are used

Globalistics and globalization studies big history and global history

This yearbook is the fourth in the series with the title Globalistics and Globalization Studies. The subtitle of the present volume is Global History & Big History. The point is that today our global world really demands global knowledge. Thus, there are a few actively developing multidisciplinary approaches and integral disciplines among which one can name Global Studies, Global History and Big History. They all provide a connection between the past, present, and future. Big History with its vast and extremely heterogeneous field of research encompasses all the forms of existence and all timescales and brings together constantly updated information from the scientific disciplines and the humanities. Global History is transnational or world history which examines history from a global perspective, making a wide use of comparative history and of the history of multiple cultures and nations. Global Studies express the view of systemic and epistemological unity of global processes. Thus, one may argue that Global Studies and Globalistics can well be combined with Global History and Big History and such a multidisciplinary approach can open wide horizons for the modern university education as it helps to form a global view of various processes

Globalistics and Globalization Studies: Big History & Global History. Yearbook

This yearbook is the fourth in the series with the title Globalistics and Globalization Studies. The subtitle of the present volume is Global History & Big History. The point is that today our global world really demands global knowledge. Thus, there are a few actively developingmultidisciplinary approaches and integral disciplines among which one can name Global Studies,Global History and Big History. They all provide a connection between the past, present, andfuture. Big History with its vast and extremely heterogeneous field of research encompasses allthe forms of existence and all timescales and brings together constantly updated information fromthe scientific disciplines and the humanities. Global History is transnational or world historywhich examines history from a global perspective, making a wide use of comparative history andof the history of multiple cultures and nations. Global Studies express the view of systemicand epistemological unity of global processes. Thus, one may argue that Global Studies and Globalistics can well be combined with Global History and Big History and such a multidisciplinary approach can open wide horizons for the modern university education as it helps to form a global view of various processes