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This book contains the papers presented at the NATO Advanced Study Institute held at Geilo, Norway, 11th - 20th April 1975. The institute was the third in a row devoted to phase transitions. The previous two dealt with 2nd- and 1st-order transitions in equilibrium systems and the proceedings have been published.i~ In order to make an overlap wi th those institutes, the first part of this institute was devoted to 1st -or der transitions with an emphasis on the problems of metast abi l i t y and instability en countered i n spinodal decomposition, nucleation etc. The main topic was, however, that of non-equilibrium systems, and the present institute was to our knowledge the first one devoted to the physics of such systems. The discovery of the analogy between phase transitions in equilibrium systems and instabilities in non-equilibrium systems was first made by Rolf Landauer in 1961 and later independently by others. The analogy was first pointed out for electronic devices (tunnel diodes, Gunn oscillators, lasers, etc. ) and the treatment of hydrodynamic instabilities followed later.
“The importance of knowledge consists not only in its direct practical utility but also in the fact the it promotes a widely contemplative habit of mind; on this ground, utility is to be found in much of the knowledge that is nowadays labelled ‘useless’. ” Bertrand Russel, In Praise of Idleness, London (1935) “Why are scientists in so many cases so deeply interested in their work ? Is it merely because it is useful ? It is only necessary to talk to such scientists to discover that the utilitarian possibilities of their work are generally of secondary interest to them. Something else is primary. ” David Bohm, On creativity, Abingdon (1996) In this volume, the dynamical critical behaviour of many-body systems far from equilibrium is discussed. Therefore, the intrinsic properties of the - namics itself, rather than those of the stationary state, are in the focus of 1 interest. Characteristically, far-from-equilibrium systems often display - namical scaling, even if the stationary state is very far from being critical. A 1 As an example of a non-equilibrium phase transition, with striking practical c- sequences, consider the allotropic change of metallic ?-tin to brittle ?-tin. At o equilibrium, the gray ?-Sn becomes more stable than the silvery ?-Sn at 13. 2 C. Kinetically, the transition between these two solid forms of tin is rather slow at higher temperatures. It starts from small islands of ?-Sn, the growth of which proceeds through an auto-catalytic reaction.
This book addresses research challenges in the rapidly developing area of nonequilibrium thermodynamics and fluctuation kinetics. This cross-disciplinary field comprises various topics, ranging from fundamental problems of nonequilibrium statistical mechanics and thermodynamics to multiple applications in plasma, fluid mechanics, nonlinear science, systems of dissipative particles, and high-Q resonators. The purpose of this book is to bring together world-leading experts in the above fields to initiate a cross-fertilization among these active research areas. The book is dedicated to and honours the memory of Professor Slava Belyi who passed away unexpectedly on May 20, 2020. He was pioneering the theory of nonequilibrium fluctuations, in particular the application of the Callen-Welton fluctuation-dissipation theorem to nonequilibrium systems and its generalization. This and related problems also feature in the book.
Quantum phase transitions, driven by quantum fluctuations, exhibit intriguing features offering the possibility of potentially new applications, e.g. in quantum information sciences. Major advances have been made in both theoretical and experimental investigations of the nature and behavior of quantum phases and transitions in cooperatively interacting many-body quantum systems. For modeling purposes, most of the current innovative and successful research in this field has been obtained by either directly or indirectly using the insights provided by quantum (or transverse field) Ising models because of the separability of the cooperative interaction from the tunable transverse field or tunneling term in the relevant Hamiltonian. Also, a number of condensed matter systems can be modeled accurately in this approach, hence granting the possibility to compare advanced models with actual experimental results. This work introduces these quantum Ising models and analyses them both theoretically and numerically in great detail. With its tutorial approach the book addresses above all young researchers who wish to enter the field and are in search of a suitable and self-contained text, yet it will also serve as a valuable reference work for all active researchers in this area.
This book describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state, and dynamical scaling in far-from-equilibrium relaxation behavior and ageing.
The study of phase transitions is among the most fascinating fields in physics. Originally limited to transition phenomena in equilibrium systems, this field has outgrown its classical confines during the last two decades. The behavior of far from equilibrium systems has received more and more attention and has been an extremely active and productive subject of research for physicists, chemists and biologists. Their studies have brought about a more unified vision of the laws which govern self-organization processes of physico-chemical and biological sys tems. A major achievement has been the extension of the notion of phase transi tion to instabilities which occur only in open nonlinear systems. The notion of phase transition has been proven fruitful in apphcation to nonequilibrium ins- bihties known for about eight decades, like certain hydrodynamic instabilities, as well as in the case of the more recently discovered instabilities in quantum optical systems such as the laser, in chemical systems such as the Belousov-Zhabotinskii reaction and in biological systems. Even outside the realm of natural sciences, this notion is now used in economics and sociology. In this monograph we show that the notion of phase transition can be extend ed even further. It apphes also to a new class of transition phenomena which occur only in nonequilibrium systems subjected to a randomly fluctuating en vironment.
Focusing on experimental results, this updated edition approaches the problem of quantum phase transitions from a new and unifying perspective.
This book investigates phase transitions and critical phenomena in disordered systems driven out of equilibrium. First, the author derives a dimensional reduction property that relates the long-distance physics of driven disordered systems to that of lower dimensional pure systems. By combining this property with a modern renormalization group technique, the critical behavior of random field spin models driven at a uniform velocity is subsequently investigated. The highlight of this book is that the driven random field XY model is shown to exhibit the Kosterlitz–Thouless transition in three dimensions. This is the first example of topological phase transitions in which the competition between quenched disorder and nonequilibrium driving plays a crucial role. The book also includes a pedagogical review of a renormalizaion group technique for disordered systems.