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Interface Between Quantum Information and Statistical Physics
This book is a collection of contributions to the Symposium on Interface between Quantum Information and Statistical Physics held at Kinki University in November 2011. Subjects of the symposium include quantum adiabatic computing, quantum simulator using bosons, classical statistical physics, among others. Contributions to this book are prepared in a self-contained manner so that a reader with a modest background may understand the subjects.
Topology and Quantum Theory in Interaction
This volume contains the proceedings of the NSF-CBMS Regional Conference on Topological and Geometric Methods in QFT, held from July 31–August 4, 2017, at Montana State University in Bozeman, Montana. In recent decades, there has been a movement to axiomatize quantum field theory into a mathematical structure. In a different direction, one can ask to test these axiom systems against physics. Can they be used to rederive known facts about quantum theories or, better yet, be the framework in which to solve open problems? Recently, Freed and Hopkins have provided a solution to a classification problem in condensed matter theory, which is ultimately based on the field theory axioms of Graeme S...
Geometric Control of Fracture and Topological Metamaterials
This thesis reports a rare combination of experiment and theory on the role of geometry in materials science. It is built on two significant findings: that curvature can be used to guide crack paths in a predictive way, and that protected topological order can exist in amorphous materials. In each, the underlying geometry controls the elastic behavior of quasi-2D materials, enabling the control of crack propagation in elastic sheets and the control of unidirectional waves traveling at the boundary of metamaterials. The thesis examines the consequences of this geometric control in a range of materials spanning many orders of magnitude in length scale, from amorphous macroscopic networks and elastic continua to nanoscale lattices.
Physical Effects of Geometric Phases
Berry phase has been widely used in condensed matter physics in the past two decades. This volume is a timely collection of essential papers in this important field, which is highlighted by 2016 Nobel Prize in physics and recent exciting developments in topological matters. Each chapter has an introduction, which helps readers to understand the reprints that follow.
Understanding Quantum Phase Transitions
Quantum phase transitions (QPTs) offer wonderful examples of the radical macroscopic effects inherent in quantum physics: phase changes between different forms of matter driven by quantum rather than thermal fluctuations, typically at very low temperatures. QPTs provide new insight into outstanding problems such as high-temperature superconductivit
The William Lowell Putnam Mathematical Competition 1985-2000
This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution and background information about the competition. The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.
Topological Phases of Matter
This important graduate level text unites the physical mechanisms behind the phenomena of topological matter within a theoretical framework.
Viscoelastic Interfaces Driven in Disordered Media
This book offers an in-depth study of two well-known models of “avalanche” dynamics, modified minimally by the inclusion of relaxation. Many complex systems respond to continuous inputs of energy by accumulation of stress over time, interrupted by sudden energy releases called avalanches. The first model studied is the viscoelastic interface driven over disorder, which is shown to display the fundamental features of friction. In the mean-field limit, the friction force derived semi-analytically is compatible with laboratory experiments (displaying both velocity weakening and contact aging). In two dimensions, large-scale numerical simulations are in good agreement with the basic features of real earthquakes (Gutenberg-Richter Law, aftershock migration). The second model is a non-Markovian variant of Directed Percolation, in which we observe that the universality class is only partly modified by relaxation, a promising finding with respect to our first model.
