This book is a collection of lecture notes/contributions from a summer school on decoherence, entanglement & entropy and a workshop on MPS (matrix product states) & DMRG (density matrix renormalization group). Subjects of the summer school include introduction to MPS, black holes, qubits and octonions, weak measurement, entanglement measures and separability, generalized Bell inequalities, among others. Subjects of the workshop are dedicated to MPS and DMRG. Applications to strongly correlated systems and integrable systems are also mentioned. Contributions to this book are prepared in a self-contained manner so that a reader with a modest background in quantum information and quantum computing may understand the subjects.

The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.

These notes are based on a course of lectures given by Professor Nelson at Princeton during the spring term of 1966. The subject of Brownian motion has long been of interest in mathematical probability. In these lectures, Professor Nelson traces the history of earlier work in Brownian motion, both the mathematical theory, and the natural phenomenon with its physical interpretations. He continues through recent dynamical theories of Brownian motion, and concludes with a discussion of the relevance of these theories to quantum field theory and quantum statistical mechanics.

This book is a collection of lecture notes from the Symposium on Quantum Computing, Thermodynamics, and Statistical Physics, held at Kinki University in March 2012. Quantum information theory has a deep connection with statistical physics and thermodynamics. This volume introduces some of the topics on interface among the mentioned fields. Subjects included in the lecture notes include quantum annealing method, nonequilibrium thermodynamics and spin glass theory, among others. These subjects were presented with much emphasis put in its relevance in quantum information theory. These lecture notes are prepared in a self-contained manner so that a reader with modest background may understand the subjects.

“With [The Universe Within’s] deeply thoughtful reflections on the place of science in society, on the need to educate the underserved, and on plenty of other topics rarely addressed in this sort of book, Turok takes you where no physicist has gone before. It’s well worth making the journey with him.” — TIME Magazine Winner of the Lane Anderson Award, longlisted for the Charles Taylor Prize, shortlisted for the Libris Award for Non-Fiction and selected as an Amazon.ca Best Book The most anticipated nonfiction book of the season, this year's Massey Lectures is a visionary look at the way the human mind can shape the future by world-renowned physicist Neil Turok. Every technology we rely on today was created by the human mind, seeking to understand the universe around us. Scientific knowledge is our most precious possession, and our future will be shaped by the breakthroughs to come. In this personal, visionary, and fascinating work, Neil Turok, Director of the Perimeter Institute for Theoretical Physics, explores the transformative scientific discoveries of the past three centuries -- from classical mechanics, to the nature of light, to the bizarre world of the quantum, and the evolution of the cosmos. Each new discovery has, over time, yielded new technologies causing paradigm shifts in the organization of society. Now, he argues, we are on the cusp of another major transformation: the coming quantum revolution that will supplant our current, dissatisfying digital age. Facing this brave new world, Turok calls for creatively re-inventing the way advanced knowledge is developed and shared, and opening access to the vast, untapped pools of intellectual talent in the developing world. Scientific research, training, and outreach are vital to our future economy, as well as powerful forces for peaceful global progress. Elegantly written, deeply provocative, and highly inspirational, The Universe Within is, above all, about the future -- of science, of society, of ourselves.