Holographic Entanglement Entropy

Author : Mukund Rangamani,Tadashi Takayanagi
Publisher : Springer
Page : 246 pages
File Size : 44,8 Mb
Release : 2017-05-08
Category : Science
ISBN : 9783319525730

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Holographic Entanglement Entropy by Mukund Rangamani,Tadashi Takayanagi Pdf

This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part focuses on the connection between entanglement and geometry. Known constraints on the holographic map, as well as, elaboration of entanglement being a fundamental building block of geometry are explained. The book is a useful resource for researchers and graduate students interested in string theory and holography, condensed matter and quantum information, as it tries to connect these different subjects linked by the common theme of quantum entanglement.

Author : Jie-qiang Wu
Publisher : Springer Nature
Page : 145 pages
File Size : 50,5 Mb
Release : 2019-10-18
Category : Science
ISBN : 9789811332128

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AdS3/CFT2 and Holographic Entanglement Entropy by Jie-qiang Wu Pdf

This book focuses on AdS3/CFT2, addressing different aspects of this correspondence in field theory and in gravity, including entanglement entropy, higher genus partition function, and conformal block. Holographic entanglement entropy is an important area in holographic and quantum information, which implies a deep relation between geometry and quantum entanglement. In this book, the authors use holographic entanglement entropy as a tool to investigate AdS3/CFT2. They study the entanglement entropy at high temperature in field theory and in holographics, and show that the results match each other in classical and one-loop order. In the AdS3/CFT2 system, they examine in detail the correspondence, exploring the higher genus partition function, entanglement entropy in a general system and conformal block, and they find good correspondence in field theory and gravity. The result strongly supports AdS3/CFT2 correspondence. In addition, they develop several important techniques in 2d CFT and 3d gravity, which also offer inspiration for other fields.

Author : Martin Ammon,Johanna Erdmenger
Publisher : Cambridge University Press
Page : 549 pages
File Size : 55,6 Mb
Release : 2015-04-09
Category : Science
ISBN : 9781107010345

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Gauge/Gravity Duality by Martin Ammon,Johanna Erdmenger Pdf

The first textbook on this important topic, for graduate students and researchers in particle and condensed matter physics.

Author : Horaƫiu Năstase
Publisher : Cambridge University Press
Page : 457 pages
File Size : 47,5 Mb
Release : 2015-09-10
Category : Science
ISBN : 9781107085855

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Introduction to AdS/CFT Correspondence by Horaƫiu Năstase Pdf

A pedagogical and self-contained introduction to AdS/CFT correspondence aimed at graduate students and researchers across theoretical physics.

Author : Albert Einstein,Max Born,Hedwig Born
Publisher : MacMillan
Page : 268 pages
File Size : 45,9 Mb
Release : 1971
Category : Physicists
ISBN : UCSD:31822004159968

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The Born-Einstein Letters by Albert Einstein,Max Born,Hedwig Born Pdf

Author : Dénes Petz
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 53,7 Mb
Release : 2007-10-20
Category : Science
ISBN : 9783540746362

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Quantum Information Theory and Quantum Statistics by Dénes Petz Pdf

This concise and readable book addresses primarily readers with a background in classical statistical physics and introduces quantum mechanical notions as required. Conceived as a primer to bridge the gap between statistical physics and quantum information, it emphasizes concepts and thorough discussions of the fundamental notions and prepares the reader for deeper studies, not least through a selection of well chosen exercises.

Author : Jorge Casalderrey-Solana,Hong Liu,David Mateos,Krishna Rajagopal,Urs Achim Wiedemann
Publisher : Cambridge University Press
Page : 469 pages
File Size : 43,7 Mb
Release : 2023-07-31
Category : Science
ISBN : 9781009403498

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Gauge/String Duality, Hot QCD and Heavy Ion Collisions by Jorge Casalderrey-Solana,Hong Liu,David Mateos,Krishna Rajagopal,Urs Achim Wiedemann Pdf

Author : Horatiu Nastase
Publisher : Cambridge University Press
Page : 631 pages
File Size : 43,8 Mb
Release : 2017-09-21
Category : Science
ISBN : 9781107180383

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String Theory Methods for Condensed Matter Physics by Horatiu Nastase Pdf

The discovery of a duality between Anti-de Sitter spaces (AdS) and Conformal Field Theories (CFT) has led to major advances in our understanding of quantum field theory and quantum gravity. String theory methods and AdS/CFT correspondence maps provide new ways to think about difficult condensed matter problems. String theory methods based on the AdS/CFT correspondence allow us to transform problems so they have weak interactions and can be solved more easily. They can also help map problems to different descriptions, for instance mapping the description of a fluid using the Navier-Stokes equations to the description of an event horizon of a black hole using Einstein's equations. This textbook covers the applications of string theory methods and the mathematics of AdS/CFT to areas of condensed matter physics. Bridging the gap between string theory and condensed matter, this is a valuable textbook for students and researchers in both fields.

Author : Charles Fefferman,C. Robin Graham
Publisher : Princeton University Press
Page : 125 pages
File Size : 46,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780691153148

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The Ambient Metric (AM-178) by Charles Fefferman,C. Robin Graham Pdf

This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics. The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincaré metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincaré metrics in four dimensions are considered as a special case, leading to a formal power series proof of LeBrun's collar neighborhood theorem proved originally using twistor methods. Conformal curvature tensors are introduced and their fundamental properties are established. A jet isomorphism theorem is established for conformal geometry, resulting in a representation of the space of jets of conformal structures at a point in terms of conformal curvature tensors. The book concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature, applying results in parabolic invariant theory.

Author : Steffen Gielen,Sylvain Carrozza,Daniele Oriti
Publisher : MDPI
Page : 338 pages
File Size : 45,9 Mb
Release : 2020-07-01
Category : Mathematics
ISBN : 9783039361786

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Progress in Group Field Theory and Related Quantum Gravity Formalisms by Steffen Gielen,Sylvain Carrozza,Daniele Oriti Pdf

Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research.

Author : Leonard Susskind
Publisher : Springer Nature
Page : 93 pages
File Size : 51,6 Mb
Release : 2020-05-11
Category : Science
ISBN : 9783030451097

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Three Lectures on Complexity and Black Holes by Leonard Susskind Pdf

These three lectures cover a certain aspect of complexity and black holes, namely the relation to the second law of thermodynamics. The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity. Lecture two reviews the connection between the second law of complexity and the interior of black holes. Prof. L. Susskind discusses how firewalls are related to periods of non-increasing complexity which typically only occur after an exponentially long time. The final lecture is about the thermodynamics of complexity, and “uncomplexity” as a resource for doing computational work. The author explains the remarkable power of “one clean qubit,” in both computational terms and in space-time terms. This book is intended for graduate students and researchers who want to take the first steps towards the mysteries of black holes and their complexity.

Author : Jiannis K. Pachos
Publisher : Cambridge University Press
Page : 220 pages
File Size : 49,7 Mb
Release : 2012-04-12
Category : Computers
ISBN : 9781107005044

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Introduction to Topological Quantum Computation by Jiannis K. Pachos Pdf

Ideal for graduate students and researchers from various sub-disciplines, this book provides an excellent introduction to topological quantum computation.

Author : Elias Kiritsis
Publisher : Princeton University Press
Page : 888 pages
File Size : 41,5 Mb
Release : 2019-04-16
Category : Science
ISBN : 9780691188966

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String Theory in a Nutshell by Elias Kiritsis Pdf

The essential introduction to modern string theory—now fully expanded and revised String Theory in a Nutshell is the definitive introduction to modern string theory. Written by one of the world’s leading authorities on the subject, this concise and accessible book starts with basic definitions and guides readers from classic topics to the most exciting frontiers of research today. It covers perturbative string theory, the unity of string interactions, black holes and their microscopic entropy, the AdS/CFT correspondence and its applications, matrix model tools for string theory, and more. It also includes 600 exercises and serves as a self-contained guide to the literature. This fully updated edition features an entirely new chapter on flux compactifications in string theory, and the chapter on AdS/CFT has been substantially expanded by adding many applications to diverse topics. In addition, the discussion of conformal field theory has been extensively revised to make it more student-friendly. The essential one-volume reference for students and researchers in theoretical high-energy physics Now fully expanded and revised Provides expanded coverage of AdS/CFT and its applications, namely the holographic renormalization group, holographic theories for Yang-Mills and QCD, nonequilibrium thermal physics, finite density physics, and entanglement entropy Ideal for mathematicians and physicists specializing in theoretical cosmology, QCD, and novel approaches to condensed matter systems An online illustration package is available to professors

Author : Leonard Susskind,James Lindesay
Publisher : World Scientific
Page : 204 pages
File Size : 47,6 Mb
Release : 2005
Category : Science
ISBN : 9812561315

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An Introduction to Black Holes, Information and the String Theory Revolution by Leonard Susskind,James Lindesay Pdf

- A unique exposition of the foundations of the quantum theory of black holes including the impact of string theory, the idea of black hole complementarily and the holographic principle bull; Aims to educate the physicist or student of physics who is not an expert on string theory, on the revolution that has grown out of black hole physics and string theory

Author : Fabrizio Tamburini,Ignazio Licata
Publisher : Unknown
Page : 140 pages
File Size : 40,8 Mb
Release : 2020-10-12
Category : Electronic
ISBN : 3039432605

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Relativistic Quantum Information by Fabrizio Tamburini,Ignazio Licata Pdf

Relativistic quantum information is one of the most exciting fields of physics today. Not only does it open possibilities for new forms of computing but it also calls into question the peaceful coexistence between classical space-time and quantum physics with scenarios that reopen the relationships between locality and nonlocality in the foundational structure of physics. Curated by two international experts Ignazio Licata and Fabrizio Tamburini, this volume hosts a selection of particularly significant essays for the new territories, and is dedicated to the 60th anniversary of Prof. Ignazio Licata.