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Serie: Springerbriefs in mathematical physics
paperbackEngels9789811033155
17-1-2017
This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. Meer
paperbackEngels9789811035050
23-2-2017
This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. Meer
paperbackEngels9789811666438
23-3-2022
Rich information-theoretic structure in out-of-equilibrium thermodynamics exists in both the classical and quantum regimes, leading to the fruitful interplay among statistical physics, quantum information theory, and mathematical theories such as matrix analysis and asymptotic probability theory. Meer
paperbackEngels9789819931491
8-8-2023
This book is based on the author's mini course delivered at Tokyo University of Marine Science and Technology in March 2019.
The shuffle approach to Drinfeld–Jimbo quantum groups of finite type (embedding their "positive" subalgebras into q-deformed shuffle algebras) was first developed independently in the 1990s by J. Meer
paperbackEngels9784431564850
17-11-2016
This book treats ensembles of Young diagrams originating from group-theoretical contexts and investigates what statistical properties are observed there in a large-scale limit. Meer
paperbackEngels9789811002748
16-2-2016
The purpose of this book is to introduce two recent topics in mathematical physics and probability theory: the Schramm–Loewner evolution (SLE) and interacting particle systems related to random matrix theory. Meer
paperbackEngels9789811300554
26-4-2018
This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov–Witten invariants of a Calabi–Yau threefold by using the Picard–Fuchs differential equation of period integrals of its mirror Calabi–Yau threefold. Meer
paperbackEngels9789811956775
19-10-2022
This book explains the mathematical structures of supersymmetric quantum field theory (SQFT) from the viewpoints of functional and infinite-dimensional analysis. Meer
paperbackEngels9783319643427
10-10-2017
This book provides a rather self-contained survey of the construction of Hadamard states for scalar field theories in a large class of notable spacetimes, possessing a (conformal) light-like boundary. Meer
paperbackEngels9783319947549
9-7-2018
Refection Positivity is a central theme at the crossroads of Lie group representations, euclidean and abstract harmonic analysis, constructive quantum field theory, and stochastic processes. Meer
paperbackEngels9783319947877
3-1-2019
What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes, deliberately unveiling the answers to these questions. Meer
paperbackEngels9783319949017
18-10-2018
This book gives a rigorous treatment of entanglement measures in the general context of quantum field theory. It covers a broad range of models and the use of fields allows us to properly take the localization of systems into account. Meer
paperbackEngels9783319951829
13-11-2018
This Brief presents in a self-contained, non-technical and illustrative fashion the state-of-the-art results and techniques for the dynamics of extremal black holes. Meer
paperbackEngels9784431557012
21-7-2015
The discovery of a virtual turning point truly is a breakthrough in WKB analysis of higher order differential equations. This monograph expounds the core part of its theory together with its application to the analysis of higher order Painlevé equations of the Noumi–Yamada type and to the analysis of non-adiabatic transition probability problems in three levels. Meer
paperbackEngels9784431559580
18-12-2015
This book explains what quantum states of light look like. Of special interest, a single photon state is explained by using a wave picture, showing that it corresponds to the complementarity of a quantum. Meer
paperbackEngels9789811040931
31-3-2017
This is the first book to treat combinatorial and geometric aspects of two-dimensional solitons. Based on recent research by the author and his collaborators, the book presents new developments focused on an interplay between the theory of solitons and the combinatorics of finite-dimensional Grassmannians, in particular, the totally nonnegative (TNN) parts of the Grassmannians. Meer
paperbackEngels9789812879950
23-12-2015
This book presents a self-consistent review of quantum computation with topological quantum codes. The book covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topological quantum error correction and topological fault-tolerant operations. Meer
paperbackEngels9789813293045
28-8-2019
This book provides self-contained proofs of the existence of ground states of several interaction models in quantum field theory. Interaction models discussed here include the spin-boson model, the Nelson model with and without an ultraviolet cutoff, and the Pauli–Fierz model with and without dipole approximation in non-relativistic quantum electrodynamics. Meer
paperbackEngels9789811311499
27-8-2018
The volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the three-dimensional sphere would give the volume of the knot complement. Meer
paperbackEngels9789811311581
17-9-2018
This book focuses on Erdélyi–Kober fractional calculus from a statistical perspective inspired by solar neutrino physics. Results of diffusion entropy analysis and standard deviation analysis of data from the Super-Kamiokande solar neutrino experiment lead to the development of anomalous diffusion and reaction in terms of fractional calculus. Meer