New Trends In Quantum Integrable Systems Proceedings Of The Infinite Analysis 09

The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto Japan from 27 to 31 July 2009. As a continuation of the RIMS Research Project a Method of Algebraic Analysis in Integrable Systemsa in 2004 the workshop's aim was to cover exciting new developments that have emerged during the recent years.Collected here are research articles based on the talks presented at the workshop including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models integrable models in quantum field theory conformal field theory mathematical aspects of Bethe ansatz special functions and integrable differential/difference equations representation theory of infinite dimensional algebras integrable models and combinatorics.Through these topics the reader can learn about the most recent developments in the field of quantum integrable systems and related areas of mathematical physics."

Annotation. The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project "Method of Algebraic Analysis in Integrable Systems" in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years. Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics. Through these topics, the reader can learn about the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.

The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project "Method of Algebraic Analysis in Integrable Systems" in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years. Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics. Through these topics, the reader is exposed to the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.

Properties of linear integral equations related to the six-vertex model with disorder parameter / Hermann Boos and Frank Gohmann -- Algebraic aspects of the correlation functions of the integrable higher-spin XXZ spin chains with arbitrary entries / Tetsuo Deguchi and Chihiro Matsui -- Characters of coinvariants in (1,p) logarithmic models / Boris L. Feigin and Ilya Yu. Tipunin -- XXZ scalar products, Miwa variables and discrete KP / Omar Foda and Gus Schrader -- Quantum spin chains at finite temperatures / Frank Gohmann and Junji Suzuki -- Tropical spectral curves, Fay's trisecant identity, and generalized ultradiscrete Toda lattice / Rei Inoue and Shinsuke Iwao -- On one-point functions of descendants in sine-Gordon model / Michio Jimbo, Tetsuji Miwa and Fedor Smirnov -- Perfect crystals for the quantum affine algebra U[symbol] / Seok-Jin Kang [und weitere] -- Boundary quantum Knizhnik-Zamolodchikov equation / Masahiro Kasatani -- A pentagon of identities, graded tensor products, and the Kirillov-Reshetikhin conjecture / Rinat Kedem -- TBA for the Toda chain / Karol Kajetan Kozlowski and Jorg Teschner -- Generalized energies and integrable D[symbol] cellular automaton / Atsuo Kuniba, Reiho Sakamoto and Yasuhiko Yamada -- Dyson's constant for the hypergeometric kernel / Oleg Lisovyy -- Representation theory of a small ramified partition algebra / Paul P. Martin -- The saga of the Ising susceptibility / Barry M. McCoy -- Bethe algebra of the [symbol] Gaudin model and algebra of functions on the critical set of the master function / Evgeny Mukhin, Vitaly Tarasov and Alexander Varchenko -- T-systems, Y-systems, and cluster algebras : Tamely laced case / Tomoki Nakanishi -- Periodic Benjamin-Ono equation with discrete Laplacian and 2D-Toda hierarchy / Jun'ichi Shiraishi and Yohei Tutiya -- KP and Toda tau functions in Bethe ansatz / Kanehisa Takasaki -- Introduction to middle convolution for differential equations with irregular singularities / Kouichi Takemura -- Differential equations compatible with boundary rational qKZ equation / Yoshihiro Takeyama -- Classification of solutions to the reflection equation for the critical Z[symbol]-symmetric vertex model I / Yuji Yamada

This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.

Over the past 30 years, significant advances have been made in the field of integrable systems and their applications in statistical mechanics and mathematical physics, yet no book on the subject has been published since 1993. This monograph, the work of established authors in quantum mechanics, introduces the subject in a clear, logical way. The treatment first builds the background in classical physics and nonlinear systems, then moves to the quantum case before presenting the latest research and applications. The authors' clear approach and examples based on concrete physical models rather.