05191nam 2200625 a 450 991045893900332120200520144314.0981-277-689-3(CKB)1000000000401120(EBL)1679588(OCoLC)879023828(SSID)ssj0000243993(PQKBManifestationID)11186039(PQKBTitleCode)TC0000243993(PQKBWorkID)10168743(PQKB)10566259(MiAaPQ)EBC1679588(WSP)00005049(Au-PeEL)EBL1679588(CaPaEBR)ebr10201301(CaONFJC)MIL505389(EXLCZ)99100000000040112020030626d2002 uy 0engur|n|---|||||txtccrSemiclassical analysis, Witten Laplacians, and statistical mechanics[electronic resource] /Bernard HelfferRiver Edge, NJ World Scientificc20021 online resource (190 p.)Series on partial differential equations and applications ;v. 1Description based upon print version of record.981-238-098-1 Includes bibliographical references (p. 169-176) and index.Contents ; Preface ; Chapter 1 Introduction ; 1.1 Laplace integrals ; 1.2 The problems in statistical mechanics ; 1.3 Semi-classical analysis and transfer operators ; 1.4 About the contents ; Chapter 2 Witten Laplacians approach ; 2.1 De Rham Complex ; 2.2 Witten Complex2.3 Witten Laplacians 2.4 Semi-classical considerations ; 2.5 An alternative point of view : Dirichlet forms ; 2.6 A nice formula for the covariance ; 2.7 Notes ; Chapter 3 Problems in statistical mechanics with discrete spins ; 3.1 The Curie-Weiss model ; 3.2 The 1-d Ising model3.3 The 2-d Ising model 3.4 Notes ; Chapter 4 Laplace integrals and transfer operators ; 4.1 Introduction ; 4.2 Classical Laplace method ; 4.2.1 Standard results ; 4.2.2 Transition between the convex case and the double well case ; 4.3 The method of transfer operators4.4 Elementary properties of operators with integral kernels 4.5 Elementary properties of the transfer operator ; 4.6 Operators with strictly positive kernel and application ; 4.7 Thermodynamic limit ; 4.8 Mean value ; 4.9 Pair correlation ; 4.10 2-dimensional lattices ; 4.11 NotesChapter 5 Semi-classical analysis for the transfer operators 5.1 Introduction ; 5.2 Explicit computations for the harmonic Kac operator ; 5.3 Harmonic approximation for the transfer operator ; 5.4 WKB constructions for the transfer operator5.5 The case of the Schrodinger operator in dimension 1 This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. In addition, it compares the Witten Laplacian approach with other techniques, such as the transfer matrix approach and its semiclassical analysis. The author concludes by providing a complete proof of the uniform Log-Sobolev inequality. <br><i>Contents:</i><ul><li>Witten Laplacians Approach</li><li>Problems in Statistical Mechanics with Discrete Spins</li><li>Laplace InSeries on partial differential equations and applications ;v. 1.Statistical mechanicsElectronic books.Statistical mechanics.530.13Helffer Bernard52445MiAaPQMiAaPQMiAaPQBOOK9910458939003321Semiclassical analysis, Witten Laplacians, and statistical mechanics2151101UNINA