LEADER 05191nam 2200625 a 450 001 9910458939003321 005 20200520144314.0 010 $a981-277-689-3 035 $a(CKB)1000000000401120 035 $a(EBL)1679588 035 $a(OCoLC)879023828 035 $a(SSID)ssj0000243993 035 $a(PQKBManifestationID)11186039 035 $a(PQKBTitleCode)TC0000243993 035 $a(PQKBWorkID)10168743 035 $a(PQKB)10566259 035 $a(MiAaPQ)EBC1679588 035 $a(WSP)00005049 035 $a(Au-PeEL)EBL1679588 035 $a(CaPaEBR)ebr10201301 035 $a(CaONFJC)MIL505389 035 $a(EXLCZ)991000000000401120 100 $a20030626d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSemiclassical analysis, Witten Laplacians, and statistical mechanics$b[electronic resource] /$fBernard Helffer 210 $aRiver Edge, NJ $cWorld Scientific$dc2002 215 $a1 online resource (190 p.) 225 1 $aSeries on partial differential equations and applications ;$vv. 1 300 $aDescription based upon print version of record. 311 $a981-238-098-1 320 $aIncludes bibliographical references (p. 169-176) and index. 327 $aContents ; 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 Complex 327 $a2.3 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 model 327 $a3.3 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 operators 327 $a4.4 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 Notes 327 $aChapter 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 operator 327 $a5.5 The case of the Schrodinger operator in dimension 1 330 $a 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.
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