LEADER 05915nam 2200745Ia 450 001 9910826995603321 005 20200520144314.0 010 $a1-281-93453-4 010 $a9786611934538 010 $a981-279-459-X 035 $a(CKB)1000000000538052 035 $a(EBL)1679534 035 $a(SSID)ssj0000194079 035 $a(PQKBManifestationID)11197899 035 $a(PQKBTitleCode)TC0000194079 035 $a(PQKBWorkID)10231529 035 $a(PQKB)11429016 035 $a(MiAaPQ)EBC1679534 035 $a(WSP)00004640 035 $a(Au-PeEL)EBL1679534 035 $a(CaPaEBR)ebr10255956 035 $a(CaONFJC)MIL193453 035 $a(OCoLC)879023737 035 $a(EXLCZ)991000000000538052 100 $a20010803d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLong time behaviour of classical and quantum systems $eproceedings of the Bologna APTEX International Conference : Bologna, Italy, 13-17 September 1999 /$feditors, Sandro Graffi & Andre Martinez 205 $a1st ed. 210 $aSingapore ;$aRiver Edge, N.J. $cWorld Scientific$dc2001 215 $a1 online resource (299 p.) 225 1 $aSeries on concrete and applicable mathematics ;$v1 300 $aDescription based upon print version of record. 311 $a981-02-4555-6 320 $aIncludes bibliographical references. 327 $aForeword; List of Participants; CONTENTS; Return to Equilibrium in Classical and Quantum Systems; 1. FIRST LECTURE; 2. SECOND LECTURE; 3. THIRD LECTURE; 4. FOURTH LECTURE; Quantum Resonances and Trapped Trajectories; 1 Introduction; 2 Definitions and first results; 3 FBI transform and upper bounds on the density of resonances; 4 Trace formulae and lower bounds on the density of resonances; 5 Resonances and a non-linear Schrodinger equation; Return to Thermal Equilibrium in Quantum Statistical Mechanics; 1. INTRODUCTION; 2. EQUILIBRIUM STATES AND DYNAMICS OF FINITE SYSTEMS 327 $a3. EQUILIBRIUM STATES AND DYNAMICS OF INFINITE SYSTEMS4. EXAMPLE: FINITE QUANTUM SYSTEM; 5. EXAMPLE: FREE QUANTIZED ELECTROMAGNETIC FIELD IN THE ARAKI-WOODS REPRESENTATION; 6. EXAMPLE: CONFINED ELECTRON AND FREE QUANTIZED ELECTROMAGNETIC FIELD - NONINTERACTING; 7. CONFINED ELECTRON COUPLED TO THE QUANTIZED RADIATION FIELD - INTERACTING CASE; Small Oscillations in Some Nonlinear PDE's; 1 Introduction; 2 The finite dimensional case; 3 The infinite dimensional case: some known results; 4 A proof of Lyapunov center theorem: the finite dimensional case; 5 The resonant case 327 $a6 A proof of the Lyapunov center theorem: the infinite dimensional case7 On the verification of the property y-NR; 8 Applications; The Semi-Classical Van-Vleck Formula. Application to the Aharonov-Bohm Effect; 1 Introduction; 2 Coherent states and quantum propagator; 3 Semi-classical approximation for the propagator; 4 The time-dependent Aharonov-Bohm Effect; Fractal Dimensions and Quantum Evolution Associated with Sparse Potential Jacobi Matrices; 1 Introduction; 2 The sparse barrier model and main results; 3 Pictures of quantum motion within sparse barriers; 4 Proof of Theorem 2 327 $a5 Proof of Theorem 36 Conclusions; Infinite Step Billiards; 1 Introduction; 2 The model and the results; 3 Outline of the proofs; Semiclassical Expansion for the Thermodynamic Limit of the Ground State Energy of Kac's Operator; 1 Introduction; 2 One-parameter families of weighted standard functions; 3 WKB constructions; 4 A formal asymptotic expansion; 5 Estimates for the thermodynamic limit; Asymptotics of Scattering Poles for Two Strictly Convex Obstacles; 1. INTRODUCTION; 2. METHOD OF THE PROOF; 3. EXPRESSION OF BROKEN RAYS CONVERGING TO THE PERIODIC RAY; 4. SOLUTIONS OF FUNCTION EQUATIONS 327 $a5. TAYLOR EXPANSION OF Tn(s+t o+r)Parabolic Dynamical Systems and Inducing; 1 Preliminaires; 2 Parabolic rational maps; QFT for Scalar Particles in External Fields on Riemannian Manifolds; 1 Introduction; 2 Invariant wave equations on Riemannnian manifolds; 3 Classical S-matrix; 4 Feynman's scattering amplitude; 5 Solvability of the equation AF = A + iAP_AF; 6 Quantum field theory in external forces; 7 Hilbert-Schmidt property on Riemannian manifolds; 8 Massless case; Existence and Born-Oppenheimer Asymptotics of the Total Scattering Cross-Section in Ion-Atom Collisions; I Introduction 327 $aII Notation assumptions and main results 330 $aThis book is centered on the two minicourses conducted by C Liverani (Rome) and J Sjoestrand (Paris) on the return to equilibrium in classical statistical mechanics and the location of quantum resonances via semiclassical analysis, respectively. The other contributions cover related topics of classical and quantum mechanics, such as scattering theory, classical and quantum statistical mechanics, dynamical localization, quantum chaos, ergodic theory and KAM techniques. Contents: Return to Equilibrium in Classical and Quantum Systems (C Liverani); Quantum Resonances and Trapped Trajectories (J S 410 0$aSeries on concrete and applicable mathematics ;$v1. 517 3 $aLong time behavior of classical and quantum systems 517 3 $aBologna APTEX International Conference 606 $aMathematical physics$vCongresses 606 $aMicrolocal analysis$vCongresses 606 $aQuantum theory$vCongresses 615 0$aMathematical physics 615 0$aMicrolocal analysis 615 0$aQuantum theory 676 $a530.1 701 $aGraffi$b S$g(Sandro),$f1943-$041343 701 $aMartinez$b Andre$00 712 12$aBologna APTEX International Conference 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910826995603321 996 $aLong time behaviour of classical and quantum systems$94086895 997 $aUNINA