LEADER 06374nam 22007214a 450 001 9910458075503321 005 20200520144314.0 010 $a981-277-685-0 035 $a(CKB)1000000000399680 035 $a(EBL)1679420 035 $a(OCoLC)879023580 035 $a(SSID)ssj0000231320 035 $a(PQKBManifestationID)11185486 035 $a(PQKBTitleCode)TC0000231320 035 $a(PQKBWorkID)10207214 035 $a(PQKB)10841742 035 $a(MiAaPQ)EBC1679420 035 $a(WSP)00005055 035 $a(Au-PeEL)EBL1679420 035 $a(CaPaEBR)ebr10201217 035 $a(CaONFJC)MIL505391 035 $a(EXLCZ)991000000000399680 100 $a20020601d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aQuantum interacting particle systems$b[electronic resource] $electure notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000 /$fedited by Luigi Accardi, Franco Fagnola 210 $aRiver Edge, N.J. $cWorld Scientific Pub.$dc2002 215 $a1 online resource (356 p.) 225 1 $aQP-PQ, quantum probability and white noise analysis ;$vv. 14 300 $aDescription based upon print version of record. 311 $a981-238-104-X 320 $aIncludes bibliographical references. 327 $aContents ; Preface ; Chapter 1 Lectures on Quantum Interacting Particle Systems ; 1.0 Introduction ; 1.1 Basic ideas of the stochastic limit ; 1.1.1 Quantum dynamics and flows ; 1.1.2 The stochastic golden rule: general scheme ; 1.1.3 Discrete spectrum systems 327 $a1.1.4 Quantum fields and white noises 1.1.5 Dipole interaction Hamiltonians ; 1.1.6 The stochastic golden rule ; 1.1.7 The Langevin equation ; 1.1.8 The quantum Feynman-Kac formula: master equation ; 1.1.9 Subalgebras invariant under the generator 327 $a1.1.10 Structure of the invariant states 1.1.11 The Langevin equation: generic systems ; 1.1.12 Appendix: Two-level system and Boltzmannian (or free) statistics ; 1.1.13 Appendix: Structure of discrete spectrum quantum dynamical systems 327 $a1.1.14 Appendix: Spectral theory for Heisenberg evolutions 1.1.15 The Langevin equation for the density matrix ; 1.1.16 The master equation for reduced density matrix ; 1.1.17 Structure of the invariant states ; 1.1.18 Evolution of the diagonal and off-diagonal elements 327 $a1.1.19 Stationary states of the reduced evolution 1.1.20 Evolution of density matrix in the generic case ; 1.1.21 Decoherence: vanishing of off-diagonal terms ; 1.1.22 Discussion of decoherence ; 1.1.23 Classical detailed balance ; 1.1.24 A Lyapunov function for the reduced dynamics 327 $a1.1.25 Non-detailed balance stationary state for a system driven by master equation 330 $aThe problem of extending ideas and results on the dynamics of infinite classical lattice systems to the quantum domain naturally arises in different branches of physics (nonequilibrium statistical mechanics, quantum optics, solid state, ...) and new momentum from the development of quantum computer and quantum neural networks (which are in fact interacting arrays of binary systems) has been found. The stochastic limit of quantum theory allowed to deduce, as limits of the usual Hamiltonian systems, a new class of quantum stochastic flows which, when restricted to an appropriate Abelian subalgebra, produces precisely those interacting particle systems studied in classical statistical mechanics. Moreover, in many interesting cases, the underlying classical process "drives" the quantum one, at least as far as ergodicity or convergence to equilibrium are concerned. Thus many deep results concerning classical systems can be directly applied to carry information on the corresponding quantum system. The thermodynamic limit itself is obtained thanks to a technique (the four-semigroup method, new even in the classical case) which reduces the infinitesimal structure of a stochastic flow to that of four semigroups canonically associated to it (Chap. 1). Simple and effective methods to analyze qualitatively the ergodic behavior of quantum Markov semigroups are discussed in Chap. 2. Powerful estimates used to control the infinite volume limit, ergodic behavior and the spectral gap (Gaussian, exponential and hypercontractive bounds, classical and quantum logarithmic Sobolev inequalities, ...) are discussed in Chap. 3. 410 0$aQP-PQ, quantum probability and white noise analysis ;$vv. 14. 606 $aQuantum theory 606 $aHamiltonian systems 606 $aStochastic processes 606 $aMathematical physics 608 $aElectronic books. 615 0$aQuantum theory. 615 0$aHamiltonian systems. 615 0$aStochastic processes. 615 0$aMathematical physics. 676 $a530.12 701 $aAccardi$b L$g(Luigi),$f1947-$0319693 701 $aFagnola$b Franco$0531525 712 02$aCentro internazionale per la ricerca matematica (Trento, Italy) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910458075503321 996 $aQuantum interacting particle systems$91915840 997 $aUNINA