Quantum Interacting Particle Systems : (Record no. 84787)

MARC details
000 -LEADER
fixed length control field 10415nam a22005053i 4500
001 - CONTROL NUMBER
control field EBC1679420
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20191126114809.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
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007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
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008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 191125s2002 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9789812776853
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9789812381040
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC1679420
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL1679420
035 ## - SYSTEM CONTROL NUMBER
System control number (CaPaEBR)ebr10201217
035 ## - SYSTEM CONTROL NUMBER
System control number (CaONFJC)MIL505391
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)879023580
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QC174.7.P7Q33 2002
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 530.12
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Accardi, Luigi.
9 (RLIN) 89541
245 10 - TITLE STATEMENT
Title Quantum Interacting Particle Systems :
Remainder of title Lecture Notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Singapore :
Name of producer, publisher, distributor, manufacturer World Scientific Publishing Co Pte Ltd,
Date of production, publication, distribution, manufacture, or copyright notice 2002.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2002.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (357 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
490 1# - SERIES STATEMENT
Series statement Qp-Pq: Quantum Probability and White Noise Analysis Ser. ;
Volume/sequential designation v.14
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Intro -- Contents -- 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 -- 1.1.4 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 -- 1.1.10 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 -- 1.1.14 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 -- 1.1.19 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 -- 1.1.25 Non-detailed balance stationary state for a system driven by master equation -- 1.1.26 Example of non-Gibbs detailed balance stationary state -- 1.1.27 The simplest non-generic master equation -- 1.1.28 Quantum detailed balance -- 1.1.29 Time reversal and invariant states -- 1.1.30 Quantum detailed balance in the sense of Frigerio-Gorini-Kossakowski-Verri -- 1.2 Equilibrium and nonequilibrium spin-boson models -- 1.2.1 The stochastic limit of the spin-boson model -- 1.2.2 The Langevin equation.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 1.2.3 Evolution of the density matrix: master equation -- 1.2.4 Decoherence for one spin -- 1.2.5 Classical subprocesses and Abelian subalgebras -- 1.3 Dynamics of quantum spin systems -- 1.3.1 Introduction -- 1.3.2 A model describing electrical conductivity in lattice systems -- 1.3.3 The stochastic limit of the model -- 1.3.4 The Langevin equation -- 1.3.5 The open Ising model -- 1.3.6 The Langevin equation for quantum spin systems -- 1.3.7 Spin systems with finite range interaction -- 1.3.8 Quasigeneric spin systems -- 1.3.9 Quantum extension of the Glauber dynamics -- 1.3.10 Master equation: generic case -- 1.3.11 Evolution in the diagonal subalgebra: the classical Glauber dynamics -- 1.3.12 Dependence of decoherence on the volume -- 1.4 Structure of the Markov flows -- 1.4.1 Introduction -- 1.4.2 Markov flows -- 1.4.3 Evolutions associated to Markov flows -- 1.4.4 Semigroups associated to Markovian cocycles -- 1.4.5 The extended semigroup of a flow -- 1.4.6 Vector flows -- 1.4.7 Existence of infinite volume dynamics -- 1.5 Existence of infinite volume flows for quantum spin systems -- 1.5.1 Form of the generator -- 1.5.2 Matsui's Lemma -- 1.5.3 Quasigeneric case -- 1.5.4 Non-quasigeneric case -- 1.5.5 Thermodynamic limit -- 1.5.6 The homomorphic property for the flow -- 1.5.7 Appendix: Convergence of the iterated series in dimension 1 -- 1.6 Appendix: Basic notions on semigroups and dissipations -- 1.6.1 Semigroups in Banach spaces -- 1.6.2 Semigroups with dissipative generators -- 1.6.3 Limits of semigroups -- 1.6.4 Dissipative operators in C*-algebras -- 1.7 Bibliography -- Chapter 2 Lectures on the Qualitative Analysis of Quantum Markov Semigroups -- 2.1 Quantum Markov semigroups and master equations -- 2.1.1 Preliminaries -- 2.1.2 Examples of master equations -- 2.1.3 The minimal quantum dynamical semigroup.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 2.2 The existence of stationary states -- 2.2.1 Tightness -- 2.2.2 A general result -- 2.2.3 Conditions on the generator -- 2.2.4 Applications -- 2.3 Faithful stationary states and irreducibility -- 2.3.1 The support of an invariant state -- 2.3.2 Subharmonic projections -- 2.3.3 Applications -- 2.4 The convergence towards the equilibrium -- 2.4.1 A result due to Frigerio and Verri -- 2.4.2 Quantum Markovian cocycles -- 2.4.3 Main results -- 2.4.4 Applications -- 2.5 Bibliography -- Chapter 3 Analysis of Classical and Quantum Interacting Particle Systems -- 3.0 Introduction -- 3.1 Construction and ergodicity of jump type dynamics - Lecture I -- 3.1.1 Introduction -- 3.1.2 Semiclassical dissipative dynamics at finite temperatures for quantum spin system on a lattice -- 3.1.3 Strong ergodicity -- 3.1.4 Construction of jump type dynamics -- 3.1.5 Regularity properties of the elementary Markov generators -- 3.1.6 Equivalence of quadratic forms and L2 ergodicity -- 3.2 Hypercontractivity and strong ergodicity for classical systems - Lecture II -- 3.2.1 Introduction -- 3.2.2 Hypercontractivity and logarithmic Sobolev inequality -- 3.2.3 Properties of the logarithmic Sobolev inequality -- 3.2.4 Strong ergodicity via hypercontractivity -- 3.2.5 Equivalence theorem -- 3.3 Logarithmic Sobolev inequality in non-commutative setting - Lecture III -- 3.3.1 Introduction -- 3.3.2 Non-commutative Lp spaces -- 3.3.3 Hypercontractive semigroup in non-commutative Lp spaces -- 3.3.4 Entropy and infinitesimal description of hypercontractivity -- 3.4 Particle structure and hypercontractivity - Lecture IV -- 3.4.1 Introduction -- 3.4.2 The general strategy -- 3.4.3 Gaussian bounds in product spaces and hypercontractivity -- 3.4.4 Hypercontractivity in non-commutative product spaces -- 3.5 Appendix I -- 3.6 Appendix II -- 3.7 Bibliography.
520 ## - SUMMARY, ETC.
Summary, etc. The 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. Contents: Lectures on Quantum Interacting Particle Systems (L Accardi & S Kozyrev): Basic Ideas of the Stochastic Limit; Equilibrium and Nonequilibrium Spin-Boson Models; Dynamics of Quantum Spin Systems; Structure of the Markov Flows; Existence of
520 8# - SUMMARY, ETC.
Summary, etc. Infinite Volume Flows for Quantum Spin Systems; Appendix: Basic Notions on Semigroups and Dissipations; Lectures on the Qualitative Analysis of Quantum Markov Semigroups (F Fagnola & R Rebolledo): Quantum Markov Semigroups and Master Equations; The Existence of Stationary States; Faithful Stationary States and Irreducibility; The Convergence Towards the Equilibrium; Analysis of Classical and Quantum Interacting Particle Systems (B Zegarlinski): Construction and Ergodicity of Jump Type Dynamics - Lecture I; Hypercontractivity and Strong Ergodicity for Classical Systems - Lecture II; Logarithmic Sobolev Inequality in Non-Commutative Setting - Lecture III; Particle Structure and Hypercontractivity - Lecture IV. Readership: Researchers in probability & statistics, stochastic, mathematical physics, quantum physics.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Quantum theory.;Hamiltonian systems.;Stochastic processes.;Mathematical physics.
9 (RLIN) 89542
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
9 (RLIN) 89543
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Fagnola, Franco.
9 (RLIN) 89544
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Accardi, Luigi
Title Quantum Interacting Particle Systems : Lecture Notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000
Place, publisher, and date of publication Singapore : World Scientific Publishing Co Pte Ltd,c2002
International Standard Book Number 9789812381040
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Qp-Pq: Quantum Probability and White Noise Analysis Ser.
9 (RLIN) 89545
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/thebc/detail.action?docID=1679420">https://ebookcentral.proquest.com/lib/thebc/detail.action?docID=1679420</a>
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