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Quantum Interacting Particle Systems

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Description: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 LimitEquilibrium and Nonequilibrium Spin-Boson ModelsDynamics of Quantum Spin SystemsStructure of the Markov FlowsExistence of Infinite Volume Flows for Quantum Spin SystemsAppendix: Basic Notions on Semigroups and Dissipations"Lectures on the Qualitative Analysis of Quantum Markov Semigroups (F Fagnola & R Rebolledo): "Quantum Markov Semigroups and Master EquationsThe Existence of Stationary StatesFaithful Stationary States and IrreducibilityThe Convergence Towards the Equilibrium"Analysis of Classical and Quantum Interacting Particle Systems (B Zegarlinski): "Construction and Ergodicity of Jump Type Dynamics Lecture IHypercontractivity and Strong Ergodicity for Classical Systems Lecture IILogarithmic Sobolev Inequality in Non-Commutative Setting Lecture IIIParticle Structure and Hypercontractivity Lecture IVReadership: Researchers in probability & statistics, stochastic, mathematical physics, quantum physics."We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Quantum Interacting Particle Systems. To get started finding Quantum Interacting Particle Systems, you are right to find our website which has a comprehensive collection of manuals listed.
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Pages: 357

Format: PDF, EPUB & Kindle Edition

Publisher: World Scientific Publishing Company

Release: 2014

ISBN: 1299741401

Description: 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 LimitEquilibrium and Nonequilibrium Spin-Boson ModelsDynamics of Quantum Spin SystemsStructure of the Markov FlowsExistence of Infinite Volume Flows for Quantum Spin SystemsAppendix: Basic Notions on Semigroups and Dissipations"Lectures on the Qualitative Analysis of Quantum Markov Semigroups (F Fagnola & R Rebolledo): "Quantum Markov Semigroups and Master EquationsThe Existence of Stationary StatesFaithful Stationary States and IrreducibilityThe Convergence Towards the Equilibrium"Analysis of Classical and Quantum Interacting Particle Systems (B Zegarlinski): "Construction and Ergodicity of Jump Type Dynamics Lecture IHypercontractivity and Strong Ergodicity for Classical Systems Lecture IILogarithmic Sobolev Inequality in Non-Commutative Setting Lecture IIIParticle Structure and Hypercontractivity Lecture IVReadership: Researchers in probability & statistics, stochastic, mathematical physics, quantum physics."We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Quantum Interacting Particle Systems. To get started finding Quantum Interacting Particle Systems, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Quantum Interacting Particle Systems

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