Quantum interacting particle systems :: lecture notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000 /
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 a...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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River Edge, N.J. :
World Scientific Pub.,
©2002.
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| Schriftenreihe: | QP-PQ, quantum probability and white noise analysis ;
v. 14. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xix, 336 pages). |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9789812776853 9812776850 9789812381040 981238104X |
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| 505 | 0 | |a Ch. 1. Lectures on quantum interacting particle systems / L. Accardi and S. Kozyrev -- ch. 2. Lectures on the qualitative analysis of quantum Markov semigroups / F. Fagnola and R. Rebolledo -- ch. 3. Analysis of classical and quantum interacting particle systems / B. Zegarliński. | |
| 520 | |a 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. | ||
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| contents | Ch. 1. Lectures on quantum interacting particle systems / L. Accardi and S. Kozyrev -- ch. 2. Lectures on the qualitative analysis of quantum Markov semigroups / F. Fagnola and R. Rebolledo -- ch. 3. Analysis of classical and quantum interacting particle systems / B. Zegarliński. |
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| indexdate | 2024-11-27T13:17:11Z |
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| series | QP-PQ, quantum probability and white noise analysis ; |
| series2 | QP-PQ, quantum probability and white noise analysis ; |
| spelling | Quantum interacting particle systems : lecture notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000 / edited by Luigi Accardi, Franco Fagnola. River Edge, N.J. : World Scientific Pub., ©2002. 1 online resource (xix, 336 pages). text txt rdacontent computer c rdamedia online resource cr rdacarrier QP-PQ, quantum probability and white noise analysis ; v. 14 Includes bibliographical references. Print version record. Ch. 1. Lectures on quantum interacting particle systems / L. Accardi and S. Kozyrev -- ch. 2. Lectures on the qualitative analysis of quantum Markov semigroups / F. Fagnola and R. Rebolledo -- ch. 3. Analysis of classical and quantum interacting particle systems / B. Zegarliński. 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. Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Hamiltonian systems. http://id.loc.gov/authorities/subjects/sh85058563 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Théorie quantique. Systèmes hamiltoniens. Processus stochastiques. Physique mathématique. SCIENCE Physics Quantum Theory. bisacsh Hamiltonian systems fast Mathematical physics fast Quantum theory fast Stochastic processes fast Accardi, L. (Luigi), 1947- https://id.oclc.org/worldcat/entity/E39PBJmp8gy7k3tkJHMt4JH6Kd http://id.loc.gov/authorities/names/n82267829 Fagnola, Franco. http://id.loc.gov/authorities/names/n2002015678 Centro internazionale per la ricerca matematica (Trento, Italy) http://id.loc.gov/authorities/names/n88056075 has work: Quantum interacting particle systems (Text) https://id.oclc.org/worldcat/entity/E39PCG37jb7dYP4BvXBkTFwWtC https://id.oclc.org/worldcat/ontology/hasWork Print version: Quantum interacting particle systems. River Edge, N.J. : World Scientific Pub., ©2002 981238104X 9789812381040 (DLC) 2002069003 (OCoLC)50041043 QP-PQ, quantum probability and white noise analysis ; v. 14. http://id.loc.gov/authorities/names/n2003016577 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210590 Volltext |
| spellingShingle | Quantum interacting particle systems : lecture notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000 / QP-PQ, quantum probability and white noise analysis ; Ch. 1. Lectures on quantum interacting particle systems / L. Accardi and S. Kozyrev -- ch. 2. Lectures on the qualitative analysis of quantum Markov semigroups / F. Fagnola and R. Rebolledo -- ch. 3. Analysis of classical and quantum interacting particle systems / B. Zegarliński. Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Hamiltonian systems. http://id.loc.gov/authorities/subjects/sh85058563 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Théorie quantique. Systèmes hamiltoniens. Processus stochastiques. Physique mathématique. SCIENCE Physics Quantum Theory. bisacsh Hamiltonian systems fast Mathematical physics fast Quantum theory fast Stochastic processes fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85109469 http://id.loc.gov/authorities/subjects/sh85058563 http://id.loc.gov/authorities/subjects/sh85128181 http://id.loc.gov/authorities/subjects/sh85082129 https://id.nlm.nih.gov/mesh/D011789 https://id.nlm.nih.gov/mesh/D013269 |
| title | Quantum interacting particle systems : lecture notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000 / |
| title_auth | Quantum interacting particle systems : lecture notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000 / |
| title_exact_search | Quantum interacting particle systems : lecture notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000 / |
| title_full | Quantum interacting particle systems : lecture notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000 / edited by Luigi Accardi, Franco Fagnola. |
| title_fullStr | Quantum interacting particle systems : lecture notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000 / edited by Luigi Accardi, Franco Fagnola. |
| title_full_unstemmed | Quantum interacting particle systems : lecture notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000 / edited by Luigi Accardi, Franco Fagnola. |
| title_short | Quantum interacting particle systems : |
| title_sort | quantum interacting particle systems lecture notes of the volterra cirm international school trento italy 23 29 september 2000 |
| title_sub | lecture notes of the Volterra-CIRM International School, Trento, Italy, 23-29 September 2000 / |
| topic | Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Hamiltonian systems. http://id.loc.gov/authorities/subjects/sh85058563 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Théorie quantique. Systèmes hamiltoniens. Processus stochastiques. Physique mathématique. SCIENCE Physics Quantum Theory. bisacsh Hamiltonian systems fast Mathematical physics fast Quantum theory fast Stochastic processes fast |
| topic_facet | Quantum theory. Hamiltonian systems. Stochastic processes. Mathematical physics. Quantum Theory Stochastic Processes Théorie quantique. Systèmes hamiltoniens. Processus stochastiques. Physique mathématique. SCIENCE Physics Quantum Theory. Hamiltonian systems Mathematical physics Quantum theory Stochastic processes |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210590 |
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