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Introduction to the statistical physics of integrable many-body systems /
"Including topics not traditionally covered in the literature, such as (1 + 1)- dimensional quantum field theory and classical two-dimensional Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied."--
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2013.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
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| 100 | 1 | |a Šamaj, Ladislav, |d 1959- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjC9djyfmMy9QWPh669jBX | |
| 245 | 1 | 0 | |a Introduction to the statistical physics of integrable many-body systems / |c Ladislav Šamaj, Zoltán Bajnok. |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c 2013. | |
| 300 | |a 1 online resource (504 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 546 | |a Text in English. | ||
| 520 | |a "Including topics not traditionally covered in the literature, such as (1 + 1)- dimensional quantum field theory and classical two-dimensional Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied."-- |c Provided by publisher | ||
| 505 | 0 | |a Part I. Spinless Bose and Fermi Gases: 1. Particles with nearest-neighbour interactions: Bethe ansatz and the ground state; 2. Bethe ansatz: zero-temperature thermodynamics and excitations; 3. Bethe ansatz: finite-temperature thermodynamics; 4. Particles with inverse-square interactions; Part II. Quantum Inverse Scattering Method: 5. QISM: Yang-Baxter equation; 6. QISM: transfer matrix and its diagonalization; 7. QISM: treatment of boundary conditions; 8. Nested Bethe ansatz for spin-1/2 fermions with delta interactions; 9. Thermodynamics of spin-1/2 fermions with delta interactions; Part III. Quantum Spin Chains: 10. Quantum Ising chain in a transverse field; 11. XXZ Heisenberg chain: Bethe ansatz and the ground state; 12. XXZ Heisenberg chain: ground state in the presence of magnetic field; 13. XXZ Heisenberg chain: excited states; 14. XXX Heisenberg chain: thermodynamics with strings; 15. XXZ Heisenberg chain: thermodynamics without strings; 16. XYZ Heisenberg chain; 17. Integrable isotropic chains with arbitrary spin; Part IV. Strongly Correlated Electrons: 18. Hubbard model; 19. Kondo effect; 20. Luttinger many-fermion model; 21. Integrable BCS superconductors; Part V. Sine-Gordon Model: 22. Classical sine-Gordon theory; 23. Conformal quantization; 24. Lagrangian quantization; 25. Bootstrap quantization; 26. UV-IR relation; 27. Exact finite volume description from XXZ; 28. Two-dimensional Coulomb gas; Appendix A. Spin and spin operators on chain; Appendix B. Elliptic functions; References; Index. | |
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references (pages 596-501) and index. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Quantum theory |x Statistical methods. | |
| 650 | 0 | |a Many-body problem. | |
| 650 | 6 | |a Théorie quantique |x Méthodes statistiques. | |
| 650 | 6 | |a Problème des N corps. | |
| 650 | 7 | |a SCIENCE |x Mathematical Physics. |2 bisacsh | |
| 650 | 7 | |a SCIENCE |x Physics |x Quantum Theory. |2 bisacsh | |
| 650 | 7 | |a Many-body problem |2 fast | |
| 650 | 7 | |a Quantum theory |x Statistical methods |2 fast | |
| 700 | 1 | |a Bajnok, Zoltán, |e author. | |
| 776 | 0 | 8 | |i Print version: |a Šamaj, Ladislav, 1959- |t Introduction to the statistical physics of integrable many-body systems. |d Cambridge : Cambridge University Press, 2013 |z 9781107030435 |w (DLC) 2012051080 |w (OCoLC)830674559 |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1182967 |z Texto completo |
| 880 | 0 | |6 505-00/(S |a Cover -- Contents -- Preface -- Part I Spinless Bose and Fermi gases -- 1 Particles with nearest-neighbor interactions: Bethe ansatz and the ground state -- 1.1 General formalism -- 1.2 Point interactions -- 1.3 Bosons with δ-potential: Bethe ansatz equations -- 1.4 Bound states for attractive bosons -- 1.5 Repulsive bosons -- 1.6 Particles with finite hard-core interactions -- Exercises -- 2 Bethe ansatz: Zero-temperature thermodynamics and excitations -- 2.1 Response of the ground state -- 2.2 Zero-temperature thermodynamics -- 2.3 Low-lying excitations -- Exercises -- 3 Bethe ansatz: Finite-temperature thermodynamics -- 3.1 The concept of holes -- 3.2 Thermodynamic equilibrium -- Exercises -- 4 Particles with inverse-square interactions -- 4.1 The two-body scattering problem -- 4.2 The ground-state wavefunction of a product form -- 4.3 Excited states for the trigonometric case -- Exercises -- Part II Quantum inverse-scattering method -- 5 QISM: Yang--Baxter equation -- 5.1 Generalized Bethe ansatz -- 5.2 Derivation of the Yang--Baxter equation -- 5.3 Lax operators, monodromy and transfer matrices -- 5.4 Two-state solutions of the YBE -- 5.5 Braid-group solution -- 5.6 Quantum groups -- Exercises -- 6 QISM: Transfer matrix and its diagonalization -- 6.1 Vertex models on the square lattice -- 6.2 Connection with quantum models on a chain -- 6.3 Diagonalization of the trigonometric transfer matrix -- Exercises -- 7 QISM: Treatment of boundary conditions -- 7.1 Formulation of boundary conditions -- 7.2 Boundary conditions and the inhomogeneous transfer matrix -- 7.3 Diagonalization of the inhomogeneous transfer matrix -- 8 Nested Bethe ansatz for spin-½ fermions with δ-interactions -- 8.1 The scattering problem -- 8.2 Nested Bethe equations for spin-½ fermions -- 8.3 Ground state and low-lying excitations -- Exercises. | |
| 880 | 8 | |6 505-00/(S |a 9 Thermodynamics of spin-½ fermions with δ-interactions -- 9.1 Repulsive regime c>0 -- 9.2 Attractive regime c<0 -- Exercises -- Part III Quantum spin chains -- 10 Quantum Ising chain in a transverse field -- 10.1 Jordan-Wigner transformation -- 10.2 Diagonalization of the quadratic form -- 10.3 Ground-state properties and thermodynamics -- 10.4 Thermodynamics of the classical 2D Ising model -- Exercises -- 11 XXZ Heisenberg chain: Bethe ansatz and the ground state -- 11.1 Symmetries of the Hamiltonian -- 11.2 Schrödinger equation -- 11.3 Coordinate Bethe ansatz -- 11.4 Orbach parameterization -- 11.5 The ground state -- 11.6 The absolute ground state for Δ<1 -- Exercises -- 12 XXZ Heisenberg chain: Ground state in the presence of a magnetic field -- 12.1 Fundamental integral equation for the λ-density -- 12.2 Formula for the magnetic field -- 12.3 Ground-state energy near half-filling -- Exercises -- 13 XXZ Heisenberg chain: Excited states -- 13.1 Strings -- 13.2 Response of the ground state to a perturbation -- 13.3 Low-lying excitations -- Exercises -- 14 XXX Heisenberg chain: Thermodynamics with strings -- 14.1 Thermodynamic Bethe ansatz -- 14.2 High-temperature expansion -- 14.3 Low-temperature expansion -- Exercises -- 15 XXZ Heisenberg chain: Thermodynamics without strings -- 15.1 Quantum transfer matrix -- 15.2 Bethe ansatz equations -- 15.3 Nonlinear integral equations for eigenvalues -- 15.4 Representations of the free energy -- Exercises -- 16 XYZ Heisenberg chain -- 16.1 Diagonalization of the transfer matrix for the eight-vertex model -- 16.2 Restricted models and the ϕ parameter -- 16.3 XYZ chain: Bethe ansatz equations -- 16.4 XYZ chain: Ground-state energy -- 16.5 XYZ chain: Critical ground-state properties -- Exercises -- 17 Integrable isotropic chains with arbitrary spin -- 17.1 Construction of the spin-s scattering matrix. | |
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