Ebook: On Three Levels: Micro-, Meso-, and Macro-Approaches in Physics

This volume contains the proceedings of a five-day NATO Advanced Research Workshop "On Three Levels, the mathematical physics of micro-, meso-, and macro­ phenomena," conducted from July 19 to 23 in Leuven, Belgium. The main purpose of the workshop was to bring together and to confront where relevant, classical and quantum approaches in the rigorous study of the relation between the various levels of physical description. The reader will find here discussions on a variety of topics involving a broad range of scales. For the micro-level, contributions are presented on models of reaction-diffusion pro­ cesses, quantum groups and quantum spin systems. The reports on quantum disorder, the quantum Hall effect, semi-classical approaches of wave mechanics and the random Schrodinger equation can be situated on the meso-level. Discussions on macroscopic quantum effects and large scale fluctuations are dealing with the macroscopic level of description. These three levels are however not independent and emphasis is put on relating these scales of description. This is especially the case for the contributions on kinetic and hydrodynamicallimits, the discussions on large deviations and the strong and weak coupling limits. The advisory board was composed of J.L. Lebowitz, J.T. Lewis and E.H. Lieb. The organizing committee was formed by Ph.A. Martin, G.L. Sewell, E.R. Speer and A.

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Quantum Kinetic Equations; H. Spohn. Microscopic Derivation of Hydrodynamics with Phase Transition in a Plasma Model; G.L. Sewell. Ferromagnetism in Itinerant Electron Systems; H. Tasaki. Homogeneity in the Ground State of the Two-Dimensional Falicov-Kimabll Model; T.Kennedy. Diffusive Limit of the Asymmetric Simple Exclusion; R.Esposito, et al. Weak Coupling Limit; L.J. Landau. Limit Laws for Recurrence Times in Expanding Maps of an Interval; P. Collet. Stochastic Geometric Aspects of Some Quantum Spin Chains; B.Nachtergaele. The Species Totally Asymmetric Simple Exclusion Process; E.R. Speer. How to Reconstruct a Heat Bath; B. K?mmerer. Interacting Particle Systems on Non-Commutative Spaces; T. Matsui. Non-Self-Averaging Effects in Sums of Random Variables, Spin Glasses, Random Maps, and Random Walks; B. Derrida. Quantum Adiabatic Evolution; A. Joye, C.E. Pfister. 48 additional articles. Index.

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Quantum Kinetic Equations; H. Spohn. Microscopic Derivation of Hydrodynamics with Phase Transition in a Plasma Model; G.L. Sewell. Ferromagnetism in Itinerant Electron Systems; H. Tasaki. Homogeneity in the Ground State of the Two-Dimensional Falicov-Kimabll Model; T.Kennedy. Diffusive Limit of the Asymmetric Simple Exclusion; R.Esposito, et al. Weak Coupling Limit; L.J. Landau. Limit Laws for Recurrence Times in Expanding Maps of an Interval; P. Collet. Stochastic Geometric Aspects of Some Quantum Spin Chains; B.Nachtergaele. The Species Totally Asymmetric Simple Exclusion Process; E.R. Speer. How to Reconstruct a Heat Bath; B. K?mmerer. Interacting Particle Systems on Non-Commutative Spaces; T. Matsui. Non-Self-Averaging Effects in Sums of Random Variables, Spin Glasses, Random Maps, and Random Walks; B. Derrida. Quantum Adiabatic Evolution; A. Joye, C.E. Pfister. 48 additional articles. Index.
Content:
Front Matter....Pages i-x
Quantum Kinetic Equations....Pages 1-10
Microscopic Derivation of Hydrodynamics with Phase Transition in a Plasma Model....Pages 11-21
Ferromagnetism in Itinerant Electron Systems: Rigorous Examples from Flat-Band Hubbard Models....Pages 23-33
Homogeneity in the Ground State of the Two-Dimensional Falicov-Kimball Model....Pages 35-41
Diffusive Limit of the Asymmetric Simple Exclusion: The Navier-Stokes Correction....Pages 43-51
Weak Coupling Limit: Feynman Diagrams....Pages 53-71
Limit Laws for Recurrence Times in Expanding Maps of an Interval....Pages 73-79
Stochastic Geometric Aspects of Some Quantum Spin Chains....Pages 81-89
The Two Species Totally Asymmetric Simple Exclusion Process....Pages 91-102
How to Reconstruct a Heat Bath....Pages 103-113
Interacting Particle Systems on Non-Commutative Spaces....Pages 115-123
Non-Self-Averaging Effects in Sums of Random Variables, Spin Glasses, Random Maps and Random Walks....Pages 125-137
Quantum Adiabatic Evolution....Pages 139-148
Semi-Classical Inelastic S-Matrix for One-Dimensional N-States Systems....Pages 149-154
Gibbsian versus Non-Gibbsian Measures: Some Results and Some Questions in Renormalization Group Theory and Stochastic Dynamics....Pages 155-160
Stabilities and Instabilities in Classical Lattice Gas Models without Periodic Ground States....Pages 161-163
One Dimensional Anomaly of the Fermi Surface....Pages 165-173
Quantum Fluctuation Limit: Examples from Solid State Physics....Pages 175-181
Large Deviations and the Thermodynamic Formalism: A New Proof of the Equivalence of Ensembles....Pages 183-192
Finitely Correlated Pure States....Pages 193-202
Stationary States of Hamiltonian Systems with Noise....Pages 203-214
Stochastic Regularization of Coherent-State Path Integrals and Quantum Hall Effect....Pages 215-223
An ADE-O Classification of Minimal Incompressible Quantum Hall Fluids....Pages 225-232
Simple Random Walks: New Developments....Pages 233-237
Symmetry Breaking and Long Range Order in Heisenberg Antiferromagnets....Pages 239-243
Integrable S=1/2 Quantum Spin Chains with Short-Range Exchange....Pages 245-251
Who is Afraid of Griffiths’ Singularities?....Pages 253-257
Micro Spectral Properties of Crystals and Their Band Structure....Pages 259-264
Stochastically Forced Burgers Equation....Pages 265-269
Glauber Evolution for KAC Potentials Analysis of Critical Fluctuations: Convergence to a Non Linear Stochastic PDE....Pages 271-274
Local Structure of Interfaces in a Kawasaki+Glauber Particle Model....Pages 275-279
Quantum Chaos, Fractal Spectra and Atomic Stabilization....Pages 281-288
Statistical Properties of Random Banded Matrices: Analytical Results....Pages 289-293
On the Wulff Construction as a Problem of Equivalence of Statistical Ensembles....Pages 295-302
Scaling Profiles of a Spreading Drop from Langevin or Monte-Carlo Dynamics....Pages 303-308
Rigorous Calculation of Collective Excitations in a Mean Field Model....Pages 309-314
The Fluid-Dynamical Limit for the BBGKY Hierarchy of a Discrete Velocity Model....Pages 315-320
Isospectral Deformation of Discrete Random Laplacians....Pages 321-330
Scattering and the Role of Operators in Bohmian Mechanics....Pages 331-338
Towards the Euclidean Formulation of Quantum Statistical Mechanics....Pages 339-346
Large Deviations in the Spherical Model....Pages 347-354
Entropy Density and the Split Property....Pages 355-359
Perturbations of Quantum Canonical Relations and Q-Independence....Pages 361-366
The Spectrum of the Spin-Boson Model....Pages 367-372
Some Results on the Projected Two-Dimensional Ising Model....Pages 373-380
The Second Virial Coefficient for Quantum-Mechanical Sticky Spheres....Pages 381-384
Bethe-Ansatz Solution of a Modified SU(3)-XXZ-Model....Pages 385-392
The Quantum Mean Field State as a Limit of Canonical States: Maxwell-Boltzmann Statistics....Pages 393-397
Multifractal Properties of Discrete Stochastic Mappings....Pages 399-404
Gibbs States of the Chern-Simons Charged Particle System in the Mean-Field Type Limit....Pages 405-407
Rigorous Bethe Ansatz for the Nonlinear Schroedinger Model....Pages 409-415
Flat Non-Regular States on Weyl Algebras....Pages 417-422
Second Virial Coefficient for One-Dimensional Systems....Pages 423-428
Self-Adjointness and the Existence of Deterministic Trajectories in Quantum Theory....Pages 429-434
An Application of the Maes-Shlosman Constructive Criteria....Pages 435-440
Brownian Trapping with Grouped Traps....Pages 441-444
Local Thermodynamic Equilibrium and Continuous Media: A Programme....Pages 445-449
Stochastic Model of a Quantum Diffusion-Reaction Process....Pages 451-456
Crystalisation of Itinerant Electrons....Pages 457-465
Molecular Chain: Dynamical Variables, Quantization and Statistical Mechanics....Pages 467-470
Back Matter....Pages 477-485
Quasiparticle’s Spin and Fractional Statistics in the Fractional Quantum Hall Effect....Pages 471-476

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Quantum Kinetic Equations; H. Spohn. Microscopic Derivation of Hydrodynamics with Phase Transition in a Plasma Model; G.L. Sewell. Ferromagnetism in Itinerant Electron Systems; H. Tasaki. Homogeneity in the Ground State of the Two-Dimensional Falicov-Kimabll Model; T.Kennedy. Diffusive Limit of the Asymmetric Simple Exclusion; R.Esposito, et al. Weak Coupling Limit; L.J. Landau. Limit Laws for Recurrence Times in Expanding Maps of an Interval; P. Collet. Stochastic Geometric Aspects of Some Quantum Spin Chains; B.Nachtergaele. The Species Totally Asymmetric Simple Exclusion Process; E.R. Speer. How to Reconstruct a Heat Bath; B. K?mmerer. Interacting Particle Systems on Non-Commutative Spaces; T. Matsui. Non-Self-Averaging Effects in Sums of Random Variables, Spin Glasses, Random Maps, and Random Walks; B. Derrida. Quantum Adiabatic Evolution; A. Joye, C.E. Pfister. 48 additional articles. Index.
Content:
Front Matter....Pages i-x
Quantum Kinetic Equations....Pages 1-10
Microscopic Derivation of Hydrodynamics with Phase Transition in a Plasma Model....Pages 11-21
Ferromagnetism in Itinerant Electron Systems: Rigorous Examples from Flat-Band Hubbard Models....Pages 23-33
Homogeneity in the Ground State of the Two-Dimensional Falicov-Kimball Model....Pages 35-41
Diffusive Limit of the Asymmetric Simple Exclusion: The Navier-Stokes Correction....Pages 43-51
Weak Coupling Limit: Feynman Diagrams....Pages 53-71
Limit Laws for Recurrence Times in Expanding Maps of an Interval....Pages 73-79
Stochastic Geometric Aspects of Some Quantum Spin Chains....Pages 81-89
The Two Species Totally Asymmetric Simple Exclusion Process....Pages 91-102
How to Reconstruct a Heat Bath....Pages 103-113
Interacting Particle Systems on Non-Commutative Spaces....Pages 115-123
Non-Self-Averaging Effects in Sums of Random Variables, Spin Glasses, Random Maps and Random Walks....Pages 125-137
Quantum Adiabatic Evolution....Pages 139-148
Semi-Classical Inelastic S-Matrix for One-Dimensional N-States Systems....Pages 149-154
Gibbsian versus Non-Gibbsian Measures: Some Results and Some Questions in Renormalization Group Theory and Stochastic Dynamics....Pages 155-160
Stabilities and Instabilities in Classical Lattice Gas Models without Periodic Ground States....Pages 161-163
One Dimensional Anomaly of the Fermi Surface....Pages 165-173
Quantum Fluctuation Limit: Examples from Solid State Physics....Pages 175-181
Large Deviations and the Thermodynamic Formalism: A New Proof of the Equivalence of Ensembles....Pages 183-192
Finitely Correlated Pure States....Pages 193-202
Stationary States of Hamiltonian Systems with Noise....Pages 203-214
Stochastic Regularization of Coherent-State Path Integrals and Quantum Hall Effect....Pages 215-223
An ADE-O Classification of Minimal Incompressible Quantum Hall Fluids....Pages 225-232
Simple Random Walks: New Developments....Pages 233-237
Symmetry Breaking and Long Range Order in Heisenberg Antiferromagnets....Pages 239-243
Integrable S=1/2 Quantum Spin Chains with Short-Range Exchange....Pages 245-251
Who is Afraid of Griffiths’ Singularities?....Pages 253-257
Micro Spectral Properties of Crystals and Their Band Structure....Pages 259-264
Stochastically Forced Burgers Equation....Pages 265-269
Glauber Evolution for KAC Potentials Analysis of Critical Fluctuations: Convergence to a Non Linear Stochastic PDE....Pages 271-274
Local Structure of Interfaces in a Kawasaki+Glauber Particle Model....Pages 275-279
Quantum Chaos, Fractal Spectra and Atomic Stabilization....Pages 281-288
Statistical Properties of Random Banded Matrices: Analytical Results....Pages 289-293
On the Wulff Construction as a Problem of Equivalence of Statistical Ensembles....Pages 295-302
Scaling Profiles of a Spreading Drop from Langevin or Monte-Carlo Dynamics....Pages 303-308
Rigorous Calculation of Collective Excitations in a Mean Field Model....Pages 309-314
The Fluid-Dynamical Limit for the BBGKY Hierarchy of a Discrete Velocity Model....Pages 315-320
Isospectral Deformation of Discrete Random Laplacians....Pages 321-330
Scattering and the Role of Operators in Bohmian Mechanics....Pages 331-338
Towards the Euclidean Formulation of Quantum Statistical Mechanics....Pages 339-346
Large Deviations in the Spherical Model....Pages 347-354
Entropy Density and the Split Property....Pages 355-359
Perturbations of Quantum Canonical Relations and Q-Independence....Pages 361-366
The Spectrum of the Spin-Boson Model....Pages 367-372
Some Results on the Projected Two-Dimensional Ising Model....Pages 373-380
The Second Virial Coefficient for Quantum-Mechanical Sticky Spheres....Pages 381-384
Bethe-Ansatz Solution of a Modified SU(3)-XXZ-Model....Pages 385-392
The Quantum Mean Field State as a Limit of Canonical States: Maxwell-Boltzmann Statistics....Pages 393-397
Multifractal Properties of Discrete Stochastic Mappings....Pages 399-404
Gibbs States of the Chern-Simons Charged Particle System in the Mean-Field Type Limit....Pages 405-407
Rigorous Bethe Ansatz for the Nonlinear Schroedinger Model....Pages 409-415
Flat Non-Regular States on Weyl Algebras....Pages 417-422
Second Virial Coefficient for One-Dimensional Systems....Pages 423-428
Self-Adjointness and the Existence of Deterministic Trajectories in Quantum Theory....Pages 429-434
An Application of the Maes-Shlosman Constructive Criteria....Pages 435-440
Brownian Trapping with Grouped Traps....Pages 441-444
Local Thermodynamic Equilibrium and Continuous Media: A Programme....Pages 445-449
Stochastic Model of a Quantum Diffusion-Reaction Process....Pages 451-456
Crystalisation of Itinerant Electrons....Pages 457-465
Molecular Chain: Dynamical Variables, Quantization and Statistical Mechanics....Pages 467-470
Back Matter....Pages 477-485
Quasiparticle’s Spin and Fractional Statistics in the Fractional Quantum Hall Effect....Pages 471-476
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