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1.

図書

図書
edited by Helmut Schwichtenberg and Ralf Steinbrüggen
出版情報: Dordrecht : Kluwer Academic, c2002  xii, 415 p. ; 25 cm
シリーズ名: NATO science series ; II . Mathematics, physics and chemistry ; v. 62
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Preface
Cartesian Closed Categories of Effective Domains / G. Hamrin ; V. Stoltenberg-Hansen
Algorithmic Game Semantics: A Tutorial Introduction / S. Abramsky
Algebra of Networks / G. Stefanescu
Computability and Complexity from a Programming Perspective / N. D. Jones
Logical Frameworks: A Brief Introduction / F. Pfenning
Ludics: An Introduction / J.-Y. Girard
Naive Computational Type Theory / R.L. Constable
Proof-Carrying Code. Design and Implementation / G. Necula
Abstractions and Reductions in Model Checking / O. Grumberg
Hoare Logic: From First-order to Propositional Formalism / J. Tiuryn
Hoare Logics in Isabelle/HOL / T. Nipkow
Proof Theoretic Complexity / G. E. Ostrin ; S. S. Wainer
Feasible Computation with Higher Types / H. Schwichtenberg ; S. J. Bellantoni
Preface
Cartesian Closed Categories of Effective Domains / G. Hamrin ; V. Stoltenberg-Hansen
Algorithmic Game Semantics: A Tutorial Introduction / S. Abramsky
2.

図書

図書
edited by Anne Bourlioux, Martin J. Gander and technical editor Gert Sabidussi
出版情報: Dordrecht : Kluwer Academic, c2002  xxii, 492 p. ; 25 cm
シリーズ名: NATO science series ; Series II . Mathematics, physics and chemistry ; v. 75
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Preface
Key to group picture
Participants
Contributors
Computation of large-scale quadratic forms and transfer functions using the theory of moments, quadrature and Pade approximation / Zhaojun Bai ; Gene Golub
Thin film dynamics: theory and applications / Andrea L. Bertozzi ; Mark Bowen
Numerical turbulent combustion: an asymptotic view via an idealized test-case / Anne Bourlioux
Multigrid methods: from geometrical to algebraic versions / Gundolf Haase ; Ulrich Langer
One-way operators, absorbing boundary conditions and domain decomposition for wave propagation / Laurence Halpern ; Adib Rahmouni
Deterministic and random dynamical systems: theory and numerics / Anthony R. Humphries ; Andrew M. Stuart
Optimal investment problems and volatility homogenization approximations / Mattias Jonsson ; Ronnie Sircar
Image processing with partial differential equations / Karol Mikula
Interface connections in domain decomposition methods / Frederic Nataf
A review of level set and fast marching methods for image processing / James A. Sethian
Recent developments in the theory of front propagation and its applications / Panagiotis E. Souganidis
Computing finite-time singularities in interfacial flows / Thomas P. Witelski
Index
Preface
Key to group picture
Participants
3.

図書

図書
edited by C. Guet ... [et al]
出版情報: Les Ulis : EDP sciences , Berlin ; Tokyo : Springer, c2001  xxxv, 584 p. ; 23 cm
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Lecturers
Preface
Contents
Experimental Aspects of Metal Clusters / T.P. MartinCourse 1:
Introduction / 1:
Subshells, shells and supershells / 2:
The experiment / 3:
Observation of electronic shell structure / 4:
Density functional calculation / 5:
Observation of supershells / 6:
Fission / 7:
Concluding remarks / 8:
Melting of Clusters / H. HaberlandCourse 2:
Cluster calorimetry
The bulk limit / 2.1:
Calorimetry for free clusters / 2.2:
Experiment
The source for thermalized cluster ions / 3.1:
Caloric curves
Melting temperatures / 4.1:
Latent heats / 4.2:
Other experiments measuring thermal properties of free clusters / 4.3:
A closer look at the experiment
Beam preparation / 5.1:
Reminder: Canonical versus microcanonical ensemble / 5.1.1:
A canonical distribution of initial energies / 5.1.2:
Free clusters in vacuum, a microcanonical ensemble / 5.1.3:
Analysis of the fragmentation process / 5.2:
Photo-excitation and energy relaxation / 5.2.1:
Mapping of the energy on the mass scale / 5.2.2:
Broadening of the mass spectra due to the statistics of evaporation / 5.2.3:
Canonical or microcanonical data evaluation / 5.3:
Results obtained from a closer look
Negative heat capacity / 6.1:
Entropy / 6.2:
Unsolved problems
Summary and outlook
Excitations in Clusters / G.F. BertschCourse 3:
Statistical reaction theory
Cluster evaporation rates
Electron emission
Radiative cooling / 2.3:
Optical properties of small particles
Connections to the bulk
Linear response and short-time behavior / 3.2:
Collective excitations / 3.3:
Calculating the electron wave function
Time-dependent density functional theory
Linear response of simple metal clusters
Alkali metal clusters
Silver clusters
Carbon structures
Chains
Polyenes
Benzene / 6.3:
C60 / 6.4:
Carbon nanotubes / 6.5:
Quantized conductance / 6.6:
Density Functional Theory, Methods, Techniques, and Applications / S. Chrétien ; D.R. SalahubCourse 4:
Density functional theory
Hohenberg and Kohn theorems
Levy's constrained search
Kohn-Sham method
Density matrices and pair correlation functions
Adiabatic connection or coupling strength integration
Comparing and constrasting KS-DFT and HF-CI
Preparing new functionals
Approximate exchange and correlation functionals
The Local Spin Density Approximation (LSDA) / 7.1:
Gradient Expansion Approximation (GEA) / 7.2:
Generalized Gradient Approximation (GGA) / 7.3:
meta-Generalized Gradient Approximation (meta-GGA) / 7.4:
Hybrid functionals / 7.5:
The Optimized Effective Potential method (OEP) / 7.6:
Comparison between various approximate functionals / 7.7:
LAP correlation functional
Solving the Kohn-Sham equations / 9:
The Kohn-Sham orbitals / 9.1:
Coulomb potential / 9.2:
Exchange-correlation potential / 9.3:
Core potential / 9.4:
Other choices and sources of error / 9.5:
Functionality / 9.6:
Applications / 10:
Ab initio molecular dynamics for an alanine dipeptide model / 10.1:
Transition metal clusters: The ecstasy, and the agony / 10.2:
Vanadium trimer / 10.2.1:
Nickel clusters / 10.2.2:
The conversion of acetylene to benzene on Fe clusters / 10.3:
Conclusions / 11:
Semiclassical Approaches to Mesoscopic Systems / M. BrackCourse 5:
Extended Thomas-Fermi model for average properties
Thomas-Fermi approximation
Wigner-Kirkwood expansion
Gradient expansion of density functionals
Density variational method / 2.4:
Applications to metal clusters / 2.5:
Restricted spherical density variation / 2.5.1:
Unrestricted spherical density variation / 2.5.2:
Liquid drop model for charged spherical metal clusters / 2.5.3:
Periodic orbit theory for quantum shell effects
Semiclassical expansion of the Green function
Trace formulae for level density and total energy
Calculation of periodic orbits and their stability
Uniform approximations / 3.4:
Supershell structure of spherical alkali clusters / 3.5:
Ground-state deformations / 3.5.2:
Applications to two-dimensional electronic systems / 3.6:
Conductance oscillations in a circular quantum dot / 3.6.1:
Integer quantum Hall effect in the two-dimensional electron gas / 3.6.2:
Conductance oscillations in a channel with antidots / 3.6.3:
Local-current approximation for linear response
Quantum-mechanical equations of motion
Variational equation for the local current density
Secular equation using a finite basis
Optic response in the jellium model / 4.4:
Optic response with ionic structure / 4.4.2:
Pairing Correlations in Finite Fermionic Systems / H. FlocardCourse 6:
Basic mechanism: Cooper pair and condensation
Condensed matter perspective: Electron pairs
Nuclear physics perspective: Two nucleons in a shell
Condensation of Cooper's pairs
Mean-field approach at finite temperature
Family of basic operators
Duplicated representation / 3.1.1:
Basic operators / 3.1.2:
BCS coefficients; quasi-particles / 3.1.3:
Wick theorem
BCS finite temperature equations
Density operator, entropy, average particle number / 3.3.1:
BCS equations / 3.3.2:
Discussion; problems for finite systems / 3.3.3:
Discussion; size of a Cooper pair / 3.3.4:
Discussion; low temperature BCS properties
First attempt at particle number restoration
Particle number projection
Projected density operator
Expectation values
Projected BCS at T = 0, expectation values
Projected BCS at T = 0, equations / 4.5:
Projected BCS at T = 0, generalized gaps and single particle shifts / 4.6:
Stationary variational principle for thermodynamics
General method for constructing stationary principles
Stationary action
Characteristic function
Transposition of the general procedure
General properties
Variational principle applied to extended BCS
Variational spaces and group properties
Extended BCS functional
Extended BCS equations
Properties of the extended BCS equations
Recovering the BCS solution
Beyond the BCS solution
Particle number projection at finite temperature
Particle number projected action
Number projected stationary equations: sketch of the method
Number parity projected BCS at finite temperature
Projection and action / 8.1:
Variational equations / 8.2:
Average values and thermodynamic potentials / 8.3:
Small temperatures / 8.4:
Even number systems / 8.4.1:
Odd number systems / 8.4.2:
Numerical illustration / 8.5:
Odd-even effects
Number parity projected free energy differences
Nuclear odd-even energy differences
Extensions to very small systems
Zero temperature
Finite temperatures
Conclusions and perspectives
Models of Metal Clusters and Quantum Dots / M. ManninenCourse 7:
Jellium model and the density functional theory
Spherical jellium clusters
Effect of the lattice
Tight-binding model
Shape deformation
Tetrahedral and triangular shapes
Odd-even staggering in metal clusters
Ab initio electronic structure: Shape and photoabsorption
Quantum dots: Hund's rule and spin-density waves
Deformation in quantum dots
Localization of electrons in a strong magnetic field / 12:
Theory of Cluster Magnetism / G.M. Pastor13:
Background on atomic and solid-state properties
Localized electron magnetism
Magnetic configurations of atoms: Hund's rules / 2.1.1:
Magnetic susceptibility of open-shell ions in insulators / 2.1.2:
Interaction between local moments: Heisenberg model / 2.1.3:
Stoner model of itinerant magnetism
Localized and itinerant aspects of magnetism in solids
Experiments on magnetic clusters
Ground-state magnetic properties of transition-metal clusters
Model Hamiltonians
Mean-field approximation
Second-moment approximation
Spin magnetic moments and magnetic order
Free clusters: Surface effects
Embedded clusters: Interface effects
Magnetic anisotropy and orbital magnetism
Relativistic corrections / 4.5.1:
Magnetic anisotropy of small clusters / 4.5.2:
Enhancement of orbital magnetism / 4.5.3:
Electron-correlation effects on cluster magnetism
The Hubbard model
Geometry optimization in graph space
Ground-state structure and total spin
Comparison with non-collinear Hartree-Fock / 5.4:
Finite-temperature magnetic properties of clusters
Spin-fluctuation theory of cluster magnetism
Environment dependence of spin fluctuation energies
Role of electron correlations and structural fluctuations
Conclusion
Electron Scattering on Metal Clusters and Fullerenes / A.V. Solov'yovCourse 9:
Jellium model: Cluster electron wave functions
Diffraction of fast electrons on clusters: Theory and experiment
Elements of many-body theory
Inelastic scattering of fast electrons on metal clusters
Plasmon resonance approximation: Diffraction phenomena, comparison with experiment and RPAE
Surface and volume plasmon excitations in the formation of the electron energy loss spectrum
Polarization effects in low-energy electron cluster collision and the photon emission process
How electron excitations in a cluster relax
Energy Landscapes / D.J. WalesCourse 10:
Levinthal's paradox / 1.1:
"Strong" and "fragile" liquids / 1.2:
The Born-Oppenheimer approximation
Normal modes
Orthogonal transformations
The normal mode transformation
Describing the potential energy landscape
Stationary points and pathways
Zero Hessian eigenvalues
Classification of stationary points
Pathways
Properties of steepest-descent pathways
Uniqueness
Steepest-descent paths from a transition state
Principal directions / 4.4.3:
Birth and death of symmetry elements / 4.4.4:
Classification of rearrangements
The Mclver-Stanton rules
Coordinate transformations / 4.7:
"Mass-weighted" steepest-descent paths / 4.7.1:
Sylvester's law of inertia / 4.7.2:
Branch points / 4.8:
Tunnelling
Tunnelling in (HF)(2)
Tunnelling in (H(2)O)(3)
Global thermodynamics
The superposition approximation
Sample incompleteness
Thermodynamics and cluster simulation
Example: Isomerisation dynamics of LJ7
Finite size phase transitions
Stability and van der Waals loops
Global optimisation
Basin-hopping global optimisation
Confinement Technique for Simulating Finite Many-Body Systems / S.F. ChekmarevCourse 11:
Key points and advantages of the confinement simulations: General remarks
Methods for generating phase trajectories
Conventional molecular dynamics
Stochastic molecular dynamics
Identification of atomic structures
Quenching procedure / .1:
Characterization of a minimum
Confinement procedures
Reversal of the trajectory at the boundary of the basin. Microcanonical ensemble
Initiating the trajectory at the point of the last quenching within the basin. Microcanonical and canonical ensembles
Confinement to a selected catchment area. Some applications
Fractional caloric curves and densities of states of the isomers
Rates of the transitions between catchment basins. Estimation of the rate of a complex transition by successive confinement
Creating a subsystem of a complex system. Self-diffusion in the subsystem of permutational isomers
Complex study of a system by successive confinement
Surveying a potential energy surface. Strategies
Strategies to survey a surface / 7.1.1:
A taboo search strategy. Fermi-like distribution over the minima / 7.1.2:
Kinetics
Equilibrium properties
Study of the alanine tetrapeptide
Molecular Clusters: Potential Energy and Free Energy Surfaces. Quantum Chemical ab initio and Computer Simulation Studies / P. HobzaCourse 12:
The hierarchy of interactions between elementary particles, atoms and molecules
The origin and phenomenological description of vdW interactions
Calculation of interaction energy
Vibrational frequencies
Potential energy surface
Free energy surface
Benzene .Ar clusters
Aromatic system dimers and oligomers
Nucleic acid-base pairs
Seminars by participants
Lecturers
Preface
Contents
4.

図書

図書
edited by M. Lesieur, A. Yaglom and F. David
出版情報: Les Ulis : EDP sciences , Berlin ; Tokyo : Springer, c2001  xxxvii, 554 p. ; 23 cm
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5.

図書

図書
edited by Didier Chatenay ... [et al.]
出版情報: Amsterdam ; Tokyo : Elsevier, 2005  xxiv, 354 p. ; 24 cm
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6.

図書

図書
edited by C.C. Chow ... [et al.]
出版情報: Amsterdam ; Tokyo : Elsevier, 2005  xxxii, 829 p. ; 24 cm
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7.

図書

図書
édité par A. Connes, K. Gawedzki, et J. Zinn-Justin
出版情報: Amsterdam ; Tokyo : Elsevier Science, c1998  xxxvii, 990 p. ; 23 cm
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Lecturers
Seminar Speakers
Participants
Preface (French)
Preface (English)
Mathematics / Part I.:
Fields, Strings and Duality / R. DijkgraafCourse 1.:
Introduction / 1.:
What is a quantum field theory? / 2.:
Axioms vs. path-integrals / 2.1.:
Duality / 2.2.:
Quantum mechanics / 3.:
Supersymmetric quantum mechanics / 3.1.:
Quantum mechanics and perturbative field theory / 3.2.:
Two-dimensional topological field theory / 4.:
Axioms of topological field theory / 4.1.:
Topological field theory in two dimensions / 4.2.:
Example - quantum cohomology / 4.3.:
Riemann surfaces and moduli / 5.:
The moduli space of curves / 5.1.:
Example - genus one / 5.2.:
Surfaces with punctures / 5.3.:
The stable compactification / 5.4.:
Conformal field theory / 6.:
Algebraic approach / 6.1.:
Functorial approach / 6.2.:
Free bosons / 6.3.:
Free fermions / 6.4.:
Sigma models and T-duality / 7.:
Two-dimensional sigma models / 7.1.:
Toroidal models / 7.2.:
Intermezzo - lattices / 7.3.:
Spectrum and moduli of toroidal models / 7.4.:
The two-torus / 7.5.:
Path-integral computation of the partition function / 7.6.:
Supersymmetric sigma models and Calabi-Yau spaces / 7.7.:
Calabi-Yau moduli space and special geometry / 7.8.:
Perturbative string theory / 8.:
Axioms for string vacua / 8.1.:
Intermezzo - twisting and supersymmetry / 8.2.:
Example - The critical bosonic string / 8.3.:
Example - Twisted N = 2 SCFT / 8.4.:
Example - twisted minimal model / 8.5.:
Example - topological string / 8.6.:
Functorial definition / 8.7.:
Tree-level amplitudes / 8.8.:
Families of string vacua / 8.9.:
The Gauss-Manin connection / 8.10.:
Anti-holomorphic dependence and special geometry / 8.11.:
Local special geometry / 8.12.:
Gauge theories and S-duality / 9.:
Introduction to four-dimensional geometry / 9.1.:
The Lorentz group / 9.2.:
Duality in Maxwell theory / 9.3.:
The partition function / 9.4.:
Higher rank groups / 9.5.:
Dehn twists and monodromy / 9.6.:
Moduli spaces / 10.:
Supersymmetric or BPS configurations / 10.1.:
Localization in topological field theories / 10.2.:
Quantization / 10.3.:
Families of QFTs / 10.4.:
Moduli spaces of vacua / 10.5.:
Supersymmetric gauge theories / 11.:
Twisting and Donaldson theory / 11.1.:
Observables / 11.3.:
Abelian models / 11.4.:
Rigid special geometry / 11.5.:
Families of abelian varieties / 11.6.:
BPS states / 11.7.:
Non-abelian N = 2 gauge theory / 11.8.:
The Seiberg-Witten solution / 11.9.:
Physical interpretation of the singularities / 11.10.:
Implications for four-manifold invariants / 11.11.:
String vacua / 12.:
Perturbative string theories / 12.1.:
IIA or IIB / 12.2.:
D-branes / 12.3.:
Compactification / 12.4.:
Singularities revisited / 12.5.:
String moduli spaces / 12.6.:
Example - Type II on T[superscript 6] / 12.7.:
BPS states and D-branes / 13.:
Perturbative string states / 13.1.:
Perturbative BPS states / 13.2.:
D-brane states / 13.3.:
Example - Type IIA on K3 = Heterotic on T[superscript 4] / 13.4.:
Example - Type II on T[superscript 4] / 13.5.:
Example - Type II on K3 [times] S[superscript 1] = Heterotic on T[superscript 5] / 13.6.:
Example - Type IIA on X = Type IIB on Y / 13.7.:
References
How the Algebraic Bethe Ansatz Works for Integrable Models / L.D. FaddeevCourse 2.:
General outline of the course
XXX[subscript 1/2] model. Description
XXX[subscript 1/2] model. Bethe Ansatz equations
XXX[subscript 1/2] model. Physical spectrum in the ferromagnetic thermodynamic limit
XXX[subscript 1/2] model. BAE for an arbitrary configuration
XXX[subscript 1/2] model. Physical spectrum in the antiferromagnetic case
XXX[subscript s] model
XXX[subscript s] spin chain. Applications to the physical systems
XXZ model
Inhomogeneous chains and discrete time shift
Examples of dynamical models in discrete space-time
Conclusions and perspectives
Comments on the literature on BAE / 14.:
Supersymmetric Quantum Theory, Non-Commutative Geometry, and Gravitation / J. Frohlich ; O. Grandjean ; A. RecknagelCourse 3.:
The classical theory of gravitation
(Non-relativistic) quantum theory
Reconciling quantum theory with general relativity: quantum space-time-matter
Classical differential topology and -geometry and supersymmetric quantum theory
Pauli's electron
The special case where M is a Lie group
Supersymmetric quantum theory and geometry put into perspective
Supersymmetry and non-commutative geometry
Spin[superscript c] non-commutative geometry
The spectral data of spin[superscript c] NCG / 5.1.1.:
Differential forms / 5.1.2.:
Integration / 5.1.3.:
Vector bundles and Hermitian structures / 5.1.4.:
Generalized Hermitian structure on [Omega superscript k](A) / 5.1.5.:
Connections / 5.1.6.:
Riemannian curvature and torsion / 5.1.7.:
Generalized Kahler non-commutative geometry and higher supersymmetry / 5.1.8.:
Aspects of the algebraic topology of N = n supersymmetric spectral data / 5.1.9.:
Non-commutative Riemannian geometry
N = (1, 1) supersymmetry and Riemannian geometry / 5.2.1.:
Unitary connections and scalar curvature / 5.2.2.:
Remarks on the relation between N = 1 and N = (1, 1) spectral data / 5.2.5.:
Riemannian and spin[superscript c] "manifolds" in non-commutative geometry / 5.2.6.:
Algebraic topology of N = [characters not reproducible] spectral data / 5.2.7.:
Central extensions of supersymmetry, and equivariance / 5.2.8.:
N = (n, n) supersymmetry, and supersymmetry breaking / 5.2.9.:
Reparametrization invariance, BRST cohomology, and target space supersymmetry
The non-commutative torus
Spin geometry (N = 1) / 6.1:
Integration and Hermitian structure over [Omega superscript 1 subscript D](A[alpha]) / 6.1.1.:
Connections on [Omega superscript 1 subscript D](A[alpha]) / 6.1.3.:
Riemannian geometry (N = [characters not reproducible]
Kahler geometry (N = [characters not reproducible]
Applications of non-commutative geometry to quantum theories of gravitation
From point-particles to strings
A Schwinger-Dyson equation for string Green functions from reparametrization invariance and world-sheet supersymmetry
Some remarks on M(atrix) models
Two-dimensional conformal field theories
Recap of two-dimensional, local quantum field theory / 7.4.1.:
A dictionary between conformal field theory and Lie group theory / 7.4.2.:
Reconstruction of (non-commutative) target spaces from conformal field theory
Superconformal field theories, and the topology of target spaces
The N = 1 super-Virasoro algebra / 7.6.1.:
N = 2 and N = 4 supersymmetry; mirror symmetry / 7.6.2.:
Conclusions
Lectures on the Quantum Geometry of String Theory / B.R. GreeneCourse 4.:
What is quantum geometry? / 1.1.:
The ingredients / 1.2.:
The N = 2 superconformal algebra
The algebra
Representation theory of the N = 2 superconformal algebra
Chiral primary fields / 2.3.:
Spectral flow and the U(1) projection / 2.4.:
Four examples / 2.5.:
Example one: free field theory / 2.5.1.:
Example two: nonlinear sigma models / 2.5.2.:
Example three: Landau-Ginzburg models / 2.5.3.:
Example four: minimal models / 2.5.4.:
Families of N = 2 theories
Marginal operators
Moduli spaces: I
Interrelations between various N = 2 superconformal theories
Landau-Ginzburg theories and minimal models
Minimal models and Calabi-Yau manifolds: a conjectured correspondence
Arguments establishing minimal-model/Calabi-Yau correspondence
Mirror manifolds
Strategy of the construction
Minimal models and their automorphisms
Direct calculation
Constructing mirror manifolds
Examples / 5.5.:
Implications / 5.6.:
Spacetime topology change
Basic ideas
Mild topology change
Kahler moduli space / 6.2.1.:
Complex structure moduli space / 6.2.3.:
Implications of mirror manifolds: revisited / 6.2.4.:
Flop transitions / 6.2.5.:
An example / 6.2.6.:
Drastic topology change
Strominger's resolution of the conifold singularity / 6.3.1.:
Conifold transitions and topology change / 6.3.3.:
Symmetry Approach to the XXZ Model / T. MiwaCourse 5.:
The XXZ Hamiltonian for [Delta] [ -1
Transfer matrix
Symmetry of U[subscript q](sl[subscript 2])
Corner transfer matrix
Level 1 highest weight module
Half transfer matrix
Intertwiners
The vacuum vector
Diagonalization of the transfer matrix
Local operators and difference equations
Superstring Dualities, Dirichlet Branes and the Small Scale Structure of Space / M.R. DouglasSeminar 1.:
Duality and solitons in supersymmetric field theory
Duality and solitons in superstring theory
Dirichlet branes
Short distances in superstring theory
Further directions
Testing the Standard Model and Beyond / J. EllisSeminar 2.:
Introduction to the Standard Model and its (non-topological) defects
Testing the Standard Model
The electroweak vacuum
Motivations for supersymmetry
Model building
Physics with the LHC
Quantum Group Approach to Strongly Coupled Two Dimensional Gravity / J.-L. GervaisSeminar 3.:
Basic points about Liouville theory
The basic relations between 6j symbols
The Liouville string
Concluding remarks
N = 2 Superalgebra and Non-Commutative Geometry / H. Grosse ; C. Klimcik ; P. PresnajderSeminar 4.:
Commutative supersphere
Non-commutative supersphere
Outlook
Lecture on N = 2 Supersymmetric Gauge Theory / W. LercheSeminar 5.:
Semi-classical N = 2 Yang-Mills theory for G = SU(2)
The exact quantum moduli space
Solving the monodromy problem
Picard-Fuchs equations
Generalization to SU(n)
Physics / Part II.:
Noncommutative Geometry: The Spectral Aspect / A. ConnesCourse 6.:
Noncommutative geometry: an introduction
Infinitesimal calculus
Local index formula and the transverse fundamental class
The notion of manifold and the axioms of geometry
The spectral geometry of space-time
The KZB Equations on Riemann Surfaces / G. FelderCourse 7.:
Conformal blocks on Riemann surfaces
Kac-Moody groups
Principal G-bundles
Conformal blocks
The connection
The energy-momentum tensor
Flat structures
Connections on bundles of projective spaces / 3.3.:
The Friedan-Shenker connection / 3.4.:
The Knizhnik-Zamolodchikov-Bernard equations
Dynamical r-matrices
An explicit form for the connection
Transformation properties
Moving points
Fixing the complex structure
Proof of Theorem 5.2
From Diffeomorphism Groups to Loop Spaces via Cyclic Homology / J.-L. LodayCourse 8.:
Diffeomorphism group and pseudo-isotopy space
Algebraic K-theory via Quillen +-construction
The +-construction
First definition of Waldhausen's space A(X)
The Grothendieck group K[subscript 0]
Hochschild and cyclic homology, Lie algebras
Hochschild homology
Cyclic homology
Relationship with the Lie algebra homology of matrices
Computing A(X) out of the loop space [Lambda]X
Algebraic K-theory via Waldhausen S.-construction and Wh(X)
Waldhausen S.-construction
A(X) and Wh(X) via the S.-construction
Relating Wh(X) to pseudo-isotopy
Notation and terminology in algebraic topology / Appendix A.:
Homotopy theory / A.1.:
Classifying spaces / A.2.:
Simplicial sets and classifying spaces / Appendix B.:
More on classifying spaces of categories / B.1.:
Bisimplicial sets / B.2.:
References with comments
Quantum Groups and Braid Groups / M. RossoCourse 9.:
The Yang-Baxter equation, braid groups and Hopf algebras
Drinfeld's quantum double
The dual double construction
The quantum double and its properties
Hopf pairings and a generalized double
The quantized enveloping algebra U[subscript q]G
Construction of U[subscript q]G
A Hopf pairing U[subscript +] [times] U[subscript -] [right arrow] C(q) / 4.1.1.:
Some results from representation theory
The quantum shuffle construction
The quantum shuffle Hopf algebra
Hopf bimodules
Braidings
The cotensor Hopf algebra
The quantum symmetric algebra
The examples from abelian group algebras
A classification result
Multiplicative bases in the quantum shuffle algebra / 5.3.1.:
Consequences of growth conditions / 5.3.2.:
From Index Theory to Non-Commutative Geometry / N. TelemanCourse 10.:
Differential forms on smooth and Lipschitz manifolds
Riemannian metrics and L[subscript 2]-forms on smooth and Lipschitz manifolds
Hodge theory on smooth and Lipschitz manifolds
Analytical index of Fredholm operators on smooth and Lipschitz manifolds
Topological K-theory
Symbols of elliptic operators on smooth manifolds and their index
Characteristic classes, Chern character
Stiefel-Whitney classes of real vector bundles
Chern classes of complex vector bundles
Pontrjagin classes of real vector bundles
Chern-Weyl theory on smooth manifolds
Thom isomorphism
Thom isomorphism in cohomology
Thom isomorphism in K-theory
Comparison between the Thom isomorphism in cohomology and K-theory
Index theorem for smooth manifolds
Index theorem for Lipschitz manifolds
Quasi local formulas for Thom-Hirzebruch classes on quasi conformal manifolds
Compact Quantum Groups / S.L. WoronowiczCourse 11.:
Definitions and results
The Haar measure
Unitary representations
Right regular representation
The Hopf algebras
Peter-Weyl theory
Groups with faithful Haar measure
Seiberg-Witten Invariants and Vortex Equations / O. Garcia-PradaSeminar 6.:
Preliminaries on spin geometry, almost-complex geometry and self-duality
The Seiberg-Witten invariants
Kahler complex surfaces
Non-Kahler complex surfaces
Symplectic four-manifolds
Non-Abelian monopole equations
Quantization of Poisson Algebraic Groups and Poisson Homogeneous Spaces / P. Eting of ; D. KazhdanSeminar 7.:
Quantization of Poisson algebraic and Lie groups
Quantization of Poisson homogeneous spaces
Eta and Torsion / J. LottSeminar 8.:
Eta-invariant
Analytic torsion
Eta-forms
Analytic torsion forms
Symplectic Formalism in Conformal Field Theory / A. SchwarzSeminar 9.:
Symplectic formalism in classical field theory
Superconformal geometry
Superconformal field theory
Quantization of geometry associated to the quantized Knizhnik-Zamolodchikov equations / A. VarchenkoSeminar 10.:
KZ equations
Hypergeometric functions
Geometry of hypergeometric functions
qKZ equations
Solutions to the qKZ equations and eigenvectors of commuting Hamiltonians
Solutions to the qKZ equations
Difference equations of the discrete connection
p-Homology theory
Conclusion
Lecturers
Seminar Speakers
Participants
8.

図書

図書
edited by Alirio E. Rodrigues, Josepf M. Calo and Norman H. Sweed
出版情報: Alphen aan den Rijn : Sijthoff & Noordhoff, 1981  vii, 600 p. ; 25 cm
シリーズ名: NATO advanced study institutes series ; . Series E, Applied sciences ; no. 51 . Multiphase chemical reactors ; v. 1
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9.

図書

図書
edited by Alirio E. Rodrigues, Josepf M. Calo and Norman H. Sweed
出版情報: Alphen aan den Rijn : Sijthoff & Noordhoff, 1981  vii, 513 p. ; 25 cm
シリーズ名: NATO advanced study institutes series ; . Series E, Applied sciences ; no. 52 . Multiphase chemical reactors ; v. 2
所蔵情報: loading…
10.

図書

図書
edited by H. Bouchiat ... [et al.]
出版情報: Amsterdam : Elsevier, 2005  xxxii, 607 p. ; 24 cm
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目次情報: 続きを見る
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Preface
Fundamental aspects of electron correlations and quantum transport in one-dimensional systems / Dmitrii L. MaslovCourse 1:
Introduction / 1:
Non-Fermi liquid features of Fermi liquids: 1D physics in higher dimensions / 2:
Long-range effective interaction / 2.1:
1D kinematics in higher dimensions / 2.2:
Infrared catastrophe / 2.3:
Dzyaloshinskii-Larkin solution of the Tomonaga-Luttinger model / 3:
Hamiltonian, anomalous commutators, and conservation laws / 3.1:
Reducible and irreducible vertices / 3.2:
Ward identities / 3.3:
Effective interaction / 3.4:
Dyson equation for the Green's function / 3.5:
Solution for the case g[subscript 2] = g[subscript 4] / 3.6:
Physical properties / 3.7:
Renormalization group for interacting fermions / 4:
Single impurity in a 1D system: scattering theory for interacting fermions / 5:
First-order interaction correction to the transmission coefficient / 5.1:
Renormalization group / 5.2:
Electrons with spins / 5.3:
Comparison of bulk and edge tunneling exponents / 5.4:
Bosonization solution / 6:
Spinless fermions / 6.1:
Fermions with spin / 6.2:
Transport in quantum wires / 7:
Conductivity and conductance / 7.1:
Dissipation in a contactless measurement / 7.2:
Conductance of a wire attached to reservoirs / 7.3:
Spin component of the conductance / 7.4:
Thermal conductance: Fabry-Perrot resonances of plasmons / 7.5:
Polarization bubble for small q in arbitrary dimensionality / Appendix A:
Polarization bubble in 1D / Appendix B:
Small q / Appendix B.1:
q near 2k[subscript F] / Appendix B.2:
Some details of bosonization procedure / Appendix C:
Anomalous commutators / Appendix C.1:
Bosonic operators / Appendix C.2:
Problem with backscattering / Appendix C.3:
References
Impurity in the Tomonaga-Luttinger model: A functional integral approach / I.V. Lerner ; I.V. YurkevichSeminar 1:
Functional integral representation
The effective action for the Tomonaga-Luttinger Model
The bosonized action for free electrons
Gauging out the interaction
Tunnelling density of states near a single impurity
Jacobian of the gauge transformation
Novel phenomena in double layer two-dimensional electron systems / J.P. EisensteinCourse 2:
Overview of physics in the quantum hall regime
Basics
Quantized hall effects
Double layer systems
Coulomb drag between parallel 2D electron gases
Basic concept
Experimental
Elementary theory of Coulomb drag
Comparison between theory and experiment
Tunneling between parallel two-dimensional electron gases
Ideal 2D-2D tunneling / 4.1:
Lifetime broadening / 4.2:
2D-2D tunneling in a perpendicular magnetic field / 4.3:
Strongly-coupled bilayer 2D electron systems and excitonic superfluidity
Quantum hall ferromagnetism
Tunneling and interlayer phase coherence at v[subscript T] = 1
Excitonic superfluidity at v[subscript T] = 1
Detecting excitonic superfluidity / 5.5:
Conclusions
Many-body theory of non-equilibrium systems / Alex KamenevCourse 3:
Motivation and outline / 1.1:
Closed time contour / 1.2:
Free boson systems
Partition function
Green functions
Keldysh rotation
Keldysh action and causality / 2.4:
Free bosonic fields / 2.5:
Collisions and kinetic equation
Interactions
Saddle point equations
Dyson equation
Self-energy
Kinetic term
Collision integral
Particle in contact with an environment
Quantum dissipative action
Saddle-point equation
Classical limit
Langevin equations / 4.4:
Martin-Siggia-Rose / 4.5:
Thermal activation / 4.6:
Fokker-Planck equation / 4.7:
From Matsubara to Keldysh / 4.8:
Dissipative chains and membranes / 4.9:
Fermions
Free fermion Keldysh action
External fields and sources
Tunneling current
Kinetic equation / 5.6:
Disordered fermionic systems
Disorder averaging
Non-linear [sigma]-model
Usadel equation / 6.3:
Fluctuations / 6.4:
Spectral statistics / 6.5:
Gaussian integration
Single particle quantum mechanics
Non-linear quantum coherence effects in driven mesoscopic systems / V.E. KravtsovCourse 4:
Weak Anderson localization in disordered systems
Drude approximation
Beyond Drude approximation
Weak localization correction
Non-linear response to a time-dependent perturbation
General structure of nonlinear response function
Approximation of single photon absorption/emission
Quantum rectification by a mesoscopic ring
Diffusion in the energy space
Quantum correction to absorption rate
Weak dynamic localization and no-dephasing points
Conclusion and open questions / 8:
Noise in mesoscopic physics / T. MartinCourse 5:
Poissonian noise
The wave packet approach
Generalization to the multi-channel case
Scattering approach based on operator averages
Average current
Noise and noise correlations
Zero frequency noise in a two terminal conductor
Noise reduction in various systems
Noise correlations at zero frequency
General considerations
Noise correlations in a Y-shaped structure
Finite frequency noise
Which correlator is measured?
Noise measurement scenarios
Finite frequency noise in point contacts
Noise in normal metal-superconducting junctions
Bogolubov transformation and Andreev current / 8.1:
Noise in normal metal-superconductor junctions / 8.2:
Noise in a single NS junction / 8.3:
Hanbury-Brown and Twiss experiment with a superconducting source of electrons / 8.4:
Noise and entanglement / 9:
Filtering spin/energy in superconducting forks / 9.1:
Tunneling approach to entanglement / 9.2:
Bell inequalities with electrons / 9.3:
Noise in Luttinger liquids / 10:
Edge states in the fractional quantum Hall effect / 10.1:
Transport between two quantum Hall edges / 10.2:
Keldysh digest for tunneling / 10.3:
Backscattering current / 10.4:
Poissonian noise in the quantum Hall effect / 10.5:
Effective charges in quantum wires / 10.6:
Higher moments of noise / Bertrand Reulet11:
The probability distribution P(i)
A simple model for a tunnel junction
Noise in Fourier space
Consequences
Effect of the environment
Imperfect voltage bias
Imperfect thermalization
Principle of the experiment
Possible methods
Experimental setup
Experimental results
Third moment vs. voltage and temperature
Effect of the detection bandwidth
Perspectives
Quantum regime
Noise thermal impedance
Conclusion
Electron subgap transport in hybrid systems combining superconductors with normal or ferromagnetic metals / F.W.J. HekkingCourse 6:
NS junctions in the clean limit
Single particle tunnelling in a tunnel junction
Bogoliubov-de Gennes equations
Disordered NIS junctions
Perturbation theory for NIS junction
Example: quasi-one-dimensional diffusive wire connected to a superconductor
Subgap noise of a superconductor-normal-metal tunnel interface
Tunnelling in a three-terminal system containing ferromagnetic metals
Co-tunnelling and crossed Andreev tunnelling rates
Discussion
Low-temperature transport through a quantum dot / Leonid I. Glazman ; Michael PustilnikCourse 7:
Model of a lateral quantum dot system
Thermally-activated conduction
Onset of Coulomb blockade oscillations
Coulomb blockade peaks at low temperature
Activationless transport through a blockaded quantum dot
Inelastic co-tunneling
Elastic co-tunneling
Kondo regime in transport through a quantum dot
Effective low-energy Hamiltonian
Linear response
Weak coupling regime: T[subscript K double less-than sign] T [double less-than sign delta]E
Strong coupling regime: T [double less-than sign] T[subscript K]
Beyond linear response
Splitting of the Kondo peak in a magnetic field
Kondo effect in quantum dots with large spin / 5.7:
Concluding remarks
Transport through quantum point contacts / Yigal MeirSeminar 3:
Spin-density-functional calculations
The Anderson model
Results
Current noise
Transport at the atomic scale: Atomic and molecular contacts / A. Levy Yeyati ; J.M. van RuitenbeekCourse 8:
Parity oscillations in atomic chains
Superconducting quantum point contacts
The Hamiltonian approach
Comparison to experimental results
Environmental effects
Classical phase diffusion
Dynamical Coulomb blockade
Single-molecule junctions
Solid State Quantum Bit Circuits / Daniel Esteve ; Denis VionCourse 9:
Why solid state quantum bits?
From quantum mechanics to quantum machines
Quantum processors based on qubits
Atom and ion versus solid state qubits / 1.3:
Electronic qubits / 1.4:
Qubits in semiconductor structures
Kane's proposal: nuclear spins of P impurities in silicon
Electron spins in quantum dots
Charge states in quantum dots
Flying qubits
Superconducting qubit circuits
Josephson qubits
How to maintain quantum coherence?
The quantronium circuit
Relaxation and dephasing in the quantronium
Readout
Coherent control of the qubit
Ultrafast 'DC' pulses versus resonant microwave pulses
NMR-like control of a qubit
Probing qubit coherence
Relaxation
Decoherence during free evolution
Decoherence during driven evolution
Qubit coupling schemes
Tunable versus fixed couplings
A tunable coupling element for Josephson qubits
Fixed coupling Hamiltonian
Control of the interaction mediated by a fixed Hamiltonian
Running a simple quantum algorithm
Conclusions and perspectives
Abstracts of seminars presented at the School
Lecturers
Seminar speakers
Participants
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