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1.

電子ブック

EB
Arkady Pikovsky, Jürgen Kurths, Michael Rosenblum
出版情報: Cambridge University Press Online Books , Cambridge : Cambridge University Press, 2001
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Preface
Introduction / 1:
Synchronization Without Formulae / Part I:
Basic notions: the self-sustained oscillator and its phase / 2:
Synchronization of a periodic oscillator by external force / 3:
Synchronization of two and many oscillators / 4:
Synchronization of chaotic systems / 5:
Detecting synchronization in experiments / 6:
Phase Locking and Frequency Entrainment / Part II:
Synchronization of periodic oscillators by periodic external action / 7:
Mutual synchronization of two interacting periodic oscillators / 8:
Synchronization in the presence of noise / 9:
Phase synchronization of chaotic systems / 10:
Synchronization in oscillatory media / 11:
Populations of globally coupled oscillators / 12:
Synchronization of Chaotic Systems / Part III:
Complete synchronization I: basic concepts / 13:
Complete synchronization II: generalizations and complex systems / 14:
Synchronization of complex dynamics by external forces / 15:
Discovery of synchronization by Christiaan Huygens / Appendix 1:
Instantaneous phase and frequency of a signal / Appendix 2:
References
Index
Cycling attractors of coupled cell systems and dynamics with symmetry / Ashwin ; Rucklidge ; Sturman
Modelling diversity by chaos and classification by synchronization / De Feo ; Hasler
Basic Principles of Direct Chaotic Communications / Dmitriev ; Panas ; Zakharchenko
Prevalence of Milnor Attractors and Chaotic Itinerancy in 'High'-dimensional Dynamical Systems / Kaneko
Generalization of the Feigenbaum-Kadanoff-Shenker Renormalization and Critical Phenomena Associated with the Golden Mean Quasiperiodicity / Kuznetsov
Synchronization and clustering in ensembles of coupled chaotic oscillators / Maistrenko ; Popovych ; Yanchuk
Nonlinear Phenomena in Nephron-Nephron Interaction / Mosekilde ; Sosnovtseva ; Holstein-Rathlou
Synchrony in Globally Coupled Chaotic, Periodic, and Mixed Ensembles of Dynamical Units / Ott ; So ; Barreto ; Antonsen
Phase synchronization of regular and chaotic self-sustained oscillators / Pikovsky ; Rosenblum
Control of dynamical systems via time-delayed feedback and unstable controller / Pyragas
Preface
Introduction / 1:
Synchronization Without Formulae / Part I:
2.

電子ブック

EB
U. Mizutani
出版情報: Cambridge University Press Online Books , Cambridge : Cambridge University Press, 2001
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Introduction to electron theory of metals / 1:
Bonding styles and the free electron model / 2:
Electrons in a metal at finite temperatures / 3:
Periodic lattice and lattice vibrations in crystals / 4:
Conduction electrons in a periodic potential / 5:
Electronic structure of pure elements in periodic table / 6:
Principles of measuring electronic structure related phenomena / 7:
Electronic structure calculations / 8:
Electronic structure of alloys / 9:
Electron transport properties in periodic systems (I) / 10:
Electronic transport properties in crystal metals (II) / 11:
Superconductivity / 12:
Magnetism, electronic structure and electron transport properties in magnetic metals / 13:
Electronic structure of strongly correlated electron systems / 14:
Electronic structure and electron transport properties of liquid metals, amorphous metals and quasicrystals / 15:
Introduction to electron theory of metals / 1:
Bonding styles and the free electron model / 2:
Electrons in a metal at finite temperatures / 3:
3.

電子ブック

EB
Harry Paul, Igor Jex
出版情報: Cambridge University Press Online Books , Cambridge : Cambridge University Press, 2004
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4.

電子ブック

EB
Rashmi C. Desai, Raymond Kapral
出版情報: Cambridge University Press Online Books , 2009
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Preface
Self-organized and self-assembled structures / 1:
Order parameter, free energy and phase transitions / 2:
Free energy functional / 3:
Phase separation kinetics / 4:
Langevin model for nonconserved order parameter systems / 5:
Langevin model for conserved order parameter systems / 6:
Interface dynamics at late times / 7:
Domain growth and structure factor for model B / 8:
Order parameter correlation function / 9:
Vector order parameter and topological defects / 10:
Liquid crystals / 11:
Lifshitz-Slyozov-Wagner theory / 12:
Systems with long-range repulsive interactions / 13:
Kinetics of systems with competing interactions / 14:
Competing interactions and defect dynamics / 15:
Diffusively-rough interfaces / 16:
Morphological instability in solid films / 17:
Propagating chemical fronts / 18:
Transverse front instabilities / 19:
Cubic autocatalytic fronts / 20:
Competing interactions and front repulsion / 21:
Labyrinthine patterns in chemical systems / 22:
Turing patterns / 23:
Excitable media / 24:
Oscillatory media and complex Ginzburg-Landau equation / 25:
Spiral waves and defect turbulence / 26:
Complex-oscillatory media / 27:
Resonantly-forced oscillatory media / 28:
Nonequilibrium patterns in laser-induced melting / 29:
Reaction dynamics and phase segregation / 30:
Active materials / 31:
References
Index
Preface
Self-organized and self-assembled structures / 1:
Order parameter, free energy and phase transitions / 2:
5.

電子ブック

EB
Jerzy Plebanski, Andrzej Krasinski
出版情報: Cambridge University Press Online Books , Leiden : Cambridge University Press, 2006
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List of figures
The scope of this text
Acknowledgements
How the theory of relativity came into being (a brief historical sketch) / 1:
Special versus general relativity / 1.1:
Space and inertia in Newtonian physics / 1.2:
Newton's theory and the orbits of planets / 1.3:
The basic assumptions of general relativity / 1.4:
Elements of differential geometry / Part I:
A short sketch of 2-dimensional differential geometry / 2:
Constructing parallel straight lines in a flat space / 2.1:
Generalisation of the notion of parallelism to curved surfaces / 2.2:
Tensors, tensor densities / 3:
What are tensors good for? / 3.1:
Differentiable manifolds / 3.2:
Scalars / 3.3:
Contravariant vectors / 3.4:
Covariant vectors / 3.5:
Tensors of second rank / 3.6:
Tensor densities / 3.7:
Tensor densities of arbitrary rank / 3.8:
Algebraic properties of tensor densities / 3.9:
Mappings between manifolds / 3.10:
The Levi-Civita symbol / 3.11:
Multidimensional Kronecker deltas / 3.12:
Examples of applications of the Levi-Civita symbol and of the multidimensional Kronecker delta / 3.13:
Exercises / 3.14:
Covariant derivatives / 4:
Differentiation of tensors / 4.1:
Axioms of the covariant derivative / 4.2:
A field of bases on a manifold and scalar components of tensors / 4.3:
The affine connection / 4.4:
The explicit formula for the covariant derivative of tensor density fields / 4.5:
Parallel transport and geodesic lines / 4.6:
Parallel transport / 5.1:
Geodesic lines / 5.2:
The curvature of a manifold; flat manifolds / 5.3:
The commutator of second covariant derivatives / 6.1:
The commutator of directional covariant derivatives / 6.2:
The relation between curvature and parallel transport / 6.3:
Covariantly constant fields of vector bases / 6.4:
A torsion-free flat manifold / 6.5:
Parallel transport in a flat manifold / 6.6:
Geodesic deviation / 6.7:
Algebraic and differential identities obeyed by the curvature tensor / 6.8:
Riemannian geometry / 6.9:
The metric tensor / 7.1:
Riemann spaces / 7.2:
The signature of a metric, degenerate metrics / 7.3:
Christoffel symbols / 7.4:
The curvature of a Riemann space / 7.5:
Flat Riemann spaces / 7.6:
Subspaces of a Riemann space / 7.7:
Flat Riemann spaces that are globally non-Euclidean / 7.8:
The Riemann curvature versus the normal curvature of a surface / 7.9:
The geodesic line as the line of extremal distance / 7.10:
Mappings between Riemann spaces / 7.11:
Conformally related Riemann spaces / 7.12:
Conformal curvature / 7.13:
Timelike, null and spacelike intervals in a 4-dimensional spacetime / 7.14:
Embeddings of Riemann spaces in Riemann spaces of higher dimension / 7.15:
The Petrov classification / 7.16:
Symmetries of Riemann spaces, invariance of tensors / 7.17:
Symmetry transformations / 8.1:
The Killing equations / 8.2:
The connection between generators and the invariance transformations / 8.3:
Finding the Killing vector fields / 8.4:
Invariance of other tensor fields / 8.5:
The Lie derivative / 8.6:
The algebra of Killing vector fields / 8.7:
Surface-forming vector fields / 8.8:
Spherically symmetric 4-dimensional Riemann spaces / 8.9:
Conformal Killing fields and their finite basis / 8.10:
The maximal dimension of an invariance group / 8.11:
Methods to calculate the curvature quickly - Cartan forms and algebraic computer programs / 8.12:
The basis of differential forms / 9.1:
The connection forms / 9.2:
The Riemann tensor / 9.3:
Using computers to calculate the curvature / 9.4:
The spatially homogeneous Bianchi type spacetimes / 9.5:
The Bianchi classification of 3-dimensional Lie algebras / 10.1:
The dimension of the group versus the dimension of the orbit / 10.2:
Action of a group on a manifold / 10.3:
Groups acting transitively, homogeneous spaces / 10.4:
Invariant vector fields / 10.5:
The metrics of the Bianchi-type spacetimes / 10.6:
The isotropic Bianchi-type (Robertson-Walker) spacetimes / 10.7:
The Petrov classification by the spinor method / 10.8:
What is a spinor? / 11.1:
Translating spinors to tensors and vice versa / 11.2:
The spinor image of the Weyl tensor / 11.3:
The Petrov classification in the spinor representation / 11.4:
The Weyl spinor represented as a 3 x 3 complex matrix / 11.5:
The equivalence of the Penrose classes to the Petrov classes / 11.6:
The Petrov classification by the Debever method / 11.7:
The theory of gravitation / 11.8:
The Einstein equations and the sources of a gravitational field / 12:
Why Riemannian geometry? / 12.1:
Local inertial frames / 12.2:
Trajectories of free motion in Einstein's theory / 12.3:
Special relativity versus gravitation theory / 12.4:
The Newtonian limit of relativity / 12.5:
Sources of the gravitational field / 12.6:
The Einstein equations / 12.7:
Hilbert's derivation of the Einstein equations / 12.8:
The Palatini variational principle / 12.9:
The asymptotically Cartesian coordinates and the asymptotically flat spacetime / 12.10:
The Newtonian limit of Einstein's equations / 12.11:
Examples of sources in the Einstein equations: perfect fluid and dust / 12.12:
Equations of motion of a perfect fluid / 12.13:
The cosmological constant / 12.14:
An example of an exact solution of Einstein's equations: a Bianchi type I spacetime with dust source / 12.15:
Other gravitation theories / 12.16:
The Brans-Dicke theory / 12.16.1:
The Bergmann-Wagoner theory / 12.16.2:
The conformally invariant Canuto theory / 12.16.3:
The Einstein-Cartan theory / 12.16.4:
The bi-metric Rosen theory / 12.16.5:
Matching solutions of Einstein's equations / 12.17:
The weak-field approximation to general relativity / 12.18:
The Maxwell and Einstein-Maxwell equations and the Kaluza-Klein theory / 12.19:
The Lorentz-covariant description of electromagnetic field / 13.1:
The covariant form of the Maxwell equations / 13.2:
The energy-momentum tensor of an electromagnetic field / 13.3:
The Einstein-Maxwell equations / 13.4:
The variational principle for the Einstein-Maxwell equations / 13.5:
The Kaluza-Klein theory / 13.6:
Spherically symmetric gravitational fields of isolated objects / 13.7:
The curvature coordinates / 14.1:
Symmetry inheritance / 14.2:
Spherically symmetric electromagnetic field in vacuum / 14.3:
The Schwarzschild and Reissner-Nordstrom solutions / 14.4:
Orbits of planets in the gravitational field of the Sun / 14.5:
Deflection of light rays in the Schwarzschild field / 14.6:
Measuring the deflection of light rays / 14.7:
Gravitational lenses / 14.8:
The spurious singularity of the Schwarzschild solution at r = 2m / 14.9:
Embedding the Schwarzschild spacetime in a flat Riemannian space / 14.10:
Interpretation of the spurious singularity at r = 2m; black holes / 14.11:
The Schwarzschild solution in other coordinate systems / 14.12:
The equation of hydrostatic equilibrium / 14.13:
The 'interior Schwarzschild solution' / 14.14:
The maximal analytic extension of the Reissner-Nordstrom solution / 14.15:
Motion of particles in the Reissner-Nordstrom spacetime with e[superscript 2] < m[superscript 2] / 14.16:
Relativistic hydrodynamics and thermodynamics / 14.17:
Motion of a continuous medium in Newtonian mechanics / 15.1:
Motion of a continuous medium in relativistic mechanics / 15.2:
The equations of evolution of [Theta], [sigma subscript alpha beta], [omega subscript alpha beta] and u[superscript alpha]; the Raychaudhuri equation / 15.3:
Singularities and singularity theorems / 15.4:
Relativistic thermodynamics / 15.5:
Relativistic cosmology I: general geometry / 15.6:
A continuous medium as a model of the Universe / 16.1:
Optical observations in the Universe - part I / 16.2:
The geometric optics approximation / 16.2.1:
The redshift / 16.2.2:
The optical tensors / 16.3:
The apparent horizon / 16.4:
The double-null tetrad / 16.5:
The Goldberg-Sachs theorem / 16.6:
Optical observations in the Universe - part II / 16.7:
The area distance / 16.7.1:
The reciprocity theorem / 16.7.2:
Other observable quantities / 16.7.3:
Relativistic cosmology II: the Robertson-Walker geometry / 16.8:
The Robertson-Walker metrics as models of the Universe / 17.1:
Optical observations in an R-W Universe / 17.2:
The redshift-distance relation / 17.2.1:
Number counts / 17.2.3:
The Friedmann equations and the critical density / 17.3:
The Friedmann solutions with [Lambda] = 0 / 17.4:
The redshift-distance relation in the [Lambda] = 0 Friedmann models / 17.4.1:
The Newtonian cosmology / 17.5:
The Friedmann solutions with the cosmological constant / 17.6:
Horizons in the Robertson-Walker models / 17.7:
The inflationary models and the 'problems' they solved / 17.8:
The value of the cosmological constant / 17.9:
Then 'history of the Universe' / 17.10:
Invariant definitions of the Robertson-Walker models / 17.11:
Different representations of the R-W metrics / 17.12:
Relativistic cosmology III: the Lemaitre-Tolman geometry / 17.13:
The comoving-synchronous coordinates / 18.1:
The spherically symmetric inhomogeneous models / 18.2:
The Lemaitre-Tolman model / 18.3:
Conditions of regularity at the centre / 18.4:
Formation of voids in the Universe / 18.5:
Formation of other structures in the Universe / 18.6:
Density to density evolution / 18.6.1:
Velocity to density evolution / 18.6.2:
Velocity to velocity evolution / 18.6.3:
The influence of cosmic expansion on planetary orbits / 18.7:
Apparent horizons in the L-T model / 18.8:
Black holes in the evolving Universe / 18.9:
Shell crossings and necks/wormholes / 18.10:
E < 0 / 18.10.1:
E = 0 / 18.10.2:
E > 0 / 18.10.3:
The influence of inhomogeneities in matter distribution on the cosmic microwave background radiation / 18.11:
Matching the L-T model to the Schwarzschild and Friedmann solutions / 18.13:
General properties of the Big Bang/Big Crunch singularities in the L-T model / 18.14:
Extending the L-T spacetime through a shell crossing singularity / 18.15:
Singularities and cosmic censorship / 18.16:
Solving the 'horizon problem' without inflation / 18.17:
The evolution of R(t, M) versus the evolution of [rho](t, M) / 18.18:
Increasing and decreasing density perturbations / 18.19:
L&T curio shop / 18.20:
Lagging cores of the Big Bang / 18.20.1:
Strange or non-intuitive properties of the L-T model / 18.20.2:
Chances to fit the L-T model to observations / 18.20.3:
An 'in one ear and out the other' Universe / 18.20.4:
A 'string of beads' Universe / 18.20.5:
Uncertainties in inferring the spatial distribution of matter / 18.20.6:
Is the matter distribution in our Universe fractal? / 18.20.7:
General results related to the L-T models / 18.20.8:
Relativistic cosmology IV: generalisations of L-T and related geometries / 18.21:
The plane- and hyperbolically symmetric spacetimes / 19.1:
G[subscript 3]/S[subscript 2]-symmetric dust solutions with R, [subscript r not equal] 0 / 19.2:
G[subscript 3]/S[subscript 2]-symmetric dust in electromagnetic field, the case R, [subscript r not equal] 0 / 19.3:
Integrals of the field equations / 19.3.1:
Matching the charged dust metric to the Reissner-Nordstrom metric / 19.3.2:
Prevention of the Big Crunch singularity by electric charge / 19.3.3:
Charged dust in curvature and mass-curvature coordinates / 19.3.4:
Regularity conditions at the centre / 19.3.5:
Shell crossings in charged dust / 19.3.6:
The Datt-Ruban solution / 19.4:
The Szekeres-Szafron family of solutions / 19.5:
The [Beta], [subscript z] = 0 subfamily / 19.5.1:
The [Beta], [subscript z] = [not equal] 0 subfamily / 19.5.2:
Interpretation of the Szekeres-Szafron coordinates / 19.5.3:
Common properties of the two subfamilies / 19.5.4:
The invariant definitions of the Szekeres-Szafron metrics / 19.5.5:
The Szekeres solutions and their properties / 19.6:
The [Beta], [subscript z not equal] 0 subfamily / 19.6.1:
The [Beta], [subscript z] = 0 family as a limit of the [Beta], [subscript z not equal] 0 family / 19.6.3:
Properties of the quasi-spherical Szekeres solutions with [Beta], [subscript z not equal] 0 = [Lambda] / 19.7:
Basic physical restrictions / 19.7.1:
The significance of [epsilon] / 19.7.2:
Conditions of regularity at the origin / 19.7.3:
Shell crossings / 19.7.4:
Regular maxima and minima / 19.7.5:
The apparent horizons / 19.7.6:
Szekeres wormholes and their properties / 19.7.7:
The mass-dipole / 19.7.8:
The Goode-Wainwright representation of the Szekeres solutions / 19.8:
Selected interesting subcases of the Szekeres-Szafron family / 19.9:
The Szafron-Wainwright model / 19.9.1:
The toroidal Universe of Senin / 19.9.2:
The discarded case in (19.103)-(19.112) / 19.10:
The Kerr solution / 19.11:
The Kerr-Schild metrics / 20.1:
The derivation of the Kerr solution by the original method / 20.2:
Basic properties / 20.3:
Derivation of the Kerr metric by Carter's method - from the separability of the Klein-Gordon equation / 20.4:
The event horizons and the stationary limit hypersurfaces / 20.5:
General geodesics / 20.6:
Geodesics in the equatorial plane / 20.7:
The maximal analytic extension of the Kerr spacetime / 20.8:
The Penrose process / 20.9:
Stationary-axisymmetric spacetimes and locally nonrotating observers / 20.10:
Ellipsoidal spacetimes / 20.11:
A Newtonian analogue of the Kerr solution / 20.12:
A source of the Kerr field? / 20.13:
Subjects omitted from this book / 20.14:
References
Index
Elements of Differential Geometry
A short sketch of two-dimensional differential geometries
Curvature of a manifold: flat manifolds
Symmetries of Rieman spaces, invariance of tensors
The spatially homogeneous Bianchi-type spacetimes
The Gravitation Theory
Spherically symmetric gravitational field of isolated objects
Relativistic cosmology III: the Lemaître-Tolman geometry
Subjects omitted in this book
List of figures
The scope of this text
Acknowledgements
6.

電子ブック

EB
Brian Cowan
出版情報: Cambridge University Press Online Books , Cambridge : Cambridge University Press, 1997
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Introduction / 1:
Theoretical background / 2:
Detection methods / 3:
Classical view of relaxation / 4:
Quantum treatment of relaxation / 5:
Dipolar lineshapes in solids / 6:
Relaxation in liquids / 7:
Some case studies / 8:
The density operator and applications / 9:
NMR imaging
Fourier transformation / Appendix A:
Random functions / Appendix B:
Interaction picture / Appendix C:
Magnetic fields and canonical momentum / Appendix D:
Alternative classical treatment of relaxation / Appendix E:
Gm(t) for rotationally invariant systems / Appendix F:
P(omega, omega zero, t) for rotational diffusion / Appendix G:
Introduction / 1:
Theoretical background / 2:
Detection methods / 3:
7.

電子ブック

EB
Michel Le Bellac
出版情報: Cambridge University Press Online Books , Cambridge : Cambridge University Press, 1996
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Preface
Introduction / 1:
Quantum statistical mechanics / 2:
The scalar field at finite temperature / 3:
Simple applications of perturbation / 4:
Dirac and gauge fields at finite temperature / 5:
Collective excitations in a plasma / 6:
Hard thermal loops and resummation / 7:
Dynamical screening / 8:
Neutrino emission from stars / 9:
Infrared problems at finite temperature / 10:
Appendices
References
Preface
Introduction / 1:
Quantum statistical mechanics / 2:
8.

電子ブック

EB
Carlo Rovelli, D. R. Nelson, S. Weinberg, P. V. Landshoff
出版情報: Cambridge University Press Online Books , Leiden : Cambridge University Press, 2004
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Preface
Acknowledgements
Terminology and notation
Relativistic Foundations / Part I:
General relativity / 1:
Relativistic mechanics / 2:
Hamiltonian general relativity / 4:
Quantum mechanics / 5:
Loop Quantum Gravity / Part II:
Quantum space / 6:
Quantum spacetime: the Hamiltonian operator / 7:
Matter / 8:
Applications / 9:
Quantum spacetime: spinfoams / 10:
Discussion / 11:
Appendices / Part III:
Mathematical appendices / A:
History / B:
On method and truth / C:
References
General ideas and heuristic picture
Mechanics
Dynamics and matter
Conclusion
Appendices: References
Index
Preface
Acknowledgements
Terminology and notation
9.

電子ブック

EB
Allan Griffin, Tetsuro Nikuni, Eugene Zaremba
出版情報: Cambridge University Press Online Books , 2009
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Preface
Overview and introduction / 1:
Historical overview of Bose superfluids / 1.1:
Summary of chapters / 1.2:
Condensate dynamics at T = 0 / 2:
Gross-Pitaevskii (GP) equation / 2.1:
Bogoliubov equations for condensate fluctuations / 2.2:
Coupled equations for the condensate and thermal cloud / 3:
Generalized GP equation for the condensate / 3.1:
Boltzmann equation for the noncondensate atoms / 3.2:
Solutions in thermal equilibrium / 3.3:
Region of validity of the ZNG equations / 3.4:
Green's functions and self-energy approximations / 4:
Overview of Green's function approach / 4.1:
Nonequilibrium Green's functions in normal systems / 4.2:
Green's functions in a Bose-condensed gas / 4.3:
Classification of self-energy approximations / 4.4:
Dielectric formalism / 4.5:
The Beliaev and the time-dependent HFB approximations / 5:
Hartree-Fock-Bogoliubov self-energies / 5.1:
Beliaev self-energy approximation / 5.2:
Beliave as time-dependent HFB / 5.3:
Density response in the Beliaev-Popov approximation / 5.4:
Kadanoff-Baym derivation of the ZNG equations / 6:
Kadanoff-Baym formalism for Bose superfluids / 6.1:
Hartree-Fock-Bogoliubov equations / 6.2:
Derivation of a kinetic equation with collisions / 6.3:
Collision integrals in the Hartree-Fock approximation / 6.4:
Generalized GP equation / 6.5:
Linearized collision integrals in collisionless theories / 6.6:
Kinetic equation for Bogoliubov thermal excitations / 7:
Generalized kinetic equation / 7.1:
Kinetic equation in the Bogoliubov-Popov approximation / 7.2:
Comments on improved theory / 7.3:
Static thermal cloud approximation / 8:
Condensate collective modes at finite temperatures / 8.1:
Phenomenological GP equations with dissipation / 8.2:
Relation to Pitaevskii's theory of superfluid relaxation / 8.3:
Vortices and vortex lattices at finite temperatures / 9:
Rotating frames of reference: classical treatment / 9.1:
Rotating frames of reference: quantum treatment / 9.2:
Transformation of the kinetic equation / 9.3:
Zaremba-Nikuni-Griffin equations in a rotating frame / 9.4:
Stationary states / 9.5:
Stationary vortex states at zero temperature / 9.6:
Equilibrium vortex state at finite temperatures / 9.7:
Nonequilibrium vortex states / 9.8:
Dynamics at finite temperatures using the moment method / 10:
Bose gas above TBEC / 10.1:
Scissors oscillations in a two-component superfluid / 10.2:
The moment of inertia and superfluid response / 10.3:
Numerical simulation of the ZNG equations / 11:
The generalized Gross-Pitaevskii equation / 11.1:
Collisionless particle evolution / 11.2:
Collisions / 11.3:
Self-consistent equilibrium properties / 11.4:
Equilibrium collision rates / 11.5:
Simulation of collective modes at finite temperature / 12:
Equilibration / 12.1:
Dipole oscillations / 12.2:
Radial breathing mode / 12.3:
Scissors mode oscillations / 12.4:
Quadrupole collective modes / 12.5:
Transverse breathing mode / 12.6:
Landau damping in trapped Bose-condensed gases / 13:
Landau damping in a uniform Bose gas / 13.1:
Landau damping in a trapped Bose gas / 13.2:
Numerical results for Landau damping / 13.3:
Landau's theory of superfluidity / 14:
History of two-fluid equations / 14.1:
First and second sound / 14.2:
Dynamic structure factor in the two-fluid region / 14.3:
Two-fluid hydrodynamics in a dilute Bose gas / 15:
Equations of motion for local equilibrium / 15.1:
Equivalence to the Landau two-fluid equations / 15.2:
First and second sound in a Bose-condensed gas / 15.3:
Hydrodynamic modes in a trapped normal Bose gas / 15.4:
Variational formulation of the Landau two-fluid equations / 16:
Zilsel's variational formulation / 16.1:
The action integral for two-fluid hydrodynamics / 16.2:
Hydrodynamic modes in a trapped gas / 16.3:
Two-fluid modes in the BCS-BEC crossover at unitarity / 16.4:
The Landau-Khalatnikov two-fluid equations / 17:
The Chapman-Enskog solution of the kinetic equation / 17.1:
Deviation from local equilibrium / 17.2:
Equivalence to Landau-Khalatnikov two-fluid equations / 17.3:
The C12 collisions and the second viscosity coefficients / 17.4:
Transport coefficients and relaxation times / 18:
Transport coefficients in trapped Bose gases / 18.1:
Relaxation times for the approach to local equilibrium / 18.2:
Kinetic equations versus Kubo formulas / 18.3:
General theory of damping of hydrodynamic modes / 19:
Review of coupled equations for hydrodynamic modes / 19.1:
Normal mode frequencies / 19.2:
General expression for damping of hydrodynamic modes / 19.3:
Hydrodynamic damping in a normal Bose gas / 19.4:
Hydrodynamic damping in a superfluid Bose gas / 19.5:
Monte Carlo calculation of collision rates / Appendix A:
Evaluation of transport coefficients: technical details / Appendix B:
Frequency-dependent transport coefficients / Appendix C:
Derivation of hydrodynamic damping formula / Appendix D:
References
Index
Preface
Overview and introduction / 1:
Historical overview of Bose superfluids / 1.1:
10.

電子ブック

EB
Thomas Thiemann
出版情報: Cambridge University Press Online Books , 2007
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Notation and conventions
Introduction
Classical Foundations, Interpretation and the Canonical Quantisation Programme / Part 1:
Classical Hamiltonian formulation of general relativity / 1:
The problem of time, locality and the interpretation of quantum mechanics / 2:
The programme of canonical quantisation / 3:
The new canonical variables of Ashtekar for general relativity / 4:
Foundations of Modern Canonical Quantum General Relativity / Part 2:
he holonomy-flux algebra [P] / 5:
quantum -algebra / 7. Step II:
representation theory of [A] / 8. Step III:
Implementation and solution of the kinematical constraints / 9. Step IV:
implementation and solution of the Hamiltonian constraint / 10. Step V:
semiclassical analysis / 11. Step VI:
Physical Applications / Part 3:
Extension to standard matter / 12:
Kinematical geometrical operators / 13:
Spin foam models / 14:
Quantum black hole physics / 15:
Applications to particle physics and quantum cosmology / 16:
Loop quantum gravity phenomenology / 17:
Mathematical Tools and their Connection to Physics / Part 4:
Tools from general topology / 18:
Differential, Riemannian, symplectic and complex geometry / 19:
Semianalytical category / 20:
Elements of fibre bundle theory / 21:
Holonomies on non-trivial fibre bundles / 22:
Geometric quantisation / 23:
The Dirac algorithm for field theories with constraints / 24:
Tools from measure theory / 25:
Elementary introduction to Gel'fand theory for Abelean C* algebras / 26:
Bohr compactification of the real line / 27:
Operatir -algebras and spectral theorem / 28:
Refined algebraic quantisation (RAQ) and direct integral decomposition (DID) / 29:
Basics of harmonic analysis on compact Lie groups / 30:
Spin network functions for SU(2) / 31:
+ Functional analytical description of classical connection dynamics / 32:
Bibliography
Index
Preface
Step I: the holonomy-flux algebra [P] / Part I:
Step II: quantum-algebra / 7:
Step III: representation theory of [A] / 8:
Step IV / 9:
Step V / 10:
Implementation and solution of the Hamiltonian constraint
Step VI: semiclassical analysis / 11:
Notation and conventions
Introduction
Classical Foundations, Interpretation and the Canonical Quantisation Programme / Part 1:
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