Details

Subject(s)

• Quantum theory [Browse]
• Many-body problem [Browse]

Series

• Fundamental Theories of Physics [More in this series]
• Fundamental Theories of Physics ; v.211 [More in this series]

Bibliographic references

Includes bibliographical references and index.

Source of description

Description based on print version record.

Contents

• Intro
• Preface
• Contents
• 1 Introduction
• 1.1 Concept of Metastability
• 1.1.1 Life Time of a Metastable State
• Part I Metastability in Classical Systems
• 2 Metastability in Thermodynamic Systems
• 2.1 Introduction
• 2.2 Mean-Field Theory for a Ferromagnetic Ising System
• 2.2.1 Self-consistent Equation of the Magnetization
• 2.2.2 Magnetization Curve
• 2.2.3 Free Energy as a Function of Magnetization
• 2.3 Rotation of Magnetization
• 2.3.1 Stoner-Wohlfarth Model
• 2.3.2 Stoner-Wohlfarth Diagram
• 2.3.3 Trajectrory
• 2.4 First-Order Phase Transitions as a Function of the Temperature
• 2.4.1 A Model with Many Degeneracy of Zero Energy States
• 2.4.2 Blume-Capel Model
• 2.4.3 Spin Crossover Systems
• 2.5 Landau Theory
• 2.5.1 Landau Theory for Temperature Induced First-Order Phase Transition
• 2.6 Gas-Liquid Phase Transition
• 2.6.1 Phenomenological Method: van der Waals (vDW) Equation
• 2.7 Statistical Treatments of the Gas-Liquid Phase Transition
• 2.7.1 Perturbational Approach
• 2.7.2 Lattice-Gas Model Approach
• 2.7.3 Mean-Field Analysis for the Lattice Gas Model
• 3 Escape Rate from the Metastable State
• 3.1 Introduction
• 3.2 Arrhenius Law
• 3.3 Kramers Method
• 3.4 Spinodal Singularity
• 3.4.1 Master Equation for the Husimi-Temperley Model
• 3.5 Nucleation in Model Short-Range Interaction
• 3.6 Dynamical Spinodal Point
• 3.7 Survival Probability of a Metastable State
• 3.7.1 Néel-Arrhenius Process
• 4 Spatial Pattern During the Transition
• 4.1 Dynamics Associated with the First-Order Phase Transition
• 4.2 Dynamics After the Temperature Quenching
• 4.2.1 Non-conserved System: k squared tk2t Scaling
• 4.2.2 A Stretched Exponential Law for Spin-Autocorrelation Function
• 4.2.3 Conserved System: Lifshitz-Slyozov-Wigner Theory k cubed tk3t Scaling
• 4.2.4 Ostwald Ripening.
• Part II First-Order Phase Transition from Viewpoints of the Eigenvalue Problem
• 5 Structure of Eigenvalues for the First-Order Phase Transition
• 5.1 Transfer Matrix
• 5.1.1 Ladder Systems
• 5.1.2 Free Energy
• 5.1.3 Correlation Functions
• 5.1.4 Temperature Dependence of the Eigenvalues
• 5.1.5 Field Dependence of the Eigenvalues Below the Critical Temperature
• 5.2 Eigenvalue Analysis of Dynamical Processes
• 5.2.1 Eigenstates of Master Equation
• 5.2.2 Approach to the Stationary State
• 5.3 Kinetic Ising Model
• 5.3.1 Demonstration in a Small System of 2 times 22times2 System
• 5.3.2 Master Equation for the Magnetization for a Model with Long-Range Interaction
• 5.3.3 Relaxation times of 4 times 34times3 System
• 5.4 Eigenvalue Problem of Quantum Master Equation
• 5.5 Free Energy at the First-Order Phase Transition
• 5.6 Langer's Argument
• 5.6.1 Langer's Analysis I: A Picture of Nucleation Cluster
• 5.6.2 Langer's Analysis II: Functional Integral
• 5.6.3 Langer's Analysis III: A Picture of the Action
• 5.6.4 Langer's Estimation of Decay Rate of Metastable State
• Part III Metastability in Quantum Systems
• 6 Collapse of Metastability by the Quantum Fluctuation
• 6.1 Introduction
• 6.2 Quantum Mechanical States in Double-Well Type Potential
• 6.2.1 Chracteristics of Metastability in the Eigenstate Spectrum StartSet upper E Subscript i Baseline left parenthesis h right parenthesis EndSet{Ei(h)} as a Function of Field
• 6.3 Characterstic of Eigenvalue Structure Around the First-Order Phase Transition
• 6.4 Particle Conveyance by a Potential-Well
• 6.4.1 Sudden Start by Changing the Velocity from Zero to cc
• 6.4.2 Smooth Acceleration
• 6.4.3 Scattering Problem
• 6.4.4 Relaxation from Metastable Potential
• 6.4.5 Carry Up the Particle
• 6.5 Quantum Tunneling in Magnetic Systems.
• 6.5.1 Metastability in Magnetic Systems
• 6.6 Relaxation of Magnetism in Small Systems
• 6.7 Single Molecular Magnets (SMM)
• 6.7.1 Tunneling Under Dissipation
• 6.7.2 Dynamics in Dissipative Environments
• 6.8 Magnetic Foehn Effect
• 6.9 Effect of Dissipation on the Relaxation of Metastable State
• 6.9.1 Free-Boson Bath Model
• 6.9.2 Dynamics of the Magnetization in Uniaxial Anisoropy
• 6.9.3 Effects of Dissipation on the Hybridized Lowest Two States
• 6.10 Quantum Stoner-Wohlfarth Model
• 6.10.1 Dynamics of Magnetization
• 6.10.2 Distribution of the Population over the States
• 6.10.3 Dynamics of Magnetization in Dissipative Environment
• 6.11 Nucleation in Quantum Systems
• 6.12 Transverse-Ising Model
• 6.12.1 Visualization of Quantum and Classical Fluctuation in a left parenthesis d plus 1 right parenthesis(d+1) Dimensional Representation of States
• 6.13 Cooperative Phenomena in a Cavity System
• 6.13.1 Cavity System
• 6.13.2 Phase Transitions of the Dicke Hamiltonian
• 6.14 Optical Bistability
• 6.14.1 Mean-Field Analysis
• 6.14.2 Analogy to a Picture of Thermodynamic Free Energy
• 6.14.3 Numerical Study of the Size Dependence
• 6.14.4 Metastability in the Bistable Region
• 6.14.5 Hysteresis Phenomena
• 6.15 Limit Cycle of the Hysteresis
• 6.15.1 Dynamics Under an Driving Force with Periodically Oscillating Amplitude
• 6.15.2 Floquet Map
• 6.15.3 Mean-Field Analysis of Limit Cycle
• Part IV Quantitative Estimation of Relaxation Time
• 7 Coercivity of Magnets
• 7.1 Introduction
• 7.2 Coercivity Estimated by the Free Energy Landscape
• 7.2.1 Minimum Energy Path (MEP) Method
• 7.2.2 Free Energy Landscape Method
• 7.3 Characteristic Quantities of Magnetization Reversal
• 7.3.1 Activation Volume
• 7.3.2 Magnetic Viscosity.
• 7.3.3 Relation Between the Activation Volume upper V Subscript normal aVa and the Magnetic Viscosity upper SS
• 7.3.4 Coercivity Obtained by a Direct Simulation of SLLG
• 7.3.5 Coercivity of Large Grains
• 7.4 Coercivity of Magnets as an Ensemble of Grains
• Part V Appendices
• 8 Appendices
• 8.1 Brief Review on the Mean-Field Approximation
• 8.1.1 Basic Idea of Mean-Field Theory
• 8.1.2 Mean-Field Free Energy as a Function of the Magnetization F(m:T,H)
• 8.1.3 Free Energy in Bragg-Williams Approximation
• 8.1.4 Free Energy of the Long-Range Interaction Model (Husimi-Temperley Model)
• 8.1.5 Free Energy as a Variational Function
• 8.2 Equation of Stochastic Processes
• 8.2.1 Master Equation and Fokker-Planck Equation
• 8.2.2 Master Equation in Differential Form
• 8.2.3 Symmetrization of the Time-Evolution Operator
• 8.2.4 Master Equation for Continuous Variable
• 8.2.5 Brownian Motion
• 8.3 Landau-Zener Scattering
• 8.4 Quantum Master Equation
• 8.4.1 Lindblad Type
• 8.4.2 Redfield Type
• 8.4.3 Redfield Type for a Single Spin
• 8.4.4 Bloch Equation
• 8.4.5 Under a Time-Dependent Field
• 8.5 Path-Integral Method
• 8.5.1 One Particle Problem
• 8.5.2 Partition Function at a Finite Temperature
• 8.5.3 Onsager-Machlup Formula for Stochastic Process
• 8.6 WKB Approximation
• 8.6.1 Semiclassical Approximation
• 8.6.2 Connection Formula
• 8.6.3 Bound State
• 8.6.4 Transmission Coefficient by WKB Approximation
• 8.6.5 Transition Matrix
• 8.6.6 Relaxation from Metastable Potential
• Appendix References
• Index.

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ISBN

9789811966682 ((electronic bk.))

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