Collapse of metastability : dynamics of first-order phase transition / / Seiji Miyashita

• Record Nr.: UNISA996499864403316
• Autore: Miyashita Seiji
• Pubbl/distr/stampa: Singapore : , : Springer, , [2022]; ©2022
• ISBN: 9789811966682; 9789811966675
• Descrizione fisica: 1 online resource (260 pages)
• Collana: Fundamental Theories of Physics ; ; v.211
• Disciplina: 016.61483
• Soggetti: Quantum theory; Many-body problem
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.