The Non-uniform Riemann Approach to Stochastic Integration

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【簡介】 This is the first book that presents the theory of stochastic integral using the generalized Riemann approach. Readers who are familiar with undergraduate calculus and want to have an easy access to the theory of stochastic integral will find most of this book pleasantly readable, especially the first four chapters. The references to the theory of classical stochastic integral and stochastic processes are also included for the convenience of readers who are familiar with the measure theoretic approach. Sample Chapter(s) Preface Chapter 1: Introduction Contents: Introduction The Itô Integral Differentiation and Differential Variational Approach to Stochastic Integration The Multiple Itô–Wiener Integral Fubini's Theorem and Hu–Meyer's Theorem Readership: Students at Masters Level doing stochastic integration theory, Non-mathematics specialist reading financial mathematics, Graduate Research students. 【目錄】

Lectures on the Non-Equilibrium Theory of Condensed Matter (2版)

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This book discusses in depth many of the key problems in non-equilibrium physics. Besides the standard subjects (Boltzmann and Master equations, linear response) it includes several new important subjects as well. The origin of macroscopic irreversible (dissipative) behavior receives an extended attention and is illustrated in the framework of solvable classical models of open systems (Chapter 3). The scaling relationship between the kinetic and hydrodynamical levels is described in Chapter 9. The QED of charged non-relativistic particles and its restriction to the states without photons to order 1/c² leading to the current-current magnetic interaction is discussed in some depth in Chapters 14 and 15. Bose–Einstein condensation in real time within the frame of rate equations, as well as soliton-like solutions of the non-linear Gross-Pitaevskii equation are discussed in Chapter 22. The presentation also includes the latest developments — quantum kinetics — related to modern ultrafast spectroscopy (Chapters 23–30). This second edition was improved, restructured, and enriched with new results from the recent papers of the author. Chapter 3 was largely extended and Chapters 14 and 15 are completely new. Chapter 22 has a new Section. Several new useful figures were added throughout the book as well. Contents: Introduction. (Why and How Non-Equilibrium?) Time-Reversal and Evolution Toward Equilibrium Solvable Classical Models of Open Systems Naive Deduction of the Rate Equation from the Heisenberg Equation of Motion Naive Quantum Kinetics Schrödinger Equation Versus Master Equation Diagonal Master Equations and Rate Equations The Boltzmann Equation Hydrodynamics as Scaling of Kinetic Theory Master Equations for the Density Operator. (Reservoir Theory) Two-Level Atom Interacting with Light Master Equations for the Density Operator with Particle-Particle Collisions (The Super-Projector Approach) Van Hove's Weak Coupling Limit and Davies's Generalization Charged Particles Interacting with the Electromagnetic Field Extension of the Electronic Hamiltonian with Transverse Current-Current Terms Linear Response to External Perturbations The Nyquist Theorem The Kubo Formulae The Longitudinal Dielectric Function of Crystals The Transverse Dielectric Function in the Nonrelativistic Quantum Electrodynamics Excitonic Absorption in a Semiconductor Bose-Einstein Condensation in Real Time Real-Time Experiments: Ultra-Short-Time Spectroscopy Keldysh's Non-Equilibrium Green Functions Keldysh-Green Functions and Time-Reversal Time-Dependent Hartree-Fock Treatment of Coulomb Interaction. The Exciton Quantum Kinetics of Electrons and Holes Scattered by LO Phonons Within the S.C. RPA and the Kadanoff-Baym Approximation Full Two-Time Quantum-Kinetics of Electrons and Holes Scattered by LO Phonons within the S.C. RPA Coulomb Quantum Kinetics of Electrons and Holes within the S.C. RPA and the Kadanoff-Baym Approximation. Time Dependent Screening Full Two-Time Quantum Kinetics of an Electron-Hole Coulomb System. Ward Identities