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

Lectures on Differential Geometry (1版)

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【簡介】 This book presents a concise introduction to differential geometry. It is aimed at advanced undergraduate students and first year graduate students who wish to have a basic solid knowledge of the subject, and it can serve as a starting point for more advanced reading. The book is organized into lectures, so it can easily be used as a textbook for a beginning graduate-level course in differential geometry. 【目錄】

Lectures on Probability and Statistics for Graduate-Level Economics

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【簡介】 Sound knowledge of rigorous probability and statistics methods is essential to pursue graduate studies in economics. These sorts of tools are largely required to conduct research in modern fields of economics such as economic theory, empirical economics, experimental economics, or data science for economics. These notes provide an intuitive roadmap to navigate graduate-level courses in mathematical probability and statistics for economists. Each chapter presents questions prevalent on each topic and lays out the state-of-the-art theoretical frameworks used to address such questions. The book offers a diverse array of solved examples to help gain intuitions on abstract concepts, as well as unsolved exercises to stimulate the readers’ training in such concepts. The book presents the theoretical side of probability and statistics in a rather concise way and stresses the importance of motivating examples and observations. 【目錄】

Lectures on Symmetry-Assisted Computation

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【簡介】 Scientific problems have an internal "beauty", called, referred to, precisely speaking, as their "symmetry". The symmetry arises, often, from the fact that the scientific problem refers to an object (a molecule, a crystal) and the object itself has some "symmetry" elements, but in more abstract situations, such as those arising in particle physics and quantum technologies, symmetry is often the only known (and relevant!) fact about the problem. The scope of these Lecture Notes is to educate how to recognize the symmetry of a scientific problem and how to use symmetry to understand, manipulate and, finally, solve it. The principle guiding these Lecture Notes is that "learning by doing" is the only way that young students can later become productive in science, business and industry. The lecture Notes have, essentially, two components. The first one reports the content of a set of lectures, held at ETH Zurich at the master and PhD level, frequented mainly by students from the department of Physics, Chemistry and Material Science. The lectures were accompanied by a set of student projects on various scientific subjects related to symmetry. These projects ended with a manuscript, worked out by the students themselves and edited into the second component of these Lecture Notes. 【目錄】 Lectures: Geometrical, Algebraic, and Analytic Aspects of Symmetry Representation Theory of Groups with Average SO3 and the General Method of Infinitesimal Transformations The Symmetry Group of the Operator and Some Practical Applications Point Groups and Space Groups of Crystallography Applications to Solid-State Physics The Relativistic Electronic Structure of Atoms and Solids Young Diagrams and Particle Physics The Permutation Group and Its Applications to Many-Body Problems Group Theory and Phase Transitions Exercises: Exercises to Lecture 1 Exercises to Lecture 2 Exercises to Lecture 3 Exercises to Lecture 4 Exercises to Lecture 5 Projects: Project for Lecture 2: Functional Analytic and Numerical Aspects of Eigenvalue Problems Project for Lecture 4: Symmetry Arguments in Classical Mechanics Project for Lecture 4: Crystal Field Splitting and the Jahn–Teller Effect Project for Lecture 4: Vibrational Modes of the NH3 Molecule Project for Lecture 5: Frieze Patterns Project for Lecture 5: An Algebraic Proof of the Hessel Theorem Project for Lecture 6: Empty-Lattice Band Structure Project for Lecture 6: Symmetry Analysis of Graphene Band Structure and Dirac Cones Project for Lecture 6: Topological Protection by Non-symmorphic Degeneracy Project for Lecture 7: Topological Aspects of Continuous Groups and the Universal Covering Groups Project for Lecture 7: Optical Spin Orientation in Atoms and Solids Project for Lecture 9: Quantum Chemistry