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Wang J: Quantitative Depth Profiling And
Diffusion In Thin Films

Quantitative Depth Profiling And Diffusion In Thin Films

Dynamics and Astrophysics of Galaxies

This will be the 7th book in the author's 'Lectures on ...' book series, and the first aimed at graduate-level readers(two additional graduate texts are in preparation). Primarily intended for physics graduate students, the book is accessible to advanced undergraduates and will appeal to students with a background in statistics and a keen interest in quantum physics. By the end of this book, readers will be well-prepared for working on research projects that require the drawing of inference from the noisy data collected in quantum experiments, as epitomized by quantum state estimation.The book begins with chapters on the basics of estimation theory and the basics of quantum theory. This includes, in particular, the roles played by the frequentist methods of statistics, which are crucial when planning an experiment, and the Bayesian methods, which are the tools for drawing inference from the actual data gathered. A central concept is that of optimal error regions that supplement the point estimators ('best guesses') with the analogs of error bars in the high-dimensional parameter space; there is, in particular, the plausible region which comprises all point estimators supported by the data.Practical applications require the evaluation of high-dimensional integrals with the aid of Monte Carlo integration. For that, one needs to draw samples of quantum states from the relevant distributions, namely the priors and posteriors of Bayesian methodology. The book discusses the algorithms well-suited for this kind of sampling, which is central to the processing of real-life data.The book illustrates all concepts with pertinent examples and offers numerous exerciseswhich the readers can practice and perfect their skills with. The presentation is detailed and does not skip technical steps, which makes the book particularly valuable for self-studying readers and as textbook adopted by lecturers teaching courses on this or related topics. While the book is based on lecture notes developed for the author's courses on quantum state estimation at NUS and BIT, this book also offers a comprehensive account of the concepts and methods developed in the author's group at CQT and presents this material in textbook form for the first time.

Lectures On Quantum State Estimation

Fundamentals, Materials, Characterization, and Developments

Metal-ion Capacitors

De Gruyter Studies in Mathematical Physics

Mirror symmetry is one of the most exciting ideas in mathematics to emerge in the last two decades. It was introduced in physics as a duality between superconformal field theories. This book discusses this rapidly developing aspect of string theory.

Laurent Polynomials in Mirror Symmetry

Many-Body Green's Functions for Time-Dependent Problems

Mathematical Physics Studies

This book presents a wide-ranging geometric approach to the stability of solitary wave solutions of Hamiltonian partial differential equations (PDEs). It blends original research with background material and a review of the literature. The overarching aim is to integrate geometry, algebra, and analysis into a theoretical framework for the spectral problem associated with the transverse instability of line solitary wave solutions—waves that travel uniformly in a horizontal plane and are embedded in two spatial dimensions. Rather than focusing on individual PDEs, the book develops an abstract class of Hamiltonian PDEs in two spatial dimensions and time, based on multisymplectic Dirac operators and their generalizations. This class models a broad range of nonlinear wave equations and benefits from a distinct symplectic structure associated with each spatial dimension and time. These structures inform both the existence theory (via variational principles, the Maslov index, and transversality conditions) and the linear stability analysis (through a multisymplectic partition of the Evans function). The spectral problem arising from linearization about a solitary wave is formulated as a dynamical system, with three symplectic structures contributing to the analysis. A two-parameter Evans function—depending on the spectral parameter and transverse wavenumber—is constructed from this system. This structure enables new results concerning the Evans function and the linear transverse instability of solitary waves. A key result is an abstract derivative formula for the Evans function in the regime of small stability exponents and transverse wavenumbers. To illustrate the theory, the book introduces a class of vector-valued nonlinear wave equations in 2+1 dimensions that are multisymplectic and admit explicit solitary wave solutions. In this example, the stable and unstable subspaces involved in the Evans function construction are each four-dimensional and can be explicitly computed. The example is used to demonstrate the geometric instability condition and to explore the inner workings of the theory in detail.

Multisymplectic Dirac Operators and the Evans Function

Transverse Instability of Solitary Waves

Selected Topics

Quantum Modelling of Economic and Financial Systems

Handbook of Electronic Structure Theory provides a much-needed learning resource that collects and demonstrates the various key methods involved in electronic structure theory, the feasibility and reliability of electronic structure calculations and their applications using computational chemistry, with a particular focus on the most modern and recent problems which are poorly covered in existing, largely outdated book literature. This handbook is designed with early career researcher learning in mind by aiming to provide a careful, structured, coherent, measured, and incremental presentation of the subject matter as well as appropriate problems and worked tutorial examples. Elements like summary boxes, worked examples, and downloadable data sets make this a holistic guide to the topic for learners from different backgrounds who require a deeper understanding of electronic structure theory. Part I one of the book focuses on the critical core theories, before Part II moves on to some of the most important recent developments and their potential future directions, including key topics such as the electronic excited states and the harnessing of machine learning. Finally, Part III then collects a range of key case study examples of applications such as for biomolecules, in spectroscopy, or for use in catalysis amongst others. Handbook of Electronic Structure Theory is written primarily for masters, PhD, and postdoctoral students in theoretical and computational chemistry as well as experimental researchers wishing to apply quantum chemical methods in a critical way. The book will also have significant relevance to those studying and teaching in the adjacent fields of computational physics, materials science, and astrochemistry, who are making use of electronic structure methods. It is also likely to be of interest to chemists working on designing new materials and compounds targeting industrial and environmental applications such as catalysis, energy harvesting or green chemistry.

Methods and Applications

Handbook of Electronic Structure Theory

This book focuses on the research and development of the renowned two-dimensional nanomaterial, white graphene, also known as boron nitride nanosheets.

Quantitative Depth Profiling And Diffusion In Thin Films

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