CLASSICAL AND QUANTUM MECHANICS WITH LIE ALGEBRAS

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How to see physics in its full picture? This book offers a new approach: start from math, in its simple and elegant tools: discrete math, geometry, and algebra, avoiding heavy analysis that might obscure the true picture. This will get you ready to master a few fundamental topics in physics: from Newtonian mechanics, through relativity, towards quantum mechanics. Thanks to simple math, both classical and modern physics follow and make a complete vivid picture of physics. This is an original and unified point of view to highlighting physics from a fresh pedagogical angle. Each chapter ends with a lot of relevant exercises. The exercises are an integral part of the chapter: they teach new material and are followed by complete solutions. This is a new pedagogical style: the reader takes an active part in discovering the new material, step by step, exercise by exercise. The book could be used as a textbook in undergraduate courses such as Introduction to Newtonian mechanics and special relativity, Introduction to Hamiltonian mechanics and stability, Introduction to quantum physics and chemistry, and Introduction to Lie algebras with applications in physics. Sample Chapter(s) 1 - Introduction to Newtonian Mechanics: Energy and Work Request Inspection Copy Contents: Introduction to Newtonian Physics: Introduction to Newtonian Mechanics: Energy-Work Angular Momentum and Its Conservation Stability in Geometrical Optics Towards Stability in Classical Mechanics: Poincare Stability in Classical Mechanics Cantor Set and Its Applications Is The Universe Infinite? Binary Trees and Chaos Theory The Binomial Formula and Quantum Statistical Mechanics: Newton's Binomial and Trinomial Formulas Applications in Quantum Statistical Mechanics Introduction to Relativity: Introduction to Special Relativity: Momentum-Energy Towards General Relativity: Spacetime and Its Coordinates Introduction to Quantum Physics and Chemistry: Introduction to Quantum Mechanics: Energy Levels and Spin Quantum Chemistry: Electronic Structure Introduction to Lie Algebras and Their Applications: Jordan Form and Algebras Design Your Lie Algebra Ideals and Isomorphism Theorems Exercises: Solvability and Nilpotency Nilpotency and Engel's Theorems Weight Space and Lie's Lemma and Theorem Cartan's Criterion for Solvability Killing Form and Simple Ideal Decomposition Hamiltonian Mechanics: Energy and Angular Momentum Lie Algebras in Quantum Mechanics and Special Relativity Appendix: Background in Calculus: Functions and Their Derivatives Polynomials and Partial Derivatives Matrices and Their Eigenvalues References Index Readership: Undergraduate and graduate students in Mathematics, Physics, and Chemistry.

ADVANCES IN QUANTUM COMPUTER MUSIC (1版)

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The modern music industry depends critically on computers. The development of conventional digital computing technology for music has been progressing in tandem with the evolution of computers since the 1950s. Therefore, future developments in quantum computing are most likely to impact the way in which musicians will create, perform, and conduct research. Classical computers manipulate information represented in terms of binary digits, each of, which can be equal to 1 (on) or 0 (off). They work with microprocessors made up of billions of tiny switches that are activated by electric signals. In contrast, a quantum computer deals with information in terms of quantum bits (qubits), which can operate at the subatomic level. In other words, they directly work in the realm of quantum physics. Since they can run algorithms that are non-tractable to run on digital computers, quantum computers are surfacing as a promising disruptive technology. Advances in Quantum Computer Music collates a comprehensive collection of chapters by pioneers of emerging interdisciplinary research at the crossroads of quantum computing and music. Together, these pioneers hope to anticipate and prototype the unprecedented new uses for this technology that are bound to emerge from their cutting-edge research. Sample Chapter(s) Foreword Chapter 1: Sonifications of Quantum Superpositions: Methods and Musical Applications Contents: Sonifications of Quantum Superpositions: Methods and Musical Applications (Walker Smith, Dmitri Volkov and Alex Alani) Quantum Feedback Delay Networks (Davide Rocchesso) Exploring Quantum Phenomena through Sound: Strategies, Challenges, and Insights (Reiko Yamada, Eloy Piñol, Samuele Grandi, Jakub Zakrzewski and Maciej Lewenstein) Quantum Memory: Measuring the Degree of Non-Markovianity of Orchestral Music (Maria Mannone and Omar Costa Hamido) An Introduction to Quantum Probability Amplitude Modulation (QPAM) from a Compositional Perspective (Eren Utku) Investigating the usefulness of Quantum Blur in Music (Marcel Pfaffhauser and James Wootton) Qubit Instrumentation of Entanglement (Mark Carney) Developing a Framework for Sonifying Variational Quantum Algorithms: Implications for Music Composition (Paulo Vitor Itaboraí, Peter Thomas, Arianna Crippa, Karl Jansen, Tim Schwägerl and María Aguado Yáñez) Music AI with Quantum Reservoir Computing (Eduardo Reck Miranda and Hari Vignesh Shaji) Readership: Academic community and researchers in the field of Unconventional Computing, specifically Quantum Computing, musicians interested and/or working with Music Technology, and students and science journalists interested in arts-science topics.