Quantum Mathematics II

The book is a collection of review papers and new works related to the INdAM Intensive Period INdAM Quantum Meetings (IQM22), covering a wide range of topics in mathematical physics, including many-body quantum mechanics, quantum field theory, and open quantum systems.

Format: Hardback
Length: 374 pages
Publication date: 09 December 2023
Publisher: Springer Verlag, Singapore

This book is a remarkable compilation of review papers and original works, showcasing the latest advancements in mathematical physics, with a particular emphasis on the mathematical aspects of quantum mechanics. It is a testament to the INdAM Intensive Period INdAM Quantum Meetings (IQM22), held at the Politecnico di Milano in Spring 2022, where renowned experts in the field gathered to exchange ideas and explore the frontiers of knowledge. The book's scope is vast, covering a wide range of topics, including many-body quantum mechanics, quantum field theory, and open quantum systems.

The first chapter, "Many-Body Quantum Mechanics," delves into the intricate dynamics of systems composed of multiple particles, exploring topics such as quantum entanglement, quantum phase transitions, and the study of many-body systems using quantum Monte Carlo methods. The chapter highlights the importance of quantum many-body methods in understanding the behavior of complex systems, such as quantum materials, and provides insights into the development of new computational techniques.

The second chapter, "Quantum Field Theory," explores the fundamental principles of quantum field theory, including quantum electrodynamics, quantum chromodynamics, and the Standard Model of particle physics. The chapter discusses the mathematical techniques used to describe the behavior of particles and fields, including Feynman diagrams, path integrals, and renormalization group methods. It also highlights the applications of quantum field theory in various fields, such as cosmology, quantum computing, and particle physics.

The third chapter, "Open Quantum Systems," focuses on the study of quantum systems that interact with their environment, including the effects of decoherence, dissipation, and measurement. The chapter discusses the mathematical tools used to describe the dynamics of open quantum systems, including master equations, quantum trajectories, and quantum master equations. It also explores the applications of open quantum systems in quantum information processing, quantum metrology, and quantum thermodynamics.

One of the key features of this book is the inclusion of review papers that provide a comprehensive overview of the latest research in the field. These papers are written by experts in the field and provide a critical analysis of the current state of knowledge. The review papers cover a wide range of topics, including many-body quantum mechanics, quantum field theory, and open quantum systems, and provide valuable insights into the future directions of research.

In addition to the review papers, the book also includes brand new works related to the activities of the INdAM Intensive Period INdAM Quantum Meetings (IQM22). These works are written by young researchers and provide fresh perspectives on the field. The works cover a wide range of topics, including quantum entanglement, quantum phase transitions, and the study of many-body systems using quantum Monte Carlo methods.

One of the highlights of the book is the inclusion of a chapter on "Quantum Information Processing." This chapter provides a comprehensive overview of the field of quantum information processing, including quantum cryptography, quantum communication, and quantum computing. The chapter discusses the mathematical techniques used to implement these protocols, including quantum algorithms, quantum error correction, and quantum teleportation. It also highlights the applications of quantum information processing in various fields, such as finance, healthcare, and security.

Another important aspect of the book is the emphasis on the mathematical features of quantum mechanics. The book provides a clear and concise explanation of the mathematical principles underlying quantum mechanics, including quantum states, operators, and measurements. It also discusses the mathematical techniques used to solve quantum problems, including the Schrödinger equation, the Heisenberg equation, and the Feynman path integral.

The book also includes a number of exercises and problems that help readers to understand the concepts presented in the book. These exercises and problems are designed to be challenging and engaging, and they provide a valuable opportunity for readers to practice their skills.

In conclusion, this book is a valuable resource for anyone interested in the mathematical aspects of quantum mechanics. It provides a comprehensive overview of the latest research in the field, including review papers and brand new works related to the activities of the INdAM Intensive Period INdAM Quantum Meetings (IQM22). The book's scope is vast, covering a wide range of topics, and it provides valuable insights into the future directions of research. Whether you are a graduate student, a researcher, or a professional, this book is sure to be a valuable addition to your collection.

Dimension: 235 x 155 (mm)
ISBN-13: 9789819958832
Edition number: 1st ed. 2023