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6881 results in Condensed Matter Physics, Nanoscience and Mesoscopic Physics

Page 8 of 345

  • 2 - Getting Familiar with Second Quantization: Model Hamiltonians

  • Gianluca Stefanucci, Università degli Studi di Roma 'Tor Vergata', Robert van Leeuwen, University of Jyväskylä, Finland
  • Book:
    Nonequilibrium Many-Body Theory of Quantum Systems
    Published online:
    02 January 2025
    Print publication:
    16 January 2025, pp 35-78

  • Summary

    The Green’s function method is among the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. With entirely new chapters and updated example problems, the second edition of this popular text continues to provide an ideal introduction to nonequilibrium many-body quantum systems and ultrafast phenomena in modern science. Retaining the unique and self-contained style of the original, this new edition has been thoroughly revised to address interacting systems of fermions and bosons, simplified many-body approaches like the GKBA, the Bloch equations, and the Boltzmann equations, and the connection between Green’s functions and newly developed time-resolved spectroscopy techniques. Small gaps in the theory have been filled, and frequently overlooked subtleties have been systematically highlighted and clarified. With an abundance of illustrative examples, insightful discussions, and modern applications, this book remains the definitive guide for students and researchers alike.

Fractionalization of Particles in Physics
  • Invertible Topological Phases of Matter
  • Christopher Mudry, Claudio Chamon
  • Published online:
    09 January 2025
    Print publication:
    23 January 2025
  • This book explores the fractionalization of particles in physics, how interactions between individual particles and with their background can modify their fundamental quantum states. Covering a large breadth of topics with an example-driven approach, this comprehensive text explains why phases of matter must be described in terms of both symmetries and their topology. The majority of important results are derived in full with explanations provided, while exercises at the end of each section allow readers to extend and develop their understanding of key topics. The first part presents polyacetylene as the paradigmatic material in which electric charge can be fractionalized, while the second part introduces the notion of invertible topological phases of matter. The final part is devoted to the 'ten-fold way', a classification of topological insulators or superconductors. The text requires a solid understanding of quantum mechanics and is a valuable resource for graduate students and researchers in physics.

Nonequilibrium Many-Body Theory of Quantum Systems
  • A Modern Introduction
  • 2nd edition
  • Gianluca Stefanucci, Robert van Leeuwen
  • Published online:
    02 January 2025
    Print publication:
    16 January 2025
  • The Green's function method is among the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. With entirely new chapters and updated example problems, the second edition of this popular text continues to provide an ideal introduction to nonequilibrium many-body quantum systems and ultrafast phenomena in modern science. Retaining the unique and self-contained style of the original, this new edition has been thoroughly revised to address interacting systems of fermions and bosons, simplified many-body approaches like the GKBA, the Bloch equations and the Boltzmann equations and the connection between Green's functions and newly developed time-resolved spectroscopy techniques. Small gaps in the theory have been filled, and frequently overlooked subtleties have been systematically highlighted and clarified. With an abundance of illustrative examples, insightful discussions and modern applications, this book remains the definitive guide for students and researchers alike.

Quantum Hall Effect
  • The First Topological Insulator
  • Saurabh Basu
  • Published online:
    31 August 2024
    Print publication:
    23 January 2025
  • This book deals with the discovery and explanation of the quantum Hall effect and its fundamental principles. It is meant for undergraduate and graduate students of physics, engineering, and applied sciences studying condensed matter physics. Doctoral students and researchers of this subject will also find it equally useful. It begins with a historical overview of this effect wherein the experiment and the physical systems are described. It progresses to cover discrete symmetries like inversion symmetry, time reversal symmetry, particle-hole symmetry, and chiral symmetry. It also examines how the Hamiltonian transforms under such symmetry operations. Two 1D models, namely the Su-Schrieffer-Heeger (SSH) model and a Kitaev chain with superconducting correlations, are discussed too. Then, the quantum Hall effect in graphene is explained. Further, the spin Hall effect is studied which may have prospects of using graphene as spintronic devices. The book ends with a brief review on fractional quantum Hall effect.

Density Matrix and Tensor Network Renormalization
  • Tao Xiang
  • Published online:
    18 January 2024
    Print publication:
    31 August 2023
  • Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area.

Discrete Variational Problems with Interfaces
  • Roberto Alicandro, Andrea Braides, Marco Cicalese, Margherita Solci
  • Published online:
    17 January 2024
    Print publication:
    21 December 2023
  • Many materials can be modeled either as discrete systems or as continua, depending on the scale. At intermediate scales it is necessary to understand the transition from discrete to continuous models and variational methods have proved successful in this task, especially for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems, and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.

Page 8 of 345