Bogoliubov-de Gennes Method and Its Applications

Bogoliubov-de Gennes Method and Its Applications

Author: Jian-Xin Zhu

Publisher: Springer

Published: 2016-06-21

Total Pages: 193

ISBN-13: 3319313142

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The purpose of this book is to provide an elementary yet systematic description of the Bogoliubov-de Gennes (BdG) equations, their unique symmetry properties and their relation to Green’s function theory. Specifically, it introduces readers to the supercell technique for the solutions of the BdG equations, as well as other related techniques for more rapidly solving the equations in practical applications. The BdG equations are derived from a microscopic model Hamiltonian with an effective pairing interaction and fully capture the local electronic structure through self-consistent solutions via exact diagonalization. This approach has been successfully generalized to study many aspects of conventional and unconventional superconductors with inhomogeneities – including defects, disorder or the presence of a magnetic field – and becomes an even more attractive choice when the first-principles information of a typical superconductor is incorporated via the construction of a low-energy tight-binding model. Further, the lattice BdG approach is essential when theoretical results for local electronic states around such defects are compared with the scanning tunneling microscopy measurements. Altogether, these lectures provide a timely primer for graduate students and non-specialist researchers, while also offering a useful reference guide for experts in the field.


Ultracold Atoms in Optical Lattices

Ultracold Atoms in Optical Lattices

Author: Maciej Lewenstein

Publisher: OUP Oxford

Published: 2012-03-08

Total Pages: 494

ISBN-13: 0191627437

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Quantum computers, though not yet available on the market, will revolutionize the future of information processing. Quantum computers for special purposes like quantum simulators are already within reach. The physics of ultracold atoms, ions and molecules offer unprecedented possibilities of control of quantum many body systems and novel possibilities of applications to quantum information processing and quantum metrology. Particularly fascinating is the possibility of using ultracold atoms in lattices to simulate condensed matter or even high energy physics. This book provides a complete and comprehensive overview of ultracold lattice gases as quantum simulators. It opens up an interdisciplinary field involving atomic, molecular and optical physics, quantum optics, quantum information, condensed matter and high energy physics. The book includes some introductory chapters on basic concepts and methods, and then focuses on the physics of spinor, dipolar, disordered, and frustrated lattice gases. It reviews in detail the physics of artificial lattice gauge fields with ultracold gases. The last part of the book covers simulators of quantum computers. After a brief course in quantum information theory, the implementations of quantum computation with ultracold gases are discussed, as well as our current understanding of condensed matter from a quantum information perspective.


Models And Methods For Quantum Condensation And Fluids

Models And Methods For Quantum Condensation And Fluids

Author: Weizhu Bao

Publisher: World Scientific

Published: 2023-01-04

Total Pages: 361

ISBN-13: 9811266069

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The Institute for Mathematical Sciences at the National University of Singapore hosted a thematic program on Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications from September 2019 to March 2020. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers. This invaluable volume collects six expanded lecture notes with self-contained tutorials. The coverage includes mathematical models and numerical methods for multidimensional solitons in linear and nonlinear potentials; Bose-Einstein condensation (BEC) with dipole-dipole interaction, higher order interaction and spin-orbit coupling; classical and quantum turbulence; and molecular dynamics process based on the first-principle in quantum chemistry.This volume serves to inspire graduate students and researchers who will embark into original research work in these fields.


Novel Superfluids

Novel Superfluids

Author: Karl-Heinz Bennemann

Publisher: OUP Oxford

Published: 2013-02-28

Total Pages: 641

ISBN-13: 0191650196

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This book reports on the latest developments in the field of Superfluidity. The phenomenon has had a tremendous impact on the fundamental sciences as well as a host of technologies. It began with the discovery of superconductivity in mercury in 1911, which was ultimately described theoretically by the theory of Bardeen Cooper and Schriever (BCS) in 1957. The analogous phenomena, superfluidity, was discovered in helium in 1938 and tentatively explained shortly thereafter as arising from a Bose-Einstein Condensation (BEC) by London. But the importance of superfluidity, and the range of systems in which it occurs, has grown enormously. In addition to metals and the helium liquids the phenomena has now been observed for photons in cavities, excitons in semiconductors, magnons in certain materials, and cold gasses trapped in high vacuum. It very likely exist for neutrons in a neutron star and, possibly, in a conjectured quark state at their center. Even the Universe itself can be regarded as being in a kind of superfluid state. All these topics are discussed by experts in the respective subfields.


High Performance Computing in Science and Engineering ́15

High Performance Computing in Science and Engineering ́15

Author: Wolfgang E. Nagel

Publisher: Springer

Published: 2016-02-05

Total Pages: 701

ISBN-13: 331924633X

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This book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2015. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe’s leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance. The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.


Quantum World Of Ultra-cold Atoms And Light, The - Book Iii: Ultra-cold Atoms

Quantum World Of Ultra-cold Atoms And Light, The - Book Iii: Ultra-cold Atoms

Author: Crispin W Gardiner

Publisher: World Scientific

Published: 2017-09-07

Total Pages: 586

ISBN-13: 178634419X

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This century has seen the development of technologies for manipulating and controlling matter and light at the level of individual photons and atoms, a realm in which physics is fully quantum-mechanical. The dominant experimental technology is the laser, and the theoretical paradigm is quantum optics.The Quantum World of Ultra-Cold Atoms and Light is a trilogy, which presents the quantum optics way of thinking and its applications to quantum devices. This book — 'Ultra-Cold Atoms' — provides a theoretical treatment of ultra-cold Bosons and Fermions and their interactions with electromagnetic fields in a form consistent with the first two books in the trilogy.The central concept is the quantum stochastic paradigm, formulated for cold collision physics. For Bosons, this yields a suite of techniques; versions of the stochastic Gross-Pitaevskii equation, using which a wide range of dynamic and thermal properties are formulated.The eBook editions of the 'Quantum World Trilogy' feature an extensive system of hyperlinks for ease of cross reference within the books, as well as links to the other books in the trilogy. In the section Viewing the eBooks we explain how these links work, and give some advice on appropriate pdf viewer applications.


New Frontiers in Multiscale Modelling of Advanced Materials

New Frontiers in Multiscale Modelling of Advanced Materials

Author: Simone Taioli

Publisher: Frontiers Media SA

Published: 2016-01-22

Total Pages: 93

ISBN-13: 2889197557

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Atomistic simulations, based on ab-initio and semi-empirical approaches, are nowadays widespread in many areas of physics, chemistry and, more recently, biology. Improved algorithms and increased computational power widened the areas of application of these computational methods to extended materials of technological interest, in particular allowing unprecedented access to the first-principles investigation of their electronic, optical, thermodynamical and mechanical properties, even where experiments are not available. However, for a big impact on the society, this rapidly growing field of computational approaches to materials science has to face the unfavourable scaling with the system size, and to beat the time-scale bottleneck. Indeed, many phenomena, such as crystal growth or protein folding for example, occur in a space/time scale which is normally out of reach of present simulations. Multi-scale approaches try to combine different scale algorithms along with matching procedures in order to bridge the gap between first-principles and continuum-level simulations. This Research Topic aims at the description of recent advances and applications in these two emerging fields of ab-inito and multi-scale materials modelling for both ground and excited states. A variety of theoretical and computational techniques are included along with the application of these methods to systems at increasing level of complexity, from nano to micro. Crossing the borders between several computational, theoretical and experimental techniques, this Research Topic aims to be of interest to a broad community, including experimental and theoretical physicists, chemists and engineers interested in materials research in a broad sense.


Superfluidity and Superconductivity

Superfluidity and Superconductivity

Author: D.R. Tilley

Publisher: Routledge

Published: 2019-07-09

Total Pages: 481

ISBN-13: 1351412795

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Superfluidity and Superconductivity, Third Edition introduces the low-temperature phenomena of superfluidity and superconductivity from a unified viewpoint. The book stresses the existence of a macroscopic wave function as a central principle, presents an extensive discussion of macroscopic theories, and includes full descriptions of relevant experimental results throughout. This edition also features an additional chapter on high-temperature superconductors. With problems at the end of most chapters as well as the careful elaboration of basic principles, this comprehensive survey of experiment and theory provides an accessible and invaluable foundation for graduate students studying low-temperature physics as well as senior undergraduates taking specialized courses.


Superconductivity in Graphene and Carbon Nanotubes

Superconductivity in Graphene and Carbon Nanotubes

Author: Pablo Burset Atienza

Publisher: Springer Science & Business Media

Published: 2013-10-02

Total Pages: 166

ISBN-13: 3319011103

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The unique electronic band structure of graphene gives rise to remarkable properties when in contact with a superconducting electrode. In this thesis two main aspects of these junctions are analyzed: the induced superconducting proximity effect and the non-local transport properties in multi-terminal devices. For this purpose specific models are developed and studied using Green function techniques, which allow us to take into account the detailed microscopic structure of the graphene-superconductor interface. It is shown that these junctions are characterized by the appearance of bound states at subgap energies which are localized at the interface region. Furthermore it is shown that graphene-supercondutor-graphene junctions can be used to favor the splitting of Cooper pairs for the generation of non-locally entangled electron pairs. Finally, using similar techniques the thesis analyzes the transport properties of carbon nanotube devices coupled with superconducting electrodes and in graphene superlattices.