Transport and Subgap States in Superconducting Heterostructures of Effective Dirac Systems

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ISBN 13 : 9783868451719
Total Pages : 0 pages
Book Rating : 4.4/5 (517 download)

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Book Synopsis Transport and Subgap States in Superconducting Heterostructures of Effective Dirac Systems by : Jacob Fuchs

Download or read book Transport and Subgap States in Superconducting Heterostructures of Effective Dirac Systems written by Jacob Fuchs and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis deals with superconducting heterostructures of both of the aforementioned materials and examines transport phenomena as well as the formation of subgap states in such systems: In the first chapter, superconducting bilayer graphene with a chemisorbed adatom is investigated and the existence of peculiar subgab states, so-called Yu-Shiba-Rusinov states, is shown. The second chapter deals with T junction devices make out of three-dimensional (3D) TI nanowires. Together with proximity induced superconductivity in one arm and external magnetic fields, this setup allows for the occurence of crossed Andreev reflection, including perfect crossed Andreev reflection, and negative nonlocal conductances. In the third chapter, Josephson junctions of 3D TI nanowires are investigated. The origin of unusual, experimentally observed supercurrent oscillations in dependence of a parallel magnetic field is examinated in a semiclassical analysis.

Electronic Transport in Topological Superconducting Heterostructures

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (141 download)

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Book Synopsis Electronic Transport in Topological Superconducting Heterostructures by : Joseph Jude Cuozzo

Download or read book Electronic Transport in Topological Superconducting Heterostructures written by Joseph Jude Cuozzo and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we study Andreev transport and Josephson effects in topological superconducting heterostructures. We study consider two platforms: quantum Hall-superconductor (QH-SC) heterostructures and Josephson junctions. In the first platform, we study QH graphene-SC systems with a focus on the influence symmetry-breaking effects have on Andreev transport. In graphene, valley and spin degeneracy lead to an approximate SU(4) symmetry that is reflected in the approximate 4-fold degeneracy of graphene's Landau levels (LL). We develop an effective low-energy description of Andreev edge states that takes into account the correction to the drift velocity of the QH-SC edge modes due to SU(4) symmetry-breaking effects. We show that Zeeman and valley splitting effects can be used to demonstrate Andreev edge state interference. We also present numerical simulations of Andreev conversion in the lowest LL of canted antiferromagnetic graphene. In the second platform, we analyze Josephson effects and the microwave response of Josephson junctions. We propose a theory for a Leggett collective mode in Dirac semimetals-based Josephson junctions and simulate the microwave response of the junction. We also study Landau-Zener transitions (LZT) between Andreev bound states in Josephson junctions. We present a protocol using superconducting quantum interference devices to differentiate between LZTs between Andreev states, which mimic signatures of Majoranas, and systems with real Majoranas.

Entanglement in Superconducting Heterostructures, and Quantum Circuit Simulation Hardware

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ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.:/5 (125 download)

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Book Synopsis Entanglement in Superconducting Heterostructures, and Quantum Circuit Simulation Hardware by : Corey I Ostrove

Download or read book Entanglement in Superconducting Heterostructures, and Quantum Circuit Simulation Hardware written by Corey I Ostrove and published by . This book was released on 2021 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: We begin this dissertation by studying noise correlations in superconducting heterostructures of various geometries. In recent years there has been a resurgence of interest in the nonlocal transport properties of superconducting heterostructures due to the possibility of their serving as a source of electronic entanglement in solid state quantum information processors. Devices designed for this purpose are called Cooper pair splitting devices. The utility of these devices as entanglement sources is known to have connections to the positivity of noise cross correlations in spatially separated leads. In Chapter 1 we outline the theoretical prerequisites for this work, outlining the scattering theory framework based on the Bogoliubov-de Gennes equations we adopt. Within this framework we apply a methodology first introduced by Demers and by Blonder, Tinkham and Klapwijk (BTK) in the early 1980s to find the scattering matrix for our superconducting structures. The current, local and nonlocal shot noise can all be expressed in terms of the underlying scattering processes. This framework allows us to investigate the behavior of the current and noise correlations in the structure as we change the geometry and other key system parameters such as the system size, superconducting phase difference and temperature. We also introduce the Andreev approximation, a commonly used approximation which simplifies the scattering theory for superconducting heterostructures. In Chapter 2, we study the local and nonlocal shot noise in a quasi-1D normal-superconducting-normal (NSN) geometry using material parameters relevant to high-T [subscript c] superconductivity. The scattering and shot noise distributions are studied in the short, intermediate and long system size limits, allowing us to examine the qualitative differences in these three parameter regimes. This allows us to, for example, identify the signatures of over-the-gap geometric resonances in the shot noise distributions that appear in the long system size limit. We also break the nonlocal shot noise distributions down further and study the individual contributions to the nonlocal shot due to particle-particle, hole-hole and particle-hole scattering processes. In Chapter 3, we extend our investigation of superconducting heterostructures to the more complicated NSNSN geometry. A novel feature introduced in the geometry is the presence of subgap quasibound states, which show up as resonances in the scattering matrix. We show that these quasibound states dramatically impact the nonlocal shot noise distributions in the system. At energies near the quasibound states the dominant transmission channel through the system is a process called particle-hole transmission, which results in sharp positive peaks in the nonlocal shot noise distribution of the system. The behavior of the nonlocal noise correlations as we change the size of the superconducting and normal regions is investigated and it is found that there is a "sweet spot'' with respect to the size of the superconducting regions that maximizes the positivity of the nonlocal noise distributions as well as a periodic-like behavior in the positivity of the noise distributions with respect to the normal region size. The results of the full scattering theory for the NSNSN geometry are compared to the results obtained using the Andreev approximation, where we find that the Andreev approximation breaks down at energies close to the quasibound state energies. In the second half of this dissertation we focus on work related to the development of a prototype special-purpose quantum circuit simulation device based on commercial off-the-shelf high-speed analog signal processing hardware. In Chapter 4 we introduce the embedding scheme used to represent quantum states and quantum gates in the frequency domain of a classical analog voltage signal. Experimental results are presented from an early two-qubit prototype device for the fidelity of the state generation and gate application circuits. In Chapter 5, a more in-depth investigation into the modeling of classical errors within our signal processing based simulation method is performed in terms of the effects this noise has on the results of the quantum computation being simulatied. It is shown, for example, that additive white gaussian noise (AWGN) in our system has the same effect as applying a depolarizing channel to the qubits in the simulation. We then perform a simulation of a simple quantum error correction (QEC) protocol using the device and show that, even in the presence of classical noise in the simulation hardware, an overall enhancement in the performance of gate operations as a result of applying QEC is observed

Signatures of Topological Superconductors

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (919 download)

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Book Synopsis Signatures of Topological Superconductors by : Shu-Ping Lee

Download or read book Signatures of Topological Superconductors written by Shu-Ping Lee and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological superconductors are particularly interesting in light of the active ongoing experimental efforts for realizing exotic physics such as Majorana zero modes. These systems have excitations with non-Abelian exchange statistics, which provides a path towards topological quantum information processing. Intrinsic topological superconductors are quite rare in nature. However, one can engineer topological superconductivity by inducing effective p-wave pairing in materials which can be grown in the laboratory. One possibility is to induce the proximity effect in topological insulators; another is to use hybrid structures of superconductors and semiconductors. The proposal of interfacing s-wave superconductors with quantum spin Hall systems provides a promising route to engineered topological superconductivity. Given the exciting recent progress on the fabrication side, identifying experiments that definitively expose the topological superconducting phase (and clearly distinguish it from a trivial state) raises an increasingly important problem. With this goal in mind, we proposed a detection scheme to get an unambiguous signature of topological superconductivity, even in the presence of ordinarily detrimental effects such as thermal fluctuations and quasiparticle poisoning. We considered a Josephson junction built on top of a quantum spin Hall material. This system allows the proximity effect to turn edge states in effective topological superconductors. Such a setup is promising because experimentalists have demonstrated that supercurrents indeed flow through quantum spin Hall edges. To demonstrate the topological nature of the superconducting quantum spin Hall edges, theorists have proposed examining the periodicity of Josephson currents respect to the phase across a Josephson junction. The periodicity of tunneling currents of ground states in a topological superconductor Josephson junction is double that of a conventional Josephson junction. In practice, this modification of periodicity is extremely difficult to observe because noise sources, such as quasiparticle poisoning, wash out the signature of topological superconductors. For this reason, We propose a new, relatively simple DC measurement that can compellingly reveal topological superconductivity in such quantum spin Hall/superconductor heterostructures. More specifically, We develop a general framework for capturing the junction's current-voltage characteristics as a function of applied magnetic flux. Our analysis reveals sharp signatures of topological superconductivity in the field-dependent critical current. These signatures include the presence of multiple critical currents and a non-vanishing critical current for all magnetic field strengths as a reliable identification scheme for topological superconductivity. This system becomes more interesting as interactions between electrons are involved. By modeling edge states as a Luttinger liquid, we find conductance provides universal signatures to distinguish between normal and topological superconductors. More specifically, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as a lead. Interestingly, arbitrarily weak interactions induce qualitative changes in the behavior relative to the free-fermion limit, leading to a sharp dichotomy in conductance for the trivial (narrow superconductor) and topological (wide superconductor) cases. Furthermore, we find that strong interactions can in principle induce parafermion excitations at a superconductor/quantum spin Hall junction. As we identify the existence of topological superconductor, we can take a step further. One can use topological superconductor for realizing Majorana modes by breaking time reversal symmetry. An advantage of 2D topological insulator is that networks required for braiding Majoranas along the edge channels can be obtained by adjoining 2D topological insulator to form corner junctions. Physically cutting quantum wells for this purpose, however, presents technical challenges. For this reason, I propose a more accessible means of forming networks that rely on dynamically manipulating the location of edge states inside of a single 2D topological insulator sheet. In particular, I show that edge states can effectively be dragged into the system's interior by gating a region near the edge into a metallic regime and then removing the resulting gapless carriers via proximity-induced superconductivity. This method allows one to construct rather general quasi-1D networks along which Majorana modes can be exchanged by electrostatic means. Apart from 2D topological insulators, Majorana fermions can also be generated in other more accessible materials such as semiconductors. Following up on a suggestion by experimentalist Charlie Marcus, I proposed a novel geometry to create Majorana fermions by placing a 2D electron gas in proximity to an interdigitated superconductor-ferromagnet structure. This architecture evades several manufacturing challenges by allowing single-side fabrication and widening the class of 2D electron gas that may be used, such as the surface states of bulk semiconductors. Furthermore, it naturally allows one to trap and manipulate Majorana fermions through the application of currents. Thus, this structure may lead to the development of a circuit that enables fully electrical manipulation of topologically-protected quantum memory. To reveal these exotic Majorana zero modes, I also proposed an interference scheme to detect Majorana fermions that is broadly applicable to any 2D topological superconductor platform.

Superconductor/Semiconductor Junctions

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Publisher : Springer
ISBN 13 : 9783642075865
Total Pages : 150 pages
Book Rating : 4.0/5 (758 download)

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Book Synopsis Superconductor/Semiconductor Junctions by : Thomas Schäpers

Download or read book Superconductor/Semiconductor Junctions written by Thomas Schäpers and published by Springer. This book was released on 2010-12-01 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, featuring the most comprehensive treatment of Josephson junctions ever published, describes superconductor/two-dimensional-electron-gas (2DEG) structures, providing a better understanding of their transport properties. It also discusses the control of junctions using gate electrodes or injection currents, and the physical effects observed in these junctions.

Theory of electron transport in superconducting heterostructures

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ISBN 13 : 9789171970220
Total Pages : 34 pages
Book Rating : 4.9/5 (72 download)

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Book Synopsis Theory of electron transport in superconducting heterostructures by : Magnus Hurd

Download or read book Theory of electron transport in superconducting heterostructures written by Magnus Hurd and published by . This book was released on 1994 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mesoscopic Electron Transport

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Publisher : Springer Science & Business Media
ISBN 13 : 9401588392
Total Pages : 680 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Mesoscopic Electron Transport by : Lydia L. Sohn

Download or read book Mesoscopic Electron Transport written by Lydia L. Sohn and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ongoing developments in nanofabrication technology and the availability of novel materials have led to the emergence and evolution of new topics for mesoscopic research, including scanning-tunnelling microscopic studies of few-atom metallic clusters, discrete energy level spectroscopy, the prediction of Kondo-type physics in the transport properties of quantum dots, time dependent effects, and the properties of interacting systems, e.g. of Luttinger liquids. The overall understanding of each of these areas is still incomplete; nevertheless, with the foundations laid by studies in the more traditional systems there is no doubt that these new areas will advance mesoscopic electron transport to a new phenomenological level, both experimentally and theoretically. Mesoscopic Electron Transport highlights selected areas in the field, provides a comprehensive review of such systems, and also serves as an introduction to the new and developing areas of mesoscopic electron transport.

Fundamentals of Superconducting Nanoelectronics

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Publisher : Springer Science & Business Media
ISBN 13 : 364220158X
Total Pages : 340 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Fundamentals of Superconducting Nanoelectronics by : Anatoli Sidorenko

Download or read book Fundamentals of Superconducting Nanoelectronics written by Anatoli Sidorenko and published by Springer Science & Business Media. This book was released on 2011-08-18 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates how the new phenomena in superconductivity on the nanometer scale (FFLO state, triplet superconductivity, Crossed Andreev Reflection, synchronized generation etc.) serve as the basis for the invention and development of novel nanoelectronic devices and systems. It demonstrates how rather complex ideas and theoretical models, like odd-pairing, non-uniform superconducting state, pi-shift etc., adequately describe the processes in real superconducting nanostructues and novel devices based on them. The book is useful for a broad audience of readers, researchers, engineers, PhD-students, lectures and others who would like to gain knowledge in the frontiers of superconductivity at the nanoscale.

Lessons from Nanoelectronics

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Publisher : World Scientific Publishing Company
ISBN 13 : 9789813209732
Total Pages : 0 pages
Book Rating : 4.2/5 (97 download)

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Book Synopsis Lessons from Nanoelectronics by : Supriyo Datta

Download or read book Lessons from Nanoelectronics written by Supriyo Datta and published by World Scientific Publishing Company. This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A. Basic concepts. Why electrons flow ; The elastic resistor ; Ballistic and diffusive transport ; Conductance from fluctuation ; Energy band model ; The nanotransistor ; Diffusion equation for ballistic transport ; Boltzmann equation ; Electrochemical potentials and quasi-Fermi levels ; Hall effect ; Smart contacts ; Thermoelectricity ; Phonon transport ; Second law ; Fuel value of information

The New Superconducting Electronics

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Publisher : Springer Science & Business Media
ISBN 13 : 940111918X
Total Pages : 460 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis The New Superconducting Electronics by : H. Weinstock

Download or read book The New Superconducting Electronics written by H. Weinstock and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the proceedings of the NATO-sponsored Advanced Studies Institute (ASn on The New Superconducting Electronics (held 9-20 August 1992 in Waterville Valley, New Hampshire USA). The contents herein are intended to provide an update to an earlier volume on the same subject (based on a NATO ASI held in 1988). Four years seems a relatively short time interval, and our title itself, featuring The New Superconducting Electronics, may appear somewhat pretentious. Nevertheless, we feel strongly that the ASI fostered a timely reexamination of the technical progress and application potential of this rapid-paced field. There are, indeed, many new avenues for technological innovation which were not envisioned or considered possible four years ago. The greatest advances by far have occurred with regard to oxide superconductors, the so-called high transition-temperature superconductors, known in short as HTS. These advances are mainly in the ability to fabricate both (1) high-quality, relatively large-area films for microwave filters and (2) multilayer device structures, principally superconducting-normal-superconducting (SNS) Josephson junctions, for superconducting-quantum-interference-device (SQUID) magnetometers. Additionally, we have seen the invention and development of the flux-flow transistor, a planar three-terminal device. During the earlier ASI only the very first HTS films with adequate critical-current density had just been fabricated, and these were of limited area and had high resistance for microwave current.

The Vortex State

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Publisher : Springer Science & Business Media
ISBN 13 : 9401109745
Total Pages : 330 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis The Vortex State by : N. Bontemps

Download or read book The Vortex State written by N. Bontemps and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most spectacular consequences of the description of the superfluid condensate in superfluid He or in superconductors as a single macroscopic quantum state is the quantization of circulation, resulting in quantized vortex lines. This book draws no distinction between superfluid He3 and He4 and superconductors. The reader will find the essential introductory chapters and the most recent theoretical and experimental progress in our understanding of the vortex state in both superconductors and superfluids, from lectures given by leading experts in the field, both experimentalists and theoreticians, who gathered in Cargèse for a NATO ASI. The peculiar features related to short coherence lengths, 2D geometry, high temperatures, disorder, and pinning are thoroughly discussed.

Single Quantum Dots

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Publisher : Springer Science & Business Media
ISBN 13 : 9783540140221
Total Pages : 370 pages
Book Rating : 4.1/5 (42 download)

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Book Synopsis Single Quantum Dots by : Peter Michler

Download or read book Single Quantum Dots written by Peter Michler and published by Springer Science & Business Media. This book was released on 2003-12-09 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special focus is given to the optical and electronic properties of single quantum dots due to their potential applications in devices operating with single electrons and/or single photons. This includes quantum dots in electric and magnetic fields, cavity-quantum electrodynamics, nonclassical light generation, and coherent optical control of excitons.

Fundamentals and Frontiers of the Josephson Effect

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Publisher : Springer Nature
ISBN 13 : 3030207269
Total Pages : 859 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Fundamentals and Frontiers of the Josephson Effect by : Francesco Tafuri

Download or read book Fundamentals and Frontiers of the Josephson Effect written by Francesco Tafuri and published by Springer Nature. This book was released on 2019-09-17 with total page 859 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and up-to-date description of the Josephson effect, a topic of never-ending interest in both fundamental and applied physics. In this volume, world-renowned experts present the unique aspects of the physics of the Josephson effect, resulting from the use of new materials, of hybrid architectures and from the possibility of realizing nanoscale junctions. These new experimental capabilities lead to systems where novel coherent phenomena and transport processes emerge. All this is of great relevance and impact, especially when combined with the didactic approach of the book. The reader will benefit from a general and modern view of coherent phenomena in weakly-coupled superconductors on a macroscopic scale. Topics that have been only recently discussed in specialized papers and in short reviews are described here for the first time and organized in a general framework. An important section of the book is also devoted to applications, with focus on long-term, future applications. In addition to a significant number of illustrations, the book includes numerous tables for comparative studies on technical aspects.

Semiconductor Nanowires

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Publisher : Elsevier
ISBN 13 : 1782422633
Total Pages : 573 pages
Book Rating : 4.7/5 (824 download)

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Book Synopsis Semiconductor Nanowires by : J Arbiol

Download or read book Semiconductor Nanowires written by J Arbiol and published by Elsevier. This book was released on 2015-03-31 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semiconductor nanowires promise to provide the building blocks for a new generation of nanoscale electronic and optoelectronic devices. Semiconductor Nanowires: Materials, Synthesis, Characterization and Applications covers advanced materials for nanowires, the growth and synthesis of semiconductor nanowires—including methods such as solution growth, MOVPE, MBE, and self-organization. Characterizing the properties of semiconductor nanowires is covered in chapters describing studies using TEM, SPM, and Raman scattering. Applications of semiconductor nanowires are discussed in chapters focusing on solar cells, battery electrodes, sensors, optoelectronics and biology. Explores a selection of advanced materials for semiconductor nanowires Outlines key techniques for the property assessment and characterization of semiconductor nanowires Covers a broad range of applications across a number of fields

Algebra, Geometry and Mathematical Physics

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Publisher : Springer
ISBN 13 : 3642553613
Total Pages : 680 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Algebra, Geometry and Mathematical Physics by : Abdenacer Makhlouf

Download or read book Algebra, Geometry and Mathematical Physics written by Abdenacer Makhlouf and published by Springer. This book was released on 2014-06-17 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers and advanced students.

Many Body Quantum Chaos

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Publisher : Mdpi AG
ISBN 13 : 9783039368327
Total Pages : 222 pages
Book Rating : 4.3/5 (683 download)

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Book Synopsis Many Body Quantum Chaos by : Sandro Wimberger

Download or read book Many Body Quantum Chaos written by Sandro Wimberger and published by Mdpi AG. This book was released on 2020-10-02 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of chaos in many-body quantum systems has a long history, going back to Wigner's simple models for heavy nuclei. Quantum chaos is being investigated in a broad variety of experimental platforms such as heavy nuclei, driven (few-electron) atoms, ultracold quantum gases, and photonic or microwave realizations. Quantum chaos plays a new and important role in many branches of physics, from condensed matter problems of many-body localization, including thermalization studies in closed and open quantum systems, and the question of dynamical stability relevant for quantum information and quantum simulation. This Special Issue and its related book address theories and experiments, methods from classical chaos, semiclassics, and random matrix theory, as well as many-body condensed matter physics. It is dedicated to Prof. Shmuel Fishman, who was one of the major representatives of the field over almost four decades, who passed away in 2019.

Bogoliubov-de Gennes Method and Its Applications

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Publisher : Springer
ISBN 13 : 3319313142
Total Pages : 193 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Bogoliubov-de Gennes Method and Its Applications by : Jian-Xin Zhu

Download or read book Bogoliubov-de Gennes Method and Its Applications written by Jian-Xin Zhu and published by Springer. This book was released on 2016-06-21 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.