Topic
Ansatz
About: Ansatz is a research topic. Over the lifetime, 8900 publications have been published within this topic receiving 189671 citations.
Papers published on a yearly basis
1 / 2
Papers
Book•
1 Jan 2004TL;DR: In this paper, the Kohn-Sham ansatz is used to solve the problem of determining the electronic structure of atoms, and the three basic methods for determining electronic structure are presented.
Abstract: Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.
3,097 citations
Posted Content•
TL;DR: In this article, a detailed explanation of Bethe Ansatz, Quantum Inverse Scattering Method and Algebraic Bether Ansatz as well as main models are Nonlinear Schrodinger equation (one dimensional Bose gas), Sine-Gordon and Thiring models.
Abstract: The book contain detailed explanation of Bethe Ansatz, Quantum Inverse Scattering Method and Algebraic Bether Ansatz as well. Main Models are Nonlinear Schrodinger equation (one dimensional Bose gas), Sine-Gordon and Thiring models. Heisenberg Antiferromagnet and Hubbard models. It is explained in detail, how to calculate correlation functions.
2,868 citations
TL;DR: The properties of the ground state configuration are elucidated to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study.
Abstract: Starting from a general ansatz, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the ad hoc introduced quality function from [J. Reichardt and S. Bornholdt, Phys. Rev. Lett. 93, 218701 (2004)] and the modularity Q as defined by Newman and Girvan [Phys. Rev. E 69, 026113 (2004)] as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further, we show how hierarchies and overlap in the community structure can be detected. Computationally efficient local update rules for optimization procedures to find the ground state are given. We show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure.
2,331 citations
TL;DR: In this paper, the existence of standing wave solutions of nonlinear Schrodinger equations was studied and sufficient conditions for nontrivial solutionsu ∈W¯¯¯¯1,2(ℝ�姫 n ) were established.
Abstract: This paper concerns the existence of standing wave solutions of nonlinear Schrodinger equations. Making a standing wave ansatz reduces the problem to that of studying the semilinear elliptic equation: (*)
$$ - \Delta u + b(x)u = f(x, u), x \in \mathbb{R}^n .$$
The functionf is assumed to be “superlinear”. A special case is the power nonlinearityf(x, z)=∥z∥
s−1
z where 1
1,807 citations
TL;DR: In this paper, the authors presented a technique which utilizes unitarity and collinear limits to construct ansatze for one-loop amplitudes in gauge theory, and proved that their $N=4$ ansatz is correct using general properties of the relevant one-loops $n$-point integrals.
Abstract: We present a technique which utilizes unitarity and collinear limits to construct ansatze for one-loop amplitudes in gauge theory. As an example, we obtain the one-loop contribution to amplitudes for $n$ gluon scattering in $N=4$ supersymmetric Yang-Mills theory with the helicity configuration of the Parke-Taylor tree amplitudes. We prove that our $N=4$ ansatz is correct using general properties of the relevant one-loop $n$-point integrals. We also give the ``splitting amplitudes'' which govern the collinear behavior of one-loop helicity amplitudes in gauge theories.
1,550 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 2 |
| 2025 | 256 |
| 2024 | 323 |
| 2023 | 849 |
| 2022 | 2,620 |
| 2021 | 540 |