Topic
Airy function
About: Airy function is a research topic. Over the lifetime, 1702 publications have been published within this topic receiving 36845 citations. The topic is also known as: Airy functions & Airy integral.
Papers published on a yearly basis
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Papers
TL;DR: In this paper, the authors derived analogues for the Airy kernel of the following properties of the sine kernel: the completely integrable system of P.D.E., the expression of the Fredholm determinant in terms of a Painleve transcendent, the existence of a commuting differential operator, and the fact that this operator can be used in the derivation of asymptotics, for generaln, of the probability that an interval contains preciselyn eigenvalues.
Abstract: Scaling level-spacing distribution functions in the “bulk of the spectrum” in random matrix models ofN×N hermitian matrices and then going to the limitN→∞ leads to the Fredholm determinant of thesine kernel sinπ(x−y)/π(x−y). Similarly a scaling limit at the “edge of the spectrum” leads to theAiry kernel [Ai(x)Ai(y)−Ai′(x)Ai(y)]/(x−y). In this paper we derive analogues for this Airy kernel of the following properties of the sine kernel: the completely integrable system of P.D.E.'s found by Jimbo, Miwa, Mori, and Sato; the expression, in the case of a single interval, of the Fredholm determinant in terms of a Painleve transcendent; the existence of a commuting differential operator; and the fact that this operator can be used in the derivation of asymptotics, for generaln, of the probability that an interval contains preciselyn eigenvalues.
2,197 citations
TL;DR: In this article, it was shown that two natural approaches to quantum gravity coincide, relying on the equivalence of each approach to KdV equations, and they also investigated related mathematical problems.
Abstract: We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical problems.
1,936 citations
TL;DR: This work investigates the acceleration dynamics of quasi-diffraction-free Airy beams in both one- and two-dimensional configurations and shows that this class of finite energy waves can retain their intensity features over several diffraction lengths.
Abstract: We investigate the acceleration dynamics of quasi-diffraction-free Airy beams in both one- and two-dimensional configurations. We show that this class of finite energy waves can retain their intensity features over several diffraction lengths. The possibility of other physical realizations involving spatiotemporal Airy wave packets is also considered.
1,892 citations
13 Dec 1997
TL;DR: In this paper, the Golden Rule is applied to properties of quantum wells and the properties of GaAs-AlAs alloys at room temperature and the Hermite's equation: harmonic oscillator.
Abstract: Preface Introduction 1. Foundations 2. Electrons and phonons in crystals 3. Heterostructures 4. Quantum wells and low-dimensional systems 5. Tunnelling transport 6. Electric and magnetic fields 7. Approximate methods 8. Scattering rates: the Golden Rule 9. The two-dimensional electron gas 10. Optical properties of quantum wells Appendix 1. Table of physical constants Appendix 2. Properties of important semiconductors Appendix 3. Properties of GaAs-AlAs alloys at room temperature Appendix 4. Hermite's equation: harmonic oscillator Appendix 5. Airy functions: triangular well Appendix 6. Kramers-Kronig relations and response functions Bibliography.
1,707 citations
TL;DR: In this article, it was shown that for a wave ψ in the form of an Airy function the probability density ψ 2 propagates in free space without distortion and with constant acceleration.
Abstract: We show that for a wave ψ in the form of an Airy function the probability density ‖ψ‖2 propagates in free space without distortion and with constant acceleration. This ’’Airy packet’’ corresponds classically to a family of orbits represented by a parabola in phase space; under the classical motion this parabola translates rigidly, and the fact that no other curve has this property shows that the Airy packet is unique in propagating without change of form. The acceleration of the packet (which does not violate Ehrenfest’s theorem) is related to the curvature of the caustic (envelope) of the family of world lines in spacetime. When a spatially uniform force F (t) acts the Airy packet continues to preserve its integrity. We exhibit the solution of Schrodinger’s equation for general F (t) and discuss the motion for some special forms of F (t).
1,577 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 12 |
| 2024 | 13 |
| 2023 | 43 |
| 2022 | 119 |
| 2021 | 67 |