Topic
Eikonal approximation
About: Eikonal approximation is a research topic. Over the lifetime, 1903 publications have been published within this topic receiving 30227 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: A semianalytic technique for determining the complex normal-mode frequencies of black holes using the WKB approximation, carried to third order beyond the eikonal approximation, which may find uses in barrier-tunneling problems in atomic and nuclear physics.
Abstract: We present a semianalytic technique for determining the complex normal-mode frequencies of black holes. The method makes use of the WKB approximation, carried to third order beyond the eikonal approximation. Mathematically, the problem is similar to studying one-dimensional quantum-mechanical scattering near the peak of a potential barrier, and determining the scattering resonances. Under such conditions, a modification of the usual WKB approach must be used. We obtain the connection formulas that relate the amplitudes of incident, reflected, and transmitted waves, to the third WKB order. By imposing the normal-mode (resonance) boundary condition of a zero incident amplitude with nonzero transmitted and reflected amplitudes, we find a simple formula that determines the real and imaginary parts of the normal-mode frequency of perturbation (or of the quantum-mechanical energy of the resonance) in terms of the derivatives (up to and including sixth order) of the barrier function evaluated at the peak, and in terms of the quantity (n+(1/2)), where n is an integer and labels the fundamental mode (resonance), first overtone, and so on. This higher-order approach may find uses in barrier-tunneling problems in atomic and nuclear physics.
987 citations
TL;DR: In this paper, the relation between evolution equations at low x that have been derived in different approaches in the last several years is analyzed and it is shown that the equation derived by Balitsky and Kovchegov is obtained from the Jalilian-Marian-Kovner-Leonidov-Weigert (JKLW) equation in the limit of small induced charge density.
Abstract: We analyze the relation between evolution equations at low x that have been derived in different approaches in the last several years. We show that the equation derived by Balitsky and Kovchegov is obtained from the Jalilian-Marian–Kovner–Leonidov–Weigert (JKLW) equation in the limit of small induced charge density. We argue that the higher nonlinearities resummed by the JKLW equation correspond, in physical terms, to the breakdown of the eikonal approximation when the gluon fields in the target are large.
591 citations
TL;DR: In this article, a method of approximating solutions of the one-dimensional Schr\"odinger equation is presented, which closely resembles the usual WKB approximation and is illustrated by treating the potential well and potential barrier problems when there are two turning points.
Abstract: A method of approximating solutions of the one-dimensional Schr\"odinger equation is presented in this paper. The method closely resembles the usual WKB approximation. Whereas in the ordinary WKB method the exponential function is used as the basis of the approximation, in this paper the solutions of an arbitrary Schr\"odinger equation are used. The general advantage is that by proper choice of the arbitrary equation an improved approximation can be obtained. The method is illustrated by treating the potential well and potential barrier problems when there are two turning points. The approximations to the wave functions are continuous even across the turning points. The barrier transmission problem is treated uniformly for energies above and below the peak of the barrier.
470 citations
TL;DR: In this paper, a theorem generalising the exponentiation property of eikonal cross sections in abelian gauge theories to the nonabelian case has been presented which generalises the well-known exponentiation properties of cross sections.
437 citations
TL;DR: In this article, the eikonal approximation is applied to the problem of large fluctuations of the number of species in spatially homogeneous chemical reactions with the probability density distribution described by a master equation.
Abstract: The eikonal approximation (instanton technique) is applied to the problem of large fluctuations of the number of species in spatially homogeneous chemical reactions with the probability density distribution described by a master equation. For both autocatalytic and nonautocatalytic reactions, the analysis of the distribution about a stable stationary state and of the transitions between coexisting stable states comes, to logarithmic accuracy, to the analysis of Hamiltonian dynamics of an auxiliary dynamical system. The latter can be done explicitly in a few cases, including one‐species systems, systems with detailed balance, and systems close to the bifurcation points where the number of the stable states changes. In the last case, the fluctuations display universal features, and, for saddle‐node bifurcation points, the logarithm of the probability of escape from the metastable state (per unit time) is proportional to the distance to the bifurcation point (in the parameter space) raised to the power 3/2. We compare the eikonal approximation for the stationary distribution of a master equation to Monte Carlo numerical solutions for two chemical two‐variable systems with multiple stationary states, where none of the cited restrictions exists. For one of the systems in the pattern of optimal paths we observe caustics emanating from the saddle point.
403 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 6 |
| 2024 | 18 |
| 2023 | 36 |
| 2022 | 116 |
| 2021 | 15 |
| 2020 | 19 |