Resonance distribution in the quantum random Lorentz gas
arXiv:2111.04410 · doi:10.1103/PhysRevA.105.042205
Abstract
The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of scattering resonances in the complex plane of the wavenumber without finding them one by one. The method is applied to two collision models for the individual scatterers, namely a resonant model, and a non-resonant hard-sphere model. The results obtained with the former are compared to the literature. In particular, the spiral arms surrounding the single-scatterer resonance are identified as proximity resonances. Moreover, the hard-sphere model is used to reveal previously unknown structures in the resonance density. Finally, it is shown how Anderson localization affects the distribution of resonance widths, especially in the one-dimensional case.
arXiv comment15 pages, 8 figures, second in a series of two papers
References in corpus (21)
- Multiple scattering of classical waves: from microscopy to mesoscopy and diffusion
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
- On the Numerical Evaluation of Fredholm Determinants
- Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions
- Introduction to Random Matrices - Theory and Practice
- Photon localization and Dicke superradiance in atomic gases
- The circular law for random matrices
- Probing Anderson localization of light via decay rate statistics
- Statistics of Resonances and Delay Times in Random Media: Beyond Random Matrix Theory
- Non-Hermitian Euclidean random matrix theory
- Eigenvalue distributions of large Euclidean random matrices for waves in random media
- Time reversal sub-wavelength focusing in bubbly media
- Ioffe-Regel criterion of Anderson localization in the model of resonant point scatterers
- Random Distance Distribution for Spherical Objects: General Theory and Applications to n-Dimensional Physics
- Finite-size scaling analysis of localization transition for scalar waves in a 3D ensemble of resonant point scatterers
- Euclidean matrix theory of random lasing in a cloud of cold atoms
- Resonance width distribution for high-dimensional random media
- Resonance width distribution in RMT: Weak coupling regime beyond Porter-Thomas
- Scattering approach to Anderson localisation
- Effective-range function methods for charged particle collisions
- Multiple scattering model of the quantum random Lorentz gas