Related papers: Scarring and the statistics of tunnelling
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…
We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behavior of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics…
The connection between scarring and tunneling in chaotic double-well potentials is studied in detail through the distribution of level splittings. The mean level splitting is found to have oscillations as a function of energy, as expected…
We calculate a tunneling time distribution by means of Nelson's quantum mechanics and investigate its statistical properties. The relationship between the average and deviation of tunneling time suggests the exsistence of ``wave-particle…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
It is shown that tunnelling splittings in ergodic double wells and resonant widths in ergodic metastable wells can be approximated as easily-calculated matrix elements involving the wavefunction in the neighbourhood of a certain real orbit.…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
Transmission of the scalar field through the random medium, represented by the system of randomly distributed dielectric cylinders is calculated numerically. System is mapped to the problem of electronic transport in disordered…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
Statistics of tunneling rates in the presence of chaotic classical dynamics is discussed on a realistic example: a hydrogen atom placed in parallel uniform static electric and magnetic fields, where tunneling is followed by ionization along…
The statistical theory of certain complex wave interference phenomena, like the statistical fluctuations of transmission and reflection of waves, is of considerable interest in many fields of physics. In this article we shall be mainly…
We analyze the effects of inelastic scattering on the tunneling time theoretically, using generalized Nelson's quantum mechanics. This generalization enables us to describe quantum system with optical potential and channel couplings in a…
Random matrix theory is a useful tool in the study of the physics of multiple scattering systems, often striking a balance between computation speed and physical rigour. Propagation of waves through thick disordered media, as arises in for…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
The anomalously strong scarring of wavefunctions found in numerical studies of quantum wells in a tilted magnetic field is shown to be due to special properties of the classical dynamics of this system. A certain subset of periodic orbits…
The lognormal distribution describing, e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the…
We describe the statistics of chaotic wavefunctions near periodic orbits using a basis of states which optimise the effect of scarring. These states reflect the underlying structure of stable and unstable manifolds in phase space and…
We investigate scarred resonances of a stadium-shaped chaotic microcavity. It is shown that two components with different chirality of the scarring pattern are slightly rotated in opposite ways from the underlying unstable periodic orbit,…
As a step towards a more accurate modelling of redshift-space distortions in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called…
We follow the evolution with sample thickness, of intensity statistics for localized light transmitted through layered media in a crossover from one to three dimensions occasioned by transverse disorder. The probability distribution of…