Random matrix description of decaying quantum systems

This contribution describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitely into account. The resulting expressions for the partial decay amplitudes and the corresponding cross sections may be considered a many-channel many-resonance generalization of Fano's original work on resonance lineshapes [Phys. Rev 124, 1866 (1961)]. A statistical (random matrix) model is then introduced. It allows to describe chaotic scattering systems with tunable couplings to the decay channels. We focus on the autocorrelation function of the total (photo) cross section, and we find that it depends on the same combination of parameters, as the Fano-parameter distribution. These combinations are statistical variants of the one-channel Fano parameter. It is thus possible to study Fano interference (i.e. the interference between direct and indirect decay paths) on the basis of the autocorrelation function, and thereby in the regime of overlapping resonances. It allows us, to study the Fano interference in the limit of strongly overlapping resonances, where we find a persisting effect on the level of the weak localization correction.Comment: 16 pages, 2 figure

Microwave fidelity studies by varying antenna coupling

The fidelity decay in a microwave billiard is considered, where the coupling to an attached antenna is varied. The resulting quantity, coupling fidelity, is experimentally studied for three different terminators of the varied antenna: a hard wall reflection, an open wall reflection, and a 50 Ohm load, corresponding to a totally open channel. The model description in terms of an effective Hamiltonian with a complex coupling constant is given. Quantitative agreement is found with the theory obtained from a modified VWZ approach [Verbaarschot et al, Phys. Rep. 129, 367 (1985)].Comment: 9 pages 5 figur

A random matrix approach to decoherence

In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing two subsystems. We introduce a random matrix model that permits to vary the coupling strength between the subsystems. The case of strong coupling is analyzed in detail, and we find no significant differences except for very low-dimensional spaces.Comment: 11 pages, 5 eps-figure

Low rank perturbations and the spectral statistics of pseudointegrable billiards

We present an efficient method to solve Schr\"odinger's equation for perturbations of low rank. In particular, the method allows to calculate the level counting function with very little numerical effort. To illustrate the power of the method, we calculate the number variance for two pseudointegrable quantum billiards: the barrier billiard and the right triangle billiard (smallest angle $\pi/5$). In this way, we obtain precise estimates for the level compressibility in the semiclassical (high energy) limit. In both cases, our results confirm recent theoretical predictions, based on periodic orbit summation.Comment: 4 page

Generic spectral properties of right triangle billiards

This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its simplicity and explicitness however allow new insight into the statistical properties of the spectra. We analyse numerically the correlations in level sequences at high level numbers (>10^5) for several examples of right triangle billiards. We find that the strength of the correlations is closely related to the genus of the invariant surface of the classical billiard flow. Surprisingly, the genus plays and important role on the quantum level also. Based on this observation a mechanism is discussed, which may explain the particular quantum-classical correspondence in right triangle billiards. Though this class of systems is rather small, it contains examples for integrable, pseudo integrable, and non integrable (ergodic, mixing) dynamics, so that the results might be relevant in a more general context.Comment: 18 pages, 8 eps-figures, revised: stylistic changes, improved presentatio

De Novo Occurrence of a Variant in ARL3 and Apparent Autosomal Dominant Transmission of Retinitis Pigmentosa.

BackgroundRetinitis pigmentosa is a phenotype with diverse genetic causes. Due to this genetic heterogeneity, genome-wide identification and analysis of protein-altering DNA variants by exome sequencing is a powerful tool for novel variant and disease gene discovery. In this study, exome sequencing analysis was used to search for potentially causal DNA variants in a two-generation pedigree with apparent dominant retinitis pigmentosa.MethodsVariant identification and analysis of three affected members (mother and two affected offspring) was performed via exome sequencing. Parental samples of the index case were used to establish inheritance. Follow-up testing of 94 additional retinitis pigmentosa pedigrees was performed via retrospective analysis or Sanger sequencing.Results and conclusionsA total of 136 high quality coding variants in 123 genes were identified which are consistent with autosomal dominant disease. Of these, one of the strongest genetic and functional candidates is a c.269A>G (p.Tyr90Cys) variant in ARL3. Follow-up testing established that this variant occurred de novo in the index case. No additional putative causal variants in ARL3 were identified in the follow-up cohort, suggesting that if ARL3 variants can cause adRP it is an extremely rare phenomenon

Fidelity and level correlations in the transition from regularity to chaos

Mean fidelity amplitude and parametric energy--energy correlations are calculated exactly for a regular system, which is subject to a chaotic random perturbation. It turns out that in this particular case under the average both quantities are identical. The result is compared with the susceptibility of chaotic systems against random perturbations. Regular systems are more susceptible against random perturbations than chaotic ones.Comment: 7 pages, 1 figur

Dysflective cones: Visual function and cone reflectivity in long-term follow-up of acute bilateral foveolitis.

PURPOSE:Confocal adaptive optics scanning laser ophthalmoscope (AOSLO) images provide a sensitive measure of cone structure. However, the relationship between structural findings of diminished cone reflectivity and visual function is unclear. We used fundus-referenced testing to evaluate visual function in regions of apparent cone loss identified using confocal AOSLO images. METHODS:A patient diagnosed with acute bilateral foveolitis had spectral-domain optical coherence tomography (SD-OCT) (Spectralis HRA + OCT system [Heidelberg Engineering, Vista, CA, USA]) images indicating focal loss of the inner segment-outer segment junction band with an intact, but hyper-reflective, external limiting membrane. Five years after symptom onset, visual acuity had improved from 20/80 to 20/25, but the retinal appearance remained unchanged compared to 3 months after symptoms began. We performed structural assessments using SD-OCT, directional OCT (non-standard use of a prototype on loan from Carl Zeiss Meditec) and AOSLO (custom-built system). We also administered fundus-referenced functional tests in the region of apparent cone loss, including analysis of preferred retinal locus (PRL), AOSLO acuity, and microperimetry with tracking SLO (TSLO) (prototype system). To determine AOSLO-corrected visual acuity, the scanning laser was modulated with a tumbling E consistent with 20/30 visual acuity. Visual sensitivity was assessed in and around the lesion using TSLO microperimetry. Complete eye examination, including standard measures of best-corrected visual acuity, visual field tests, color fundus photos, and fundus auto-fluorescence were also performed. RESULTS:Despite a lack of visible cone profiles in the foveal lesion, fundus-referenced vision testing demonstrated visual function within the lesion consistent with cone function. The PRL was within the lesion of apparent cone loss at the fovea. AOSLO visual acuity tests were abnormal, but measurable: for trials in which the stimulus remained completely within the lesion, the subject got 48% correct, compared to 78% correct when the stimulus was outside the lesion. TSLO microperimetry revealed reduced, but detectible, sensitivity thresholds within the lesion. CONCLUSIONS AND IMPORTANCE:Fundus-referenced visual testing proved useful to identify functional cones despite apparent photoreceptor loss identified using AOSLO and SD-OCT. While AOSLO and SD-OCT appear to be sensitive for the detection of abnormal or absent photoreceptors, changes in photoreceptors that are identified with these imaging tools do not correlate completely with visual function in every patient. Fundus-referenced vision testing is a useful tool to indicate the presence of cones that may be amenable to recovery or response to experimental therapies despite not being visible on confocal AOSLO or SD-OCT images

Evanescent wave approach to diffractive phenomena in convex billiards with corners

What we are going to call in this paper "diffractive phenomena" in billiards is far from being deeply understood. These are sorts of singularities that, for example, some kind of corners introduce in the energy eigenfunctions. In this paper we use the well-known scaling quantization procedure to study them. We show how the scaling method can be applied to convex billiards with corners, taking into account the strong diffraction at them and the techniques needed to solve their Helmholtz equation. As an example we study a classically pseudointegrable billiard, the truncated triangle. Then we focus our attention on the spectral behavior. A numerical study of the statistical properties of high-lying energy levels is carried out. It is found that all computed statistical quantities are roughly described by the so-called semi-Poisson statistics, but it is not clear whether the semi-Poisson statistics is the correct one in the semiclassical limit.Comment: 7 pages, 8 figure