Multifractal eigenstates of quantum chaos and the Thue-Morse sequence

We analyze certain eigenstates of the quantum baker's map and demonstrate, using the Walsh-Hadamard transform, the emergence of the ubiquitous Thue-Morse sequence, a simple sequence that is at the border between quasi-periodicity and chaos, and hence is a good paradigm for quantum chaotic states. We show a family of states that are also simply related to Thue-Morse sequence, and are strongly scarred by short periodic orbits and their homoclinic excursions. We give approximate expressions for these states and provide evidence that these and other generic states are multifractal.Comment: Substantially modified from the original, worth a second download. To appear in Phys. Rev. E as a Rapid Communicatio

Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map

We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms that do significantly better, thus nearly solving for many states of the quantum baker's map. These new transforms, which combine the standard Fourier and Hadamard transforms in an interesting manner, are constructed from eigenvectors of the shift permutation operator that are also simultaneous eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal) symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title; corrected minor error

Quantum chaos in the spectrum of operators used in Shor's algorithm

We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the eigenangles as well as the distribution of the eigenvector components follow the CUE ensemble of random matrices, of relevance to quantized chaotic systems that violate time-reversal symmetry. However, as the algorithm tracks the evolution of a single state, it is possible to employ other operators, in particular it is possible that the generic quantum chaos found above becomes of a nongeneric kind such as is found in the quantum cat maps, and in toy models of the quantum bakers map.Comment: Title and paper modified to include interesting additional possibilities. Principal results unaffected. Accepted for publication in Phys. Rev. E as Rapid Com

Integrated analytical models for flexible manufacturing systems

Product form queueing networks (PFQN) and generalized stochastic Petri nets (GSPN) have emerged as the principal performance modelling tools for flexible manufacturing systems (FMS). In this paper, we present integrated PFQN-GSPN models, which combine the computational efficiency of PFQN and representational power of GSPN by employing the principle of flow-equivalence. We show that FMS that include non-product form characteristics such as dynamic routing and synchronization can be evaluated efficiently and accurately using the integrated models

Modeling Basal Ganglia for understanding Parkinsonian Reaching Movements

We present a computational model that highlights the role of basal ganglia (BG) in generating simple reaching movements. The model is cast within the reinforcement learning (RL) framework with the correspondence between RL components and neuroanatomy as follows: dopamine signal of substantia nigra pars compacta as the Temporal Difference error, striatum as the substrate for the Critic, and the motor cortex as the Actor. A key feature of this neurobiological interpretation is our hypothesis that the indirect pathway is the Explorer. Chaotic activity, originating from the indirect pathway part of the model, drives the wandering, exploratory movements of the arm. Thus the direct pathway subserves exploitation while the indirect pathway subserves exploration. The motor cortex becomes more and more independent of the corrective influence of BG, as training progresses. Reaching trajectories show diminishing variability with training. Reaching movements associated with Parkinson's disease (PD) are simulated by (a) reducing dopamine and (b) degrading the complexity of indirect pathway dynamics by switching it from chaotic to periodic behavior. Under the simulated PD conditions, the arm exhibits PD motor symptoms like tremor, bradykinesia and undershoot. The model echoes the notion that PD is a dynamical disease.Comment: Neural Computation, In Pres

Distribution of resonances for open quantum maps

We analyze simple models of classical chaotic open systems and of their quantizations (open quantum maps on the torus). Our models are similar to models recently studied in atomic and mesoscopic physics. They provide a numerical confirmation of the fractal Weyl law for the density of quantum resonances of such systems. The exponent in that law is related to the dimension of the classical repeller (or trapped set) of the system. In a simplified model, a rigorous argument gives the full resonance spectrum, which satisfies the fractal Weyl law. For this model, we can also compute a quantity characterizing the fluctuations of conductance through the system, namely the shot noise power: the value we obtain is close to the prediction of random matrix theory.Comment: 60 pages, no figures (numerical results are shown in other references

Ruthenium ion catalysed C–C bond activation in lignin model compounds – towards lignin depolymerisation

Lignin is the most abundant renewable feedstock to produce aromatic chemicals, however its depolymerisation involves the breaking of several C–O and C–C inter-unit linkages that connect smaller aromatic units that are present in lignin. Several strategies have been reported for the cleavage of the C–O inter-unit linkages in lignin. However, till today, only a few methodologies have been reported for the effective breaking or the conversion of the recalcitrant C–C inter unit linkages in lignin. Here we report the ruthenium ion catalysed oxidative methodology as an effective system to activate or convert the most recalcitrant inter unit linkages such as β-5 and 5–5′ present in lignin. Initially, we used biphenyl as a model compound to study the effectiveness of the RICO methodology to activate the 5–5′ C–C linkage. After 4 h reaction at 22 °C, we achieved a 30% conversion with 75% selectivity towards benzoic acid and phenyl glyoxal as the minor product. To the best of our knowledge this is the first ever oxidative activation of the C–C bond that connects the two phenyl rings in biphenyl. DFT calculation revealed that the RuO4 forms a [3 + 2] adduct with one of the aromatic C–C bonds resulting in the opening of the phenyl ring. Biphenyl conversion could be increased by increasing the amount of oxidant; however, this is accompanied by a reduction in the carbon balance because of the formation of CO2 and other unknown products. We extended this RICO methodology for the oxidative depolymerisation of lignin model hexamer containing β-5, 5–5′ and β-O-4 linkages. Qualitative and quantitative analyses of the reaction mixture were done using 1H, 13C NMR spectroscopy methods along with GC-MS and Gel Permeation Chromatographic (GPC) methods. Advanced 2D NMR spectroscopic methods such as HSQC, HMBC and 31P NMR spectroscopy after phosphitylation of the mixture were employed to quantitatively analyse the conversion of the β-5, 5–5′ and β-O-4 linkages and to identify the products. After 30 min, >90% of the 5–5′ and linkages and >80% of the β-5′ are converted with this methodology. This is the first report on the conversion of the 5–5′ linkage in lignin model hexamer

Nanostructured AgBr loaded TiO2: An efficient sunlight active photocatalyst for degradation of Reactive Red 120

The AgBr loaded TiO2 catalyst was prepared by a feasible approach with AgBr and tetraisopropyl orthotitanate and characterized by BET surface area measurement, diffuse reflectance spectra (DRS), scanning electron microscope (SEM), energy dispersive spectra (EDS), X-ray diffraction (XRD), transmission electron microscope (TEM) and atomic force microscope (AFM) analysis. The results of characterization reveal that AgBr loaded TiO2 has a nanostructure. Formation of the nanostructure in AgBr loaded TiO2 results in substantial shifting of the absorption edge of TiO2 to red and enhancement of visible light absorption. Electrochemical impedance spectroscopy measurements reveal that AgBr loaded TiO2 has a higher photoconductivity than prepared TiO2 due to higher separation efficiency of electron-hole pairs. Cyclic voltammetric studies reveal enhanced conductivity in AgBr loaded TiO2, which causes an increase in its photocatalytic activity. AgBr loaded TiO2 exhibited a higher photocatalytic activity than TiO2-P25 and prepared TiO2 in the photodegradation of Reactive Red 120 (RR 120)

Risk factors for myocardial infarction among low socioeconomic status South Indian population

<p>Abstract</p> <p>Background</p> <p>As longevity increases, cases of myocardial infarction (MI) are likely to be more. Cardiovascular disease (CVD) is a major global health problem reaching epidemic proportions in the Indian subcontinent, also among low socio-economic status (SES) and thin individuals.</p> <p>Objectives</p> <p>The present study was undertaken to elicit risk factors for MI among low SES Southern Indians and to find out its association with body mass index (BMI).</p> <p>Materials and methods</p> <p>A case-control study of patients with MI matched against healthy control subjects was carried out in a tertiary care teaching hospital. Standard methods were followed to elicit risk factors and BMI. Chi-square and Fishers exact test for categorical versus categorical, to show relationship with risk factors were analyzed.</p> <p>Results</p> <p>A total of 949 patients (male (M) = 692 and post menopausal female (F) = 257) and 611 age and sex matched healthy controls were included. In our study, BMI was below 23 in 48.2% of patients and below 21 in 22.5%. The risk of developing MI was significantly more in males (odds ratio (OR) = 3.3, 95% confidence interval (C.I.) = 2.69-4.13), among females with post-menopausal duration (PMD) of more than or equal to 3 years (OR = 9.27, 95% C.I. = 6.36-13.50) and in those with BMI less than 23 with one or other risk factors (P = 0.002, OR = 1.38, 95% C.I. = 1.13-1.70).</p> <p>Conclusion</p> <p>BMI cannot be considered as a lone independent risk factor, as the study population had low BMI but had one or more modifiable risk factors. It would be advisable to keep BMI at least 21 kg/m²for screening program. Health education on life style modification and programs to diagnose and control diabetes and hypertension have to be initiated at community level in order to reduce the occurrence.</p