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Prasanta K. Panigrahi

Publications and source records attributed to Prasanta K. Panigrahi.

At least 199 records · Page 11Linked to original sources

Simultaneous weak value amplification of angular Goos-Hänchen and Imbert-Fedorov shifts in partial reflection

The optical analogue of quantum weak measurements have shown considerable promise for the amplification and observation of tiny optical beam shifts, namely, the Goos-Hänchen (GH) and the Imbert-Fedorov (IF) shifts. Here, we demonstrate simultaneous weak value amplification of both the angular GH and the IF shifts in partial reflection of fundamental Gaussian beam at planar dielectric interfaces. We employ pre- and post selection schemes with appropriate linear polarization basis states for simultaneous weak measurements and amplification of both these shifts. The experimentally observed enhancement of the beam shifts and their dependence on the angle of incidence are analyzed / interpreted via quantum mechanical treatment of weak measurements.

physics.optics↗

Rogue solitons in Heisenberg spin chain

Following the connection of the non-linear Schrödinger equation with the continuum Heisenberg spin chain, we find the rogue soliton equivalent in the spin system. The breathers are also mapped to the corresponding space or time localized oscillatory modes, through the moving curve analogy. The spatio-temporal evolution of the curvature and torsion of the curve, underlying these dynamical systems, are explicated to illustrate the localization property of the rogue waves.

nlin.PS↗

Tracking down localized modes in PT-symmetric Hamiltonians under the influence of a competing nonlinearity

The relevance of parity and time reversal (PT)-symmetric structures in optical systems is known for sometime with the correspondence existing between the Schrodinger equation and the paraxial equation of diffraction where the time parameter represents the propagating distance and the refractive index acts as the complex potential. In this paper, we systematically analyze a normalized form of the nonlinear Schrodinger system with two new families of PT-symmetric potentials in the presence of competing nonlinearities. We generate a class of localized eigenmodes and carry out a linear stability analysis on the solutions. In particular, we find an interesting feature of bifurcation charaterized by the parameter of perturbative growth rate passing through zero where a transition to imaginary eigenvalues occurs.

quant-ph↗

Non-stationary Dynamics in the Bouncing Ball: A Wavelet perspective

The non-stationary dynamics of a bouncing ball, comprising of both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signature of self-similarity, complex scaling behavior and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding to neutral turbulence, viscous dissipation regions and different time varying periodic modulations.

math-ph↗

Multi-scale dynamics of glow discharge plasma through wavelets: Self-similar behavior to neutral turbulence and dissipation

The multiscale dynamics of glow discharge plasma is analysed through wavelet transform, whose scale dependent variable window size aptly captures both transients and non-stationary periodic behavior. The optimal time-frequency localization ability of the continuous Morlet wavelet is found to identify the scale dependent periodic modulations efficiently, as also the emergence of neutral turbulence and dissipation, whereas the discrete Daubechies basis set has been used for detrending the temporal behavior to reveal the multi-fractality of the underlying dynamics. The scaling ex- ponents and the Hurst exponent have been estimated through wavelet based detrended fluctuation analysis,and also Fourier methods and rescale range analysis.

quant-ph↗

Application of Fourier and Wavelet Transform for analysing 300 years Sunspot numbers to Explain the Solar Cycles

In this paper Fourier Transform and Wavelet Transform are applied in case of recent 300 years of sunspot numbers to explain the solar cycles. Here basically parallel study of Fourier and Wavelet analysis are done and we have observed that the better result can be obtained from Wavelet analysis during sunspot number analysis. We are able to show various minima and maxima in the recent ages of solar cycles with this tool. The exact periodicity and other possible periodicities in the cyclic phenomenon of sunspot activity are determined.

cs.CE↗

A Semi-automated Statistical Algorithm for Object Separation

We explicate a semi-automated statistical algorithm for object identification and segregation in both gray scale and color images. The algorithm makes optimal use of the observation that definite objects in an image are typically represented by pixel values having narrow Gaussian distributions about characteristic mean values. Furthermore, for visually distinct objects, the corresponding Gaussian distributions have negligible overlap with each other and hence the Mahalanobis distance between these distributions are large. These statistical facts enable one to sub-divide images into multiple thresholds of variable sizes, each segregating similar objects. The procedure incorporates the sensitivity of human eye to the gray pixel values into the variable threshold size, while mapping the Gaussian distributions into localized δ-functions, for object separation. The effectiveness of this recursive statistical algorithm is demonstrated using a wide variety of images.

cs.CV↗

On Berezinskii-Kosterlitz-Thouless phase transition and universal breathing mode in two dimensional photon gas

A system of two dimensional photon gas has recently been realized experimentally. It is pointed out that this setup can be used to observe a universal breathing mode of photon gas. It is shown that a modification in the experimental setup would open up a possibility of observing the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in such a system. It is shown that the universal jump in the superfluid density of light in the output channel can be used as an unambiguous signature for the experimental verification of the BKT transition.

physics.optics↗

Quasi-Exact Solvability and Deformations of Sl(2) Algebra

Algebraic structure of a class of differential equations including Heun is shown to be related with the deformations of sl(2) algebra. These include both quadratic and cubic ones. The finite dimensional representation of cubic algebra is explicitly shown to describe a quasi-exactly solvable system, not connected with sl(2) symmetry. Known finite dimensional representations of sl(2) emerge under special conditions. We answer affirmatively the question raised by Turbiner: Are there quasi- exactly solvable problems which can not be represented in terms of sl(2) generators? and give the explicit deformed symmetry underlying this system.

math-ph↗

Quadrature Uncertainty and Information Entropy of Quantum Elliptical Vortex States

We study the quadrature uncertainty of the quantum elliptical vortex state using the associated Wigner function. Deviations from the minimum uncertainty states were observed due to the absence of the Gaussian nature. In our study of the entropy, we noticed that with increasing vorticity, entropy increases for both the modes. We further observed that, there exists an optimum value of ellipticity which gives rise to maximum entanglement of the two modes of the quantum elliptical vortex states. A further increase in ellipticity reduces the entropy thereby resulting in a loss of information carrying capacity. We check the validity of the entropic inequality relations, namely the subaddivity and the Araki-Lieb inequality. The later was satisfied only for a very small range of the ellipticity of the vortex while the former seemed to be valid at all values.

quant-ph↗

Multiscale periodicities in aerosol optical depth over India

Aerosols exhibit periodic or cyclic variations depending on natural and anthropogenic sources over a region, which can get modulated by synoptic meteorological parameters such as winds, rainfall and relative humidity, and long-range transport. Information on periodicity and phase in aerosol properties assumes significance in prediction as well as to examine the radiative and climate effects of aerosols including its association with changes in cloud properties and rainfall. Periodicity in aerosol optical depth, which is a columnar measure of aerosol distribution, is determined using continuous wavelet transform over 35 locations in India. Continuous wavelet transform is used in the study because it is better suited to extract the periodic and local modulations present at various frequency ranges, as these features are invisible in conventional methods such as Fourier Transform. Monthly mean aerosol optical depths (AODs) from MODerate Resolution Imaging Spectroradiometer (MODIS) on board the Terra satellite from January 2001 to December 2012 are used. Annual and quasi-biennial oscillations (QBO) in AOD are evident in addition to the weak semi-annual and quasi-triennial. The semi-annual and annual oscillations are consistent with the seasonal and yearly cycle of variations in AODs. The 40-month periodicity indicates the presence of long term correlations in AOD. The observed periodicities in MODIS Terra AODs are also evident in the ground-based AOD measurements made over Kanpur in the Indo-Gangetic Plain. The phase of the periodicity in AOD is stable in the mid-frequency range, while local disturbances in the high-frequency range and long term changes in the atmospheric composition give rise to unstable phases in low-frequency range. That modulations in AOD over one location/region can influence the other is revealed by the presence of phase relation among different locations.

physics.ao-ph↗

Controlled transportation of mesoscopic particles by enhanced spin orbit interaction of light in an optical trap

We study the effects of the spin orbit interaction (SOI) of light in an optical trap and show that the propagation of the tightly focused trapping beam in a stratified medium can lead to significantly enhanced SOI. For a plane polarized incident beam the SOI manifests itself by giving rise to a strong anisotropic linear diattenuation effect which produces polarization-dependent off-axis high intensity side lobes near the focal plane of the trap. Single micron-sized asymmetric particles can be trapped in the side lobes, and transported over circular paths by a rotation of the plane of input polarization. We demonstrate such controlled motion on single pea-pod shaped single soft oxometalate (SOM) particles of dimension around $1\times 0.5μ$m over lengths up to $\sim$15 $μ$m . The observed effects are supported by calculations of the intensity profiles based on a variation of the Debye-Wolf approach. The enhanced SOI could thus be used as a generic means of transporting mesoscopic asymmetric particles in an optical trap without the use of complex optical beams or changing the alignment of the beam into the trap.

physics.optics↗

The Kerr medium as an {\sf SU(2)} system

The Kerr medium in the presence of damping and associated with SU(1,1) symmetry, is solved using the techniques of Thermo field Dynamics (TFD).These TFD techniques, well studied earlier (Chaturvedi and Srinivasan, 1991), help us to exactly solve the Kerr medium as a spin damped system associated with SU(2) symmetry. Using TFD, the association with SU(2) is exploited to express the dynamics of the system as a Schrodinger-like equation, whose solution is obtained using the appropriate disentanglement theorem. These considerations are extended to a system with multi-mode coupled nonlinear oscillators."

quant-ph↗

Non-uniform Quantization of Detail Components in Wavelet Transformed Image for Lossy JPEG2000 Compression

The paper introduces the idea of non-uniform quantization in the detail components of wavelet transformed image. It argues that most of the coefficients of horizontal, vertical and diagonal components lie near to zeros and the coefficients representing large differences are few at the extreme ends of histogram. Therefore, this paper advocates need for variable step size quantization scheme which preserves the edge information at the edge of histogram and removes redundancy with the minimal number of quantized values. To support the idea, preliminary results are provided using a non-uniform quantization algorithm. We believe that successful implementation of non-uniform quantization in detail components in JPEG-2000 still image standard will improve image quality and compression efficiency with lesser number of quantized values.

cs.MM↗

Multisegmentation through wavelets: Comparing the efficacy of Daubechies vs Coiflets

In this paper, we carry out a comparative study of the efficacy of wavelets belonging to Daubechies and Coiflet family in achieving image segmentation through a fast statistical algorithm.The fact that wavelets belonging to Daubechies family optimally capture the polynomial trends and those of Coiflet family satisfy mini-max condition, makes this comparison interesting. In the context of the present algorithm, it is found that the performance of Coiflet wavelets is better, as compared to Daubechies wavelet.

cs.CV↗

Diffraction limit of the sub-Planck structures

The orthogonality of cat and displaced cat states, underlying Heisenberg limited measurement in quantum metrology, is studied in the limit of large number of states. The asymptotic expression for the corresponding state overlap function, controlled by the sub-Planck structures arising from phase space interference, is obtained exactly. The validity of large phase space support, in which context the asymptotic limit is achieved, is discussed in detail. For large number of coherent states, uniformly located on a circle, it identically matches with the diffraction pattern for a circular ring with uniform angular source strength. This is in accordance with the van Cittert-Zernike theorem, where the overlap function, similar to the mutual coherence function matches with a diffraction pattern.

quant-ph↗

Characterizing price index behavior through fluctuation dynamics

We study the nature of fluctuations in variety of price indices involving companies listed on the New York Stock Exchange. The fluctuations at multiple scales are extracted through the use of wavelets belonging to Daubechies basis. The fact that these basis sets satisfy vanishing moments conditions makes them ideal to extract local polynomial trends, through the low pass or `average coefficients'. Subtracting the trends from the original time series yields the fluctuations, at different scales, depending on the level of low-pass coefficients used for finding the `average behavior'. The fluctuations are then studied using wavelet based multifractal detrended fluctuation analysis to analyze their self-similar and non-statistical properties. Due to the multifractality of such time series, they deviate from Gaussian behavior in different frequency regimes. Their departure from random matrix theory predictions in such regimes is also analyzed. These deviations and non-statistical properties of the fluctuations can be instrumental in throwing significant light on the dynamics of financial markets.

q-fin.ST↗

Solving Linear Differential Equations: A Novel Approach

We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the equations under study, as well as that of the solutions are made transparent. We demonstrate the efficacy of the method by showing the common structure of the solution space of a wide variety of differential equations viz. Hermite, Laguerre, Jocobi, Bessel and hypergeometric etc. We also illustrate the use of the procedure to develop approximate solutions, as well as in finding solutions of many particle interacting systems.

math-ph↗