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Isao Noda - One of the best experts on this subject based on the ideXlab platform.

  • extension of quadrature orthogonal signal corrected two dimensional qosc 2d correlation spectroscopy i principal component analysis based qosc 2d
    Applied Spectroscopy, 2007
    Co-Authors: Isao Noda
    Abstract:

    The present study proposes a new quadrature orthogonal signal correlation (QOSC) filtering method based on principal component analysis (PCA). The external Perturbation Variable vector typically used in the QOSC operation is replaced with a matrix consisting of the spectral data principal components (PCs) and their quadrature counterparts obtained by using the discrete Hilbert–Noda transformation. Thus, QOSC operation can be carried out for a dataset without the explicit knowledge of the external Variables information. The PCA-based QOSC filtering can be most effectively applied to two-dimensional (2D) correlation analysis. The performance of this filtering operation on the simulated spectra data set with the interference of strong random noise demonstrated that the PCA-based QOSC filtering not only eliminates the influence of signals that are unrelated to the final target but also preserves the out-of-phase information in the data matrix essential for asynchronous correlation analysis. The result of 2D correlation analysis has also demonstrated that essentially only one principal component is necessary for PCA-based QOSC to perform well. Although the present PCA-based QOSC filtering scheme is not as powerful as that based on the explicit knowledge of the external Variable vector, it still can significantly improve the quality of 2D correlation spectra and enables OSC 2D to deal with the problems of losing the quadrature (or out-of-phase) information. In particular, it opens a way to perform QOSC for the spectral dataset without external Variables information. The proposed approach should have wide applications in 2D correlation analysis of spectra driven by multiplicative effects in complicated systems in biological, pharmaceutical, and agriculture fields, and so on, where the explicit nature of the external Perturbation cannot always be known.

  • graphical representation of two dimensional correlation in vector space
    Vibrational Spectroscopy, 2004
    Co-Authors: Isao Noda
    Abstract:

    Abstract The concept of two-dimensional (2D) correlation analysis may be regarded as a form of manipulation and comparison of vectors, representing spectral intensity variations measured at two independent spectral Variables along a Perturbation Variable. Such vector operations can be represented graphically for easier visualization. Graphical representation provides a more intuitive understanding of different forms of 2D correlation methods. Interestingly, we observed that synchronous correlation and disrelation analysis seem to form a more natural pair as complementary techniques, because they share very similar sets of vector manipulations, although some steps of operations are geometrically perpendicular to each other. Asynchronous correlation, on the other hand, seems to belong to a different class of vector operations, as it is not confined to a fixed plane in a vector space but spans additional dimensions. This finding suggests the possible existence of many other vector comparison methods not yet being explored by utilizing the full scope of a given vector space. The graphical representation not only gives a unified tool to compare various forms of current 2D correlation methods but also may potentially assist further evolution of useful correlation methods not yet being developed.

Sayantan Choudhury - One of the best experts on this subject based on the ideXlab platform.

  • the cosmological otoc formulating new cosmological micro canonical correlation functions for random chaotic fluctuations in out of equilibrium quantum statistical field theory
    Symmetry, 2020
    Co-Authors: Sayantan Choudhury
    Abstract:

    The out-of-time-ordered correlation (OTOC) function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. In this paper, using for the first time the slogan “Cosmology meets Condensed Matter Physics”, we demonstrate a formalism to compute the Cosmological OTOC during the stochastic particle production during inflation and reheating following the canonical quantization technique. In this computation, two dynamical time scales are involved—out of them, at one time scale, the cosmological Perturbation Variable, and for the other, the canonically conjugate momentum, is defined, which is the strict requirement to define the time scale-separated quantum operators for OTOC and is perfectly consistent with the general definition of OTOC. Most importantly, using the present formalism, not only one can study the quantum correlation during stochastic inflation and reheating, but can also study quantum correlation for any random events in Cosmology. Next, using the late time exponential decay of cosmological OTOC with respect to the dynamical time scale of our universe which is associated with the canonically conjugate momentum operator in this formalism, we study the phenomenon of quantum chaos by computing the expression for the Lyapunov spectrum. Furthermore, using the well known Maldacena Shenker Stanford (MSS) bound on the Lyapunov exponent, λ≤2π/β, we propose a lower bound on the equilibrium temperature, T=1/β, at the very late time scale of the universe. On the other hand, with respect to the other time scale with which the Perturbation Variable is associated, we find decreasing, but not exponentially decaying, behaviour, which quantifies the random quantum correlation function out-of-equilibrium. We have also studied the classical limit of the OTOC and checked the consistency with the large time limiting behaviour of the correlation. Finally, we prove that the normalized version of OTOC is completely independent of the choice of the preferred definition of the cosmological Perturbation Variable.

Choudhury Sayantan - One of the best experts on this subject based on the ideXlab platform.

  • The Cosmological OTOC: Formulating new cosmological micro-canonical correlation functions for random chaotic fluctuations in Out-of-Equilibrium Quantum Statistical Field Theory
    'MDPI AG', 2020
    Co-Authors: Choudhury Sayantan
    Abstract:

    The out-of-time-ordered correlation (OTOC) function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. In this paper, with the slogan "Cosmology meets Condensed Matter Physics" we demonstrate a formalism using which for the first time we compute the Cosmological OTOC during the stochastic particle production during inflation and reheating following canonical quantization technique. In this computation, two dynamical time scales are involved, out of them at one time scale the cosmological Perturbation Variable and for the other the canonically conjugate momentum is defined, which is the strict requirement to define time scale separated quantum operators for OTOC and perfectly consistent with the general definition of OTOC. Most importantly, using the present formalism not only one can study the quantum correlation during stochastic inflation and reheating, but also study quantum correlation for any random events in Cosmology. Next, using the late time exponential decay of cosmological OTOC with respect to the dynamical time scale of our universe which is associated with the canonically conjugate momentum operator in this formalism we study the phenomena of quantum chaos by computing the expression for {\it Lyapunov spectrum}. Further, using the well known Maldacena Shenker Stanford (MSS) bound, on Lyapunov exponent, $\lambda\leq 2\pi/\beta$, we propose a lower bound on the equilibrium temperature, $T=1/\beta$, at the very late time scale of the universe. On the other hand, with respect to the other time scale with which the Perturbation Variable is associated, we find decreasing but not exponentially decaying behaviour, which quantifies the random correlation at out-of-equilibrium. Finally, we have studied the classical limit of the OTOC to check the consistency with the large time limiting behaviour.Comment: 211 pages, 21 figures, This work is written in the memory of the great physicist Professor Freeman J. Dyson with whom I had the chance to meet during my visit at IAS, Princeton on the first week of December, 2019. This project is the part of "Quantum Structures of the Space-Time and Matter (QASTM)". Accepted for publication in Symmetry (Special Issue "New Advances of Cosmology and Astrophysics"

Choudhury S. - One of the best experts on this subject based on the ideXlab platform.

  • The Cosmological OTOC: Formulating new cosmological micro-canonical correlation functions for random chaotic fluctuations in Out-of-Equilibrium Quantum Statistical Field Theory
    'MDPI AG', 2020
    Co-Authors: Choudhury S.
    Abstract:

    The out-of-time-ordered correlation (OTOC) function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. In this paper, with the slogan "Cosmology meets Condensed Matter Physics" we demonstrate a formalism using which for the first time we compute the Cosmological OTOC during the stochastic particle production during inflation and reheating following canonical quantization technique. In this computation, two dynamical time scales are involved, out of them at one time scale the cosmological Perturbation Variable and for the other the canonically conjugate momentum is defined, which is the strict requirement to define time scale separated quantum operators for OTOC and perfectly consistent with the general definition of OTOC. Most importantly, using the present formalism not only one can study the quantum correlation during stochastic inflation and reheating, but also study quantum correlation for any random events in Cosmology. Next, using the late time exponential decay of cosmological OTOC with respect to the dynamical time scale of our universe which is associated with the canonically conjugate momentum operator in this formalism we study the phenomena of quantum chaos by computing the expression for {\it Lyapunov spectrum}. Further, using the well known Maldacena Shenker Stanford (MSS) bound, on Lyapunov exponent, $\lambda\leq 2\pi/\beta$, we propose a lower bound on the equilibrium temperature, $T=1/\beta$, at the very late time scale of the universe. On the other hand, with respect to the other time scale with which the Perturbation Variable is associated, we find decreasing but not exponentially decaying behaviour, which quantifies the random correlation at out-of-equilibrium. Finally, we have studied the classical limit of the OTOC to check the consistency with the large time limiting behaviour

Saridakis, Emmanuel N. - One of the best experts on this subject based on the ideXlab platform.

  • Background evolution and growth of structures in interacting dark energy through dynamical system analysis
    2021
    Co-Authors: Khyllep Wompherdeiki, Dutta Jibitesh, Basilakos Spyros, Saridakis, Emmanuel N.
    Abstract:

    We apply the formalism of dynamical system analysis to investigate the evolution of interacting dark energy scenarios at the background and Perturbation levels in a unified way. Since the resulting dynamical system contains the extra Perturbation Variable related to the matter overdensity, the critical points of the background analysis split, corresponding to different behavior of matter Perturbations, and hence to stability properties. From the combined analysis, we find critical points that describe the non-accelerating matter-dominated epoch with the correct growth of matter structure, and the fact that they are saddle provides the natural exist from this phase. Furthermore, we find stable attractors at late times corresponding to a dark energy-dominated accelerated solution with constant matter Perturbations, as required by observations. Thus, interacting cosmology can describe the matter and dark energy epochs correctly, both at the background and Perturbation levels, and since this is not possible in standard, i.e. non-interacting, quintessence, it reveals the crucial effect of the interaction.Comment: 12 pages, 5 figure