Out-of-time-order correlation and detection of phase structure in Floquet transverse Ising spin system

We study the out-of-time-order correlation (OTOC) of the Floquet transverse Ising model and use it to verify the phase diagram of the system. First, we present the exact analytical solution of the transverse magnetization OTOC using the Jorden-Wigner transformation. In order to get the phase structure of the Floquet transverse Ising system, we use the longitudinal magnetization OTOC as it is known to serve as an order parameter of the system. We show the phase structure numerically in the transverse Ising Floquet system by using the long time average of the longitudinal magnetization OTOC. In both the open and the closed chain systems, we find distinct phases out of which two are paramagnetic (0-paramagnetic and $\pi$-paramagnetic), and two are ferromagnetic (0-ferromagnetic and $\pi$-ferromagnetic) as defined in the literature.Comment: 9 Pages, 7 Figure

V-line 2-tensor tomography in the plane

In this article, we introduce and study various V-line transforms (VLTs) defined on symmetric 2-tensor fields in $\mathbb{R}^2$. The operators of interest include the longitudinal, transverse, and mixed VLTs, their integral moments, and the star transform. With the exception of the star transform, all these operators are natural generalizations to the broken-ray trajectories of the corresponding well studied concepts defined for straight-line paths of integration. We characterize the kernels of the VLTs and derive exact formulas for reconstruction of tensor fields from various combinations of these transforms. The star transform on tensor fields is an extension of the corresponding concepts that have been previously studied on vector fields and scalar fields (functions). We describe all injective configurations of the star transform on symmetric 2-tensor fields and derive an exact, closed-form inversion formula for that operator.Comment: 26 pages, 2 figure

Isolation and Structure Elucidation of Quercetin like Structure from Dalbergia sissoo (Fabaceae)

The present study was conducted to isolate and classify Dalbergia sissoo (L.) bioactive compounds. The genus consists of 300 species in India, including 25 species. The generic name Dalbergia honors the 18th century Swedish brothers Nils and Carl Dalberg. Various phytoconstituents of alkaloids, glycosides, flavanoids, tannins, saponins, sterols and terpenoids were isolated and classified from different parts of the plant. Thin Layer Chromatography, High Performance Thin Layer Chromatography, and Column Chromatography were used to isolate spots from the fraction of the crude extract to elucidate the chemical structure of Dalbergia sissoo (L.) leaf extract. Potential spots have been exposed to techniques of FTIR, NMR and mass spectroscopy. Column chromatography was exposed to the raw extract, obtaining 125 fractions, conducting TLC. Among them was a single band in TLC, characterized by FTIR, NMR spectroscopy and mass spectroscopy, and the structure was known as Quercetin. The results of this study indicate the effective potential compound of the ethanolic fraction of Dalbergia sissoo (L.). Keywords: Dalbergia sissoo; Isolation & Structure Elucidation; FTIR; NMR spectroscopy; Mass spectroscopy