Relation Between The Roughness, Linear Entropy and Visibility of A Quantum State, The Jaynes-Cummings Model.

In this work, an analysis of the Jaynes-Cummings Model is conducted in the parameter spaces, composed of Roughness, Concurrence/Linear Entropy and Visibility. The analysis was carried out without including the effects of the environment and with the inclusion of a dispersive environment. As Roughness measures the state’s degree of non-classicality, its inclusion in the analysis allows to identify points in the dynamics that are not usually perceived by traditional analysis. It is observed that the parameter space is almost completely occupied when the dispersive term is small, and is concentrated in the region of less roughness and less purity as the dispersive coefficient is increased.

Modulational Stability of Envelope Soliton in a Quantum Electron-Ion Plasma in Three Dimension - A generalised Nonlinear Schr ̈odinger Equ ation in 3D

Modulational stability of envelope soliton is studied in a quantum dusty plasma in three dimension.<br>The Krylov-Bogoliubov-Mitropolsky method is applied to the three dimension plasma governing<br>equations. A generalised form of Nonlinear Schr¨odinger equation is obtained whose dispersive term<br>has a tensorial character. Stability condition is deduced abintio and the stability zones are plotted<br>as a function of plasma parameters

Modulational Stability of Envelope Soliton in a Quantum Electron-Ion Plasma in Three Dimension - A generalised Nonlinear Schr ̈odinger Equ ation in 3D

Modulational stability of envelope soliton is studied in a quantum dusty plasma in three dimension.<br>The Krylov-Bogoliubov-Mitropolsky method is applied to the three dimension plasma governing<br>equations. A generalised form of Nonlinear Schr¨odinger equation is obtained whose dispersive term<br>has a tensorial character. Stability condition is deduced abintio and the stability zones are plotted<br>as a function of plasma parameters

4-Nitrobenzyl 3,4-bis(acetyloxy)-2-(4-methoxyphenyl)pyrrolidine-1-carboxylate: crystal structure, Hirshfeld surface analysis and computational chemistry

The title compound, C23H24N2O9, is a tetra-substituted pyrrolidine derivative with a twisted conformation, with the twist evident in the C—C bond bearing the adjacent acetyloxy substituents. These are flanked on one side by a C-bound 4-methoxyphenyl group and on the other by a methylene group. The almost sp 2-N atom [sum of angles = 357°] bears a 4-nitrobenzyloxycarbonyl substituent. In the crystal, ring-methylene-C—H...O(acetyloxy-carbonyl) and methylene-C—H...O(carbonyl) interactions lead to supramolecular layers lying parallel to (\overline{1}01); the layers stack without directional interactions between them. The analysis of the calculated Hirshfeld surfaces indicates the combined importance of H...H (42.3%), H...O/O...H (37.3%) and H...C/C...H (14.9%) surface contacts. Further, the interaction energies, largely dominated by the dispersive term, point to the stabilizing influence of H...H and O...O contacts in the inter-layer region.

Error estimates of finite difference schemes for the Korteweg–de Vries equation

This article deals with the numerical analysis of the Cauchy problem for the Korteweg–de Vries equation with a finite difference scheme. We consider the explicit Rusanov scheme for the hyperbolic flux term and a 4-point $\theta $-scheme for the dispersive term. We prove the convergence under a hyperbolic Courant–Friedrichs–Lewy condition when $\theta \geq \frac{1}{2}$ and under an ‘Airy’ Courant–Friedrichs–Lewy condition when $\theta &lt;\frac{1}{2}$. More precisely, we get a first-order convergence rate for strong solutions in the Sobolev space $H^s(\mathbb{R})$, $s \geq 6$ and extend this result to the nonsmooth case for initial data in $H^s(\mathbb{R})$, with $s\geq \frac{3}{4}$, at the price of a reduction in the convergence order. Numerical simulations indicate that the orders of convergence may be optimal when $s\geq 3$.