The system shows superstructure phenomenon similar to that appeared from the effect of the Kerr-like medium on the Jaynes-Cummings model. Introduction The density matrix was introduced, with different motivations, by von Neumann and by Lev Landau. Two variants of the von Neumann entropy exist based on the graph Laplacian and normalized graph Laplacian, respectively. Employing this solution and for chosen values more » of different parameters we discuss numerically the atomic occupation probabilities as well as the degree of entanglement through the entropy of the field. The von Neumann entropy of a graph is a spectral complexity measure that has recently found applications in complex networks analysis and pattern recognition. Under a certain condition the exact solution to the Schroedinger equation is obtained. Using IBMs publicly accessible quantum computers, we have analyzed the entropies of Schrdingers cat states, which have the form (1/2)1/2 0 0 00. The von Neumann measure of a pure state, even if it is an unknown state, is zero. The model in one hand can be regarded as a generalization of the Jaynes-Cummings model (JCM), however, in the other hand it can be considered as a generalization of the parametric amplifier model. Von Neumann derived his measure of quantum entropy 1,2, using arguments similar to that of Boltzmann in his earlier derivation of thermodynamic entropy, by counting the different microstates associated with the system. The interaction between the fields has been taken into account and considered to be in the parametric amplifier form. In the present article, we introduce a Hamiltonian model that consists of two modes of the field in a perfect cavity to interact with a single two-level atom.

Von neumann entropy