Eigenstates and spectrum properties of a resonant field in a Kerr-like medium

Abstract

We investigate the energy eigenvalues and eigenstates of a resonant field in a Kerr-like medium by an efficient method. All the energy eigenvalues and eigenstates can be obtained for an arbitrary total particle number N and other parameters involved in the system. We show that the eigenstates can be explicitly expressed analytically in terms of a single parameter γ whose values are determined by the roots of a polynomial of the order of at most 1+ int(N/2) with int(x) being x's integer part. By studying the spectra, the erratic level crossings appear apparent when N 40 and γ over critical values.

Exact analytical solutions to the mean-field model depicting microcavity containing semiconductor quantum wells

“…A stands for the strength of exciton-exciton coupling which arose from the Coulomb interaction. We may see that it is similar to the model describing a single-mode field coupled with a nonlinear medium [29] or a Bose-Einstein condensate (BEC) in a tilted double well. [30−33] The energy eigenvalues and eigenstates for the fully quantized Hamiltonian depicting these systems can be obtained by using proper methods.…”

“…[30−33] The energy eigenvalues and eigenstates for the fully quantized Hamiltonian depicting these systems can be obtained by using proper methods. [29] We shall pay our attention to the dynamics under mean-field approximation. Using the well-known Schwinger representation of the angular momentum, [34]…”

Enhancement of Photocatalytic Degradation of Methylene Blue Dye Using Graphene Oxide Based Ternary Nanocomposite

“…To degrade the dye effluents effectively, various hybrid‐based TiO 2 photocatalyst were developed either by doping it with transition metals [14–16] nitrogen, sulfur, [17,18] etc. or by nanocomposites of activated carbon, CNT, graphene based TiO 2 hybrid [19–22] In recent years, it has been found that hematite (Fe 2 O 3 ), is the efficient metal oxide that improve the photocatalytic performance of TiO 2 [23–26] . Fe 2 O 3 has a narrow band gap and it is easier for visible light to excite the electron‐hole pairs in its valence band (VB) (2.0–2.2 eV) [27] .…”

Phase diffusion of a two-component Bose-Einstein condensates: exact and short-time solutions for arbitrary coherent spin state

“…Due to the presence of atom-atom interaction (χ = 0), each number state has different phase evolution rate, which in turn lead to collapse and revival of the Rabi oscillation, a phenomenon that is wellknown in quantum optics [14]. Similar effect has been investigated in two-component BECs [24], atom-molecular BECs [25][26][27], and exciton emission [28][29][30].…”