Berry phases for 3D Hartree type equations with a quadratic potential and a uniform magnetic field

A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for 3D Hartree type equations with a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is the adiabatic evolution time. A generalization of the Berry phase of the linear Schr\"odinger equation is formulated for the Hartree type equation. For the solutions constructed, the Berry phases are found in explicit form.Comment: 15 pages, no figure

Semiclassical Propagation of Coherent States for the Hartree equation

In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent state, whose phase and amplitude can be determined by a classical flow. The error can be estimated in $L^2$ by C \sqrt {\var}, \var being the Planck constant. Finally we present a full formal asymptotic expansion

Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is the adiabatic evolution time. A generalization of the Berry phase of the linear Schr\"odinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.Comment: 13 pages, no figure

The evolution operator of the Hartree-type equation with a quadratic potential

Based on the ideology of the Maslov's complex germ theory, a method has been developed for finding an exact solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically concentrated functions. The nonlinear evolution operator has been obtained in explicit form in the class of semiclassically concentrated functions. Parametric families of symmetry operators have been found for the Hartree-type equation. With the help of symmetry operators, families of exact solutions of the equation have been constructed. Exact expressions are obtained for the quasi-energies and their respective states. The Aharonov-Anandan geometric phases are found in explicit form for the quasi-energy states.Comment: 23 pege

Oncogenic role of DDX3 in breast cancer biogenesis

Benzo[a] pyrene diol epoxide (BPDE), the active metabolite of benzo[a] pyrene present in tobacco smoke, is a major cancer-causing compound. To evaluate the effects of BPDE on human breast epithelial cells, we exposed an immortalized human breast cell line, MCF 10A, to BPDE and characterized the gene expression pattern. Of the differential genes expressed, we found consistent activation of DDX3, a member of the DEAD box RNA helicase family. Overexpression of DDX3 in MCF 10A cells induced an epithelial-mesenchymal- like transformation, exhibited increased motility and invasive properties, and formed colonies in soft-agar assays. Besides the altered phenotype, MCF 10A-DDX3 cells repressed E-cadherin expression as demonstrated by both immunoblots and by E-cadherin promoter-reporter assays. In addition, an in vivo association of DDX3 and the E-cadherin promoter was demonstrated by chromatin immunoprecipitation assays. Collectively, these results demonstrate that the activation of DDX3 by BPDE, can promote growth, proliferation and neoplastic transformation of breast epithelial cell