Semiclassical limit for Schr\"odinger equations with magnetic field and Hartree-type nonlinearities

The semi-classical regime of standing wave solutions of a Schr\"odinger equation in presence of non-constant electric and magnetic potentials is studied in the case of non-local nonlinearities of Hartree type. It is show that there exists a family of solutions having multiple concentration regions which are located around the minimum points of the electric potential.Comment: 34 page

Architecture of viral genome-delivery molecular machines.

From the abyss of the ocean to the human gut, bacterial viruses (or bacteriophages) have colonized all ecosystems of the planet earth and evolved in sync with their bacterial hosts. Over 95% of bacteriophages have a tail that varies greatly in length and complexity. The tail complex interrupts the icosahedral capsid symmetry and provides both an entry for viral genome-packaging during replication and an exit for genome-ejection during infection. Here, we review recent progress in deciphering the structure, assembly and conformational dynamics of viral genome-delivery tail machines. We focus on the bacteriophages P22 and T7, two well-studied members of the Podoviridae family that use short, non-contractile tails to infect Gram-negative bacteria. The structure of specialized tail fibers and their putative role in host anchoring, cell-surface penetration and genome-ejection is discussed

Band gap renormalization in photoexcited semiconductor quantum wire structures in the GW approximation

We investigate the dynamical self-energy corrections of the electron-hole plasma due to electron-electron and electron-phonon interactions at the band edges of a quasi-one dimensional (1D) photoexcited electron-hole plasma. The leading-order $GW$ dynamical screening approximation is used in the calculation by treating electron-electron Coulomb interaction and electron-optical phonon Fr\"{o}hlich interaction on an equal footing. We calculate the exchange-correlation induced band gap renormalization (BGR) as a function of the electron-hole plasma density and the quantum wire width. The calculated BGR shows good agreement with existing experimental results, and the BGR normalized by the effective quasi-1D excitonic Rydberg exhibits an approximate one-parameter universality.Comment: 11 pages, 3 figure

Multiple solutions to a magnetic nonlinear Choquard equation

We consider the stationary nonlinear magnetic Choquard equation [(-\mathrm{i}\nabla+A(x))^{2}u+V(x)u=(\frac{1}{|x|^{\alpha}}\ast |u|^{p}) |u|^{p-2}u,\quad x\in\mathbb{R}^{N}%] where $A\$is a real valued vector potential, $V$ is a real valued scalar potential$,$ $N\geq3$, $\alpha\in(0,N)$ and $2-(\alpha/N) <p<(2N-\alpha)/(N-2)$. \ We assume that both $A$ and $V$ are compatible with the action of some group $G$ of linear isometries of $\mathbb{R}^{N}$. We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition $$u(gx)=\tau(g)u(x)\text{\ \ \ for all}g\in G,\text{}x\in\mathbb{R}^{N},$$ where $\tau:G\rightarrow\mathbb{S}^{1}$ is a given group homomorphism into the unit complex numbers.Comment: To appear on ZAM

On fractional Schrodinger equations with Hartree type nonlinearities

Goal of this paper is to study the following doubly nonlocal equation in the case of general nonlinearities of Berestycki-Lions type. We prove existence of ground states and we obtain regularity and asymptotic decay of general solutions, extending some results by Moroz and Van Schaftingen