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تسجيل مستخدم جديدOn orbital stability of ground states for finite crystals in fermionic Schrodinger--Poisson model
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We consider the Schrodinger--Poisson--Newton equations for finite crystals under periodic boundary conditions with one ion per cell of a lattice. The electron field is described by the $N$-particle Schrodinger equation with antisymmetric wave function. Our main results are i) the global dynamics with moving ions, and ii) the orbital stability of periodic ground state under a novel Jellium and Wiener-type conditions on the ion charge density. Under Jellium condition both ionic and electronic charge densities of the ground state are uniform.
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We consider the Schrodinger-Poisson-Newton equations for finite crystals under periodic boundary conditions with one ion per cell of a lattice. The electrons are described by one-particle Schrodinger equation. Our main results are i) the global dynam
ics with moving ions; ii) the orbital stability of periodic ground state under a novel Jellium and Wiener-type conditions on the ion charge density. Under the Jellium condition both ionic and electronic charge densities for the ground state are uniform.
The Schrodinger-Poisson-Newton equations for crystals with a cubic lattice and one ion per cell are considered. The ion charge density is assumed i) to satisfy the Wiener and Jellium conditions introduced in our previous paper [28], and ii) to be exp
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We give short survey on the question of asymptotic stability of ground states of nonlinear Schrodinger equations, focusing primarily on the so called nonlinear Fermi Golden Rule.
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u(x)|^{2}|u(y)|^2}{|x-y|}dxdy-betaint_{R^{3}}|u|^{frac{8}{3}}dx$$ $alpha,beta>0$ and $rho>0$ is small enough. The minimization problem is $L^2$ critical and in order to characterize of the values $alpha, beta>0$ such that $I^{alpha, beta}(rho)>-infty$ for every $rho>0$, we prove a new lower bound on the Coulomb energy involving the kinetic energy and the exchange energy. We prove the existence of a constant $S>0$ such that $$frac{1}{S}frac{|varphi|_{L^frac 83(R^3)}}{|varphi|_{dot H^frac 12(R^3)}^frac 12}leq left (intint_{R^3times R^3} frac{|varphi(x)|^2|varphi(y)|^2}{|x-y|}dxdyright)^frac 18 $$ for all $varphiin C^infty_0(R^3)$. Eventually we show that similar compactness property fails provided that in the energy above we replace the inhomogeneous Sobolev norm $|u|^2_{H^frac 12(R^3)}$ by the homogeneous one $|u|_{dot H^frac 12(R^3)}$.
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