论文标题
Q.M.中的联系互动伽玛收敛和玻色网凝结
Contact interactions in Q.M. Gamma convergence and Bose-Einstein condensation
论文作者
论文摘要
我们描述\ emph {零范围}（触点）相互作用，弱且强。强烈的接触导致Efimov在低能核物理学中的效应，弱接触导致Bose-Einstein凝结和超导性库珀对的存在。在B-E中。情况，我们得出了毛 - 位于毛的方程。对于库珀对的冷凝水，我们得出了一个\ emph {不同的}立方本地焦点P.D.E.我们证明，在强烈的回避意义上，强烈的和弱接触的汉密尔顿人都是限制，对范围很短的哈密顿人的局限性。 Q.M.中标准工具的零件形式我们使用伽马收敛触点相互作用，伽马收敛在颗粒的固态物理（传导电子）中也具有作用，该物理（传导电子）满足Pauli方程并在具有$ y $形的顶点的晶格附近移动。所得\ emph {fermi sea}是用$ \ frac {1} {\ log n} $降低负特征值的Efimov序列的Efimov序列。接触相互作用也描述了相对论和非偏见主义的\ emph {contect}（nelson）极性（与质量零场的大量相互作用（接触）相互作用）。我们将在其他地方描述这些结构。
We describe \emph{zero range} (contact) interactions, weak and strong. Strong contact leads to the Efimov effect in Low Energy Nuclear Physics, weak contact leads to Bose-Einstein condensation and to the presence of Cooper pairs in superconductivity . In the B-E. case we derive the Gross-Pitayewskii equation. For a condensate of Cooper pairs we derive a \emph{different} cubic local focusing P.D.E. We prove that both strong and weak contact hamiltonians are limits, in strong resolvent sense, of hamiltonians with potentials of very short range. A part form standard tools in Q.M. we use Gamma convergence Contact interactions and Gamma convergence have a role also in Solid State Physics for particles (conduction electrons) which satisfy the Pauli equation and move in the neighborhood of a lattice with $Y$-shaped vertices. The resulting \emph{Fermi sea} is the filling of an Efimov sequence of bound states with $ \frac{1}{\log n}$ rate of decrease of the negative eigenvalues. Contact interactions describe also a \emph{contact} (Nelson) Polaron (massive particle in (contact) interaction with a mass zero field), both relativistic and non-relativistic. We shall describe elsewhere these structures.
