标题： 三粒子系统在光晶格中的束缚态的存在 显示英文标题

标题： The existence of bound states in a system of three particles in an optical lattice

摘要： 我们考虑一个由三个粒子（两个相同的费米子和一个不同的粒子）组成的系统的哈密顿量$\mathrm{H}_{\mu},\mu\in \R$，这些粒子在晶格${\Z}^d ,\, d=1,2 $上运动，通过排斥性$(\mu>0)$或吸引力$(\mu<0)$的零范围两体势$\mu V$相互作用。 We prove for any $\mu\ne0$ the existence of bound state of the discrete three-particle Schrödinger operator $H_{\mu}(K),\,K\in \T^d$ being the three-particle quasi-momentum, associated to the hamiltonian $\mathrm{H}_{\mu}$. 显示英文摘要

摘要： We consider the hamiltonian $\mathrm{H}_{\mu},\mu\in \R$ of a system of three-particles (two identical fermions and one different particle) moving on the lattice ${\Z}^d ,\, d=1,2 $ interacting through repulsive $(\mu>0)$ or attractive $(\mu<0)$ zero-range pairwise potential $\mu V$. We prove for any $\mu\ne0$ the existence of bound state of the discrete three-particle Schr\"odinger operator $H_{\mu}(K),\,K\in \T^d$ being the three-particle quasi-momentum, associated to the hamiltonian $\mathrm{H}_{\mu}$.