论文标题
强耦合极化子的绑定状态的无处不在
Ubiquity of bound states for the strongly coupled polaron
论文作者
论文摘要
我们研究以固定的总动量为极化子的FröhlichHamiltonian的频谱。我们证明了基态能量与强耦合时基本频谱之间的激发特征值的存在。实际上，我们的主要结果表明，激发能带的数量在强耦合极限下发散。为了证明这一点，我们得出了相应的哈密顿纤维的最低最大值的上限，并将其与必需频谱的底部进行比较，这是最近在[1]中获得的下限。上限是根据由bogoliubov-type的有效的哈密顿量确定的非动量激发能移动的基态能带。
We study the spectrum of the Fröhlich Hamiltonian for the polaron at fixed total momentum. We prove the existence of excited eigenvalues between the ground state energy and the essential spectrum at strong coupling. In fact, our main result shows that the number of excited energy bands diverges in the strong coupling limit. To prove this we derive upper bounds for the min-max values of the corresponding fiber Hamiltonians and compare them with the bottom of the essential spectrum, a lower bound on which was recently obtained in [1]. The upper bounds are given in terms of the ground state energy band shifted by momentum-independent excitation energies determined by an effective Hamiltonian of Bogoliubov-type.
