We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant lambda. We show that the ground state energy is an analytic function of lambda and that the corresponding ground state can also be chosen to be an analytic function of lambda. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground state energy can be calculated using regular analytic perturbation theory.
Symmetry and Exact Solutions of General Spin-Boson Models
The Basque Country University (EHU/UPV)（巴斯克国家大学）；Ikerbasque, Basque Foundation for Science（伊卡巴斯科，巴斯克科学基金会）；University of the Basque Country UPV/EHU（巴斯克国家大学）；Beijing Key Laboratory of Quantum Matter State Control and Ultra-Precision Measurement Technology（北京量子物质态控制与超精密测量技术重点实验室）
Bosons in a Trap: Asymptotic Exactness of the Gross-Pitaevskii Ground State Energy Formula
近年来在处理稀玻色气体方面的实验突破使人们重新对它们的量子力学描述产生了兴趣，分别是对它们的近似描述。被限制在外势中并通过短程排斥力相互作用的稀玻色气体的基态性质通常用Gross-Pitaevskii能量泛函描述。在与Elliott H. Lieb和Jakob Yngvason最近严格地澄清了它作为量子力学多体基态问题近似的地位。我们提出了一个总结这项工作，为二维和三维的情况下。
