论文标题
红外旋转玻色子模型中的基态存在
Existence of Ground States in the Infrared-Critial Spin Boson Model
论文作者
论文摘要
我们回顾了有关红外临界旋转玻色子模型的基态存在的最新结果，该模型描述了无质量骨磁场与两态量子系统的相互作用。明确地，我们得出了一个关键耦合$λ_{\ Mathsf C}> 0 $，以便旋转玻色子模型显示出耦合常数$λ$与$ | |λ|<λ_{\ mathsf c} $的基态状态。该证明将用于自旋玻色子模型的Feynman-Kac-Nelson公式与外部磁场，1D-修饰模型相关结合以及Fock空间中的紧凑性参数结合在一起。详细阐述了与远程1D模型的连接，我们简要讨论了自旋玻色子模型在大耦合处没有基态的猜想。该注释是基于与David Hasler和Oliver Siebert的共同合作。
We review recent results on the existence of ground states for the infrared-critical spin boson model, which describes the interaction of a massless bosonic field with a two-state quantum system. Explicitly, we derive a critical coupling $λ_{\mathsf c}>0$ such that the spin boson model exhibits a ground state for coupling constants $λ$ with $|λ|<λ_{\mathsf c}$. The proof combines a Feynman-Kac-Nelson formula for the spin boson model with external magnetic field, a 1D-Ising model correlation bound and a compactness argument in Fock space. Elaborating on the connection to a long-range 1D-Ising model, we briefly discuss the conjecture that the spin boson model does not have a ground state at large coupling. This note is based on joint work with David Hasler and Oliver Siebert.
