论文标题
准古典基态。 I.线性耦合Pauli-Fierz Hamiltonians
Quasi-classical Ground States. I. Linearly Coupled Pauli-Fierz Hamiltonians
论文作者
论文摘要
我们考虑了一个由外部电势结合的无旋转的非相关粒子，并线性耦合到量化的辐射场。 $ u \ otimesψ_f$的产品状态的能量$ \ MATHCAL {E}（u，f）$，其中$ u $是粒子的正常化状态，$ψ_f$是该领域的连贯状态，它提供了Klein-Gordon-Schr \'odinger''''''''''的能量。我们将其自然能量空间上的功能性$ \ Mathcal {e}（u，f）$最小化。我们证明了基态在耦合函数的一般条件下基态的存在和唯一性。特别是，均未施加紫外线截止和红外截止。我们的结果确定了klein-gordon-schr \''odinger能量功能的基态和基态的紫外线限制的收敛，并提供小耦合处基态能量的二阶渐近膨胀。
We consider a spinless, non-relativistic particle bound by an external potential and linearly coupled to a quantized radiation field. The energy $\mathcal{E}(u,f)$ of product states of the form $u\otimes Ψ_f$, where $u$ is a normalized state for the particle and $Ψ_f$ is a coherent state in Fock space for the field, gives the energy of a Klein-Gordon--Schr\''odinger system. We minimize the functional $\mathcal{E}(u,f)$ on its natural energy space. We prove the existence and uniqueness of a ground state under general conditions on the coupling function. In particular, neither an ultraviolet cutoff nor an infrared cutoff is imposed. Our results establish the convergence in the ultraviolet limit of both the ground state and ground state energy of the Klein-Gordon--Schr\''odinger energy functional, and provide the second-order asymptotic expansion of the ground state energy at small coupling.
