论文标题
准经典制度中的基态特性
Ground State Properties in the Quasi-Classical Regime
论文作者
论文摘要
我们研究了在准经典近似中耦合非相关量子颗粒和诸如辐射等力的bose场的基态能量和基态。每当携带力场具有大量的激发，因此以半经典的方式行事时，后者非常有用，而另一方面的非相关粒子则保留其显微镜特征。我们证明，完全显微镜模型的基态能收敛到非线性准经典功能之一，这取决于粒子的波函数和磁场的经典配置。同等地，该能量可以解释为pekar样功能的最低能量，仅适用于粒子的有效非线性相互作用。如果粒子被限制，则微观系统的基态也会收敛到概率度量，该测度集中在准经典能量的一组最小化器上。
We study the ground state energy and ground states of systems coupling non-relativistic quantum particles and force-carrying Bose fields, such as radiation, in the quasi-classical approximation. The latter is very useful whenever the force-carrying field has a very large number of excitations,and thus behaves in a semiclassical way, while the non-relativistic particles, on the other hand, retain their microscopic features. We prove that the ground state energy of the fully microscopic model converges to the one of a nonlinear quasi-classical functional depending on both the particles' wave function and the classical configuration of the field. Equivalently, this energy can be interpreted as the lowest energy of a Pekar-like functional with an effective nonlinear interaction for the particles only. If the particles are confined, the ground state of the microscopic system converges as well, to a probability measure concentrated on the set of minimizers of the quasi-classical energy.
