论文标题
热哈密顿的光谱理论：1D情况
Spectral Theory of the Thermal Hamiltonian: 1D Case
论文作者
论文摘要
1964年，J。M。Luttinger引入了量子热传输的模型。在本文中，我们研究了与Luttinger模型相关的Hamiltonian操作员的光谱理论，并在一维情况下特别重点。结果表明，（所谓的）热哈密顿量具有一个单参数的自我偶会扩展家族，并且明确计算了频谱，时间 - 散热器组和绿色功能。此外，分析了卷积型电势的散射。最后，还完全解决了相关的经典问题，从而提供了经典行为和量子行为之间的比较。本文的目的是在构造热哈密顿的完整理论方面做出的第一项贡献。
In 1964 J. M. Luttinger introduced a model for the quantum thermal transport. In this paper we study the spectral theory of the Hamiltonian operator associated to the Luttinger's model, with a special focus at the one-dimensional case. It is shown that the (so called) thermal Hamiltonian has a one-parameter family of self-adjoint extensions and the spectrum, the time-propagator group and the Green function are explicitly computed. Moreover, the scattering by convolution-type potentials is analyzed. Finally, also the associated classical problem is completely solved, thus providing a comparison between classical and quantum behavior. This article aims to be a first contribution in the construction of a complete theory for the thermal Hamiltonian.
