热哈密顿量的谱理论:一维情况

IF 1 3区数学 Q1 MATHEMATICS

Journal of Spectral Theory Pub Date : 2020-02-24 DOI:10.4171/jst/376

G. Nittis, Vicente Lenz

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引用次数: 1

摘要

1964年，卢廷格提出了一个量子热输运模型。在本文中，我们研究了与Luttinger模型相关的哈密顿算子的谱理论，特别关注一维情况。结果表明，（所谓的）热哈密顿量具有一个自伴扩展的单参数族，并且显式地计算了谱、时间传播子群和格林函数。此外，还分析了卷积型势的散射。最后，相关的经典问题也得到了完全解决，从而提供了经典行为和量子行为之间的比较。本文旨在为建立完整的热哈密顿量理论做出第一个贡献。

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Spectral theory of the thermal Hamiltonian: 1D case

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.

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来源期刊

Journal of Spectral Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome. The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory. Schrödinger operators, scattering theory and resonances; eigenvalues: perturbation theory, asymptotics and inequalities; quantum graphs, graph Laplacians; pseudo-differential operators and semi-classical analysis; random matrix theory; the Anderson model and other random media; non-self-adjoint matrices and operators, including Toeplitz operators; spectral geometry, including manifolds and automorphic forms; linear and nonlinear differential operators, especially those arising in geometry and physics; orthogonal polynomials; inverse problems.