The Bethe–Salpeter eigenvalue problem is solved in condense matter physics to estimate the absorption spectrum of solids. It is a structured eigenvalue problem. Its special structure appears in other approaches for studying electron excitation in molecules or solids also. When the Bethe–Salpeter Hamiltonian matrix is definite, the corresponding eigenvalue problem can be reduced to a symmetric eigenvalue problem. However, its special structure leads to a number of interesting spectral properties. We describe these properties that are crucial for developing efficient and reliable numerical algorithms for solving this class of problems.
CITATION STYLE
Shao, M., & Yang, C. (2017). Properties of definite Bethe–Salpeter eigenvalue problems. In Lecture Notes in Computational Science and Engineering (Vol. 117, pp. 91–105). Springer Verlag. https://doi.org/10.1007/978-3-319-62426-6_7
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