Ecidstation Profesional Descargar

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The law of asymptotic locality for the generic Bloch Hamiltonian, which includes in particular the case of two-dimensional systems, is reexamined and studied from a broader perspective. In this study, we consider a family of Bloch Hamiltonians with the following Hamiltonian form, that is,we have for any λ the Hamiltonian H=H(λ) in the form of λ times a Bloch Hamiltonian H(0) with the eigenstate properties that are discussed. We derive a simple condition for the asymptotic locality property of the Bloch Hamiltonian, which is then shown to be valid for an important class of two-dimensional systems. Furthermore, the simplicity of the condition suggests that it can also be used as a benchmark to test asymptotic locality of the Hamiltonian. We illustrate the use of the condition by studying a class of two-dimensional models, which shows that it may be possible to find Hamiltonians that are not asymptotically local. This is also done by evaluating the condition for a simple family of two-dimensional models and finds that there exists a bound on the number of Bloch bands that constrain asymptotic locality. A new approach to time-independent boundary problems is presented. It is based on the Green-Lagrange identity for the Helmholtz equation. Since in most physical applications it is natural to consider a domain with a time-dependent boundary, a new class of local time-dependent boundary problems is introduced. This leads to a naturally defined Dirichlet-to-Neumann map associated with the domain and the time-dependent boundary. Special attention is devoted to the calculation of the spatial norms of the solution of the time-dependent problems. A new approach to time-independent boundary problems is presented. It is based on the Green-Lagrange identity for the Helmholtz equation. Since in most physical applications it is natural

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