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Register a new userA Jacobi Algorithm in Phase Space: Diagonalizing (skew-) Hamiltonian and Symplectic Matrices with Dirac-Majorana Matrices
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Added by
Christian Baumgarten
Publication date
2020
fields
Physics
and research's language is
English
Authors
Christian Baumgarten
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Jacobis method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report about the generalization of these elementary rotations towards canonical transformations acting in Hamiltonian phase spaces. This generalization allows to use Jacobis method in order to compute eigenvalues and eigenvectors of Hamiltonian (and skew-Hamiltonian) matrices with either purely real or purely imaginary eigenvalues by successive elementary symplectic decoupling-transformations.
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For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end we develop a method for obtaining uniform asymptotics, with respect to the spectral parameter, of the generalized eigenvectors. Our technique can be applied to a wide range of Jacobi matrices.
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