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>Dual Lanczos vector space. I. A formal and numerical framework for the theoretical investigation of relaxation processes
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Dual Lanczos vector space. I. A formal and numerical framework for the theoretical investigation of relaxation processes
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机译：Dual Lanczos vector space. I. A formal and numerical framework for the theoretical investigation of relaxation processes
We lay down the mathematical foundations of a matrix formulation of relaxation processes that places no symmetry restrictions on the Liouville operator appearing in the relevant linear equation of motion for the density distribution function or density operator. Adopting a dual Lanczos vector space, we construct a lsquo;lsquo;globalrsquo;rsquo; dual Lanczos transformation scheme that may be utilized to facilitate spectral density and transient behavior calculations. It is shown that the basis vectors adopted in the Mori projection operator method correspond to the results obtained in a restricted global dual Lanczos transformation scheme limited to reversible systems, i.e., systems described by a Hermitian Liouville operator. Since the present approach places no symmetry restrictions on the Liouville operator, we are able to provide a mathematical framework that can handle relaxation processes in both reversible and irreversible systems.
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