Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-03-17
Physics
Condensed Matter
Statistical Mechanics
5 pages; "International Conference on Theoretical Physics (TH-2002)"; 22 July 2002 - 27 July 2002; Paris, France, UNESCO; Them
Scientific paper
We apply concepts of random differential geometry connected to the random matrix ensembles of the random linear operators acting on finite dimensional Hilbert spaces. The values taken by random linear operators belong to the Liouville space. This Liouville space is endowed with topological and geometrical random structure. The considered random eigenproblems for the operators are applied to the quantum statistical systems. In the case of random quantum Hamiltonians we study both hermitean (self-adjoint) and non-hermitean (non-self-adjoint) operators leading to Gaussian and Ginibre ensembles Refs. [1], [2], [3]. [1] M. M. Duras, ``Finite-difference distributions for the Ginibre ensemble,'' {\em J. Opt. B: Quantum Semiclass. Opt.} {\bf 2}, 287-291, 2000. [2] M. M. Duras, K. Sokalski, ``Finite Element Distributions in Statistical Theory of Energy Levels in Quantum Systems,'' {\em Physica} {\bf D125}, 260-274, 1999. [3] M. M. Duras, K. Sokalski, ``Higher-order finite-element distributions in statistical theory of nuclear spectra,'' {\em Phys. Rev. E} {\bf 54}, 3142-3148, 1996.
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