Spectral theorem for the Lindblad equation for quadratic open fermionic systems

Details Spectral theorem for the Lindblad equation for quadratic open fermionic systems Spectral theorem for the Lindblad equation for quadratic open fermionic systems

2010-05-05

arxiv.org/abs/1005.0763v1

Physics

Quantum Physics

19 pages, no figures

Scientific paper

The spectral theorem is proven for the quantum dynamics of quadratic open systems of n fermions described by the Lindblad equation. Invariant eigenspaces of the many-body Liouvillean dynamics and their largest Jordan blocks are explicitly constructed for all eigenvalues. For eigenvalue zero we describe an algebraic procedure for constructing (possibly higher dimensional) spaces of (degenerate) non-equilibrium steady states.

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