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Spectral theorem for the Lindblad equation for quadratic open fermionic systems

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arxiv 1005.0763 v1 pith:MY2WK7HC submitted 2010-05-05 quant-ph

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keywords dynamicsequationlindbladopenquadraticspectralsystemstheorem
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Exact operator dynamics in Lindbladian Wess-Zumino-Witten conformal field theories

    cond-mat.stat-mech 2026-06 unverdicted novelty 7.0 of 10

    Abelian U(1)_k WZW Lindbladians admit exact closed operator dynamics for arbitrary jump rates via current algebra, while non-Abelian versions require symmetric dissipation and close only for single operators.

  2. Exact Lindbladian Dynamics from Conformal Embeddings and Topological Defects in Conformal Field Theory

    cond-mat.stat-mech 2026-07 accept novelty 6.0 of 10

    Conformal embeddings and Verlinde defect lines make adjoint Lindbladians triangular or diagonal on natural CFT operator spaces, yielding exact open dynamics.

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