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.
Spectral theorem for the Lindblad equation for quadratic open fermionic systems
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abstract
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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cond-mat.stat-mech 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Exact operator dynamics in Lindbladian Wess-Zumino-Witten conformal field theories
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.