Spectral theorem for the Lindblad equation for quadratic open fermionic systems

By Tomaz Prosen. 2010

135 citations recorded by the source corpus.

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 Liouvillian 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/7d44e1dad26b48f0bfd665f429cde6108620e6dd

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Geometry of quantum phase transitions (2019, background): “(239) should be considered, which adds an extra polynomial dependence in (241)[388, 177].”
Engineered Open Systems and Quantum Simulations with Atoms and Ions (2012, background): “…different terms of the dissipative Liouvillian, have been anticipated in Verstraete et al. (2009), and discussed in more detail in Eisert and Prosen (2010) and Hoening et al. (2010), where in particular the key aspect of criticality in terms of diverging length and time scales has been…”
Exceptional topology of non-Hermitian systems (2019, unknown): “…of topological phases such as topological insulators and semimetals has revolutionized the classification of matter and led to groundbreaking discoveries of topologically robust physical phenomena (Hasan and Kane, 2010; Qi and Zhang, 2011; Chiu et al. , 2016; Armitage, Mele, and Vishwanath, 2018).”
Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps (2019, background): “[43] T.”
Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories (2020, background): “To every Lindblad master equation corresponds a nonHermitian Liouvillian superoperator L which can display Liouvillian exceptional points (LEPs) [12, 23, 46–52].”