Open-system quantum complexity is governed by a sub-Finslerian geometry whose curvature depends on the cost penalties for unitary and dissipative controls.
Lindbladian dynamics of the Sachdev-Ye-Kitaev model
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abstract
We study the Lindbladian dynamics of the Sachdev-Ye-Kitaev (SYK) model, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Here, the linear jump operators are non-random while the quadratic jump operators are sampled from a Gaussian distribution. In the limit of large $N$, where $N$ is the number of Majorana fermion operators, and also in the limit of large $N$ and $M$, where $M$ is the number of jump operators, the SYK Lindbladians are analytically tractable, and we obtain their stationary Green's functions, from which we can read off the decay rate. For finite $N$, we also study the distribution of the eigenvalues of the SYK Lindbladians.
representative citing papers
Hard-core boson two-body models with random interactions exhibit chaotic spectral statistics, operator growth, and eigenstate properties approaching those of random matrices and the SYK model.
citing papers explorer
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The Geometry of Quantum Complexity in Open Systems
Open-system quantum complexity is governed by a sub-Finslerian geometry whose curvature depends on the cost penalties for unitary and dissipative controls.
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Complexity of Quadratic Quantum Chaos
Hard-core boson two-body models with random interactions exhibit chaotic spectral statistics, operator growth, and eigenstate properties approaching those of random matrices and the SYK model.