The Spin-MInt algorithm is proven symplectic for general K electronic states via explicit verification of the condition MJM^T = J on the coadjoint orbit of the su(K) Lie-Poisson algebra.
Humphreys.Introduction to Lie Algebras and Representation Theory, volume 9 of Graduate Texts in Mathematics
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The paper establishes a Lie-algebraic framework for exact Krylov dynamics in time-dependent quantum systems and introduces a quantum speed limit for complexity growth that retains its time-independent form but saturates only when the Hamiltonian commutes with itself at different times.
Under a division condition, tangential CR cohomology on compact Lie groups with left-invariant CR structures is finite-dimensional and computable on maximal tori, with necessity shown for a class of structures.
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On the Symplectic Propagation of the Spin-MInt Algorithm for Non-Adiabatic Quantum Dynamics
The Spin-MInt algorithm is proven symplectic for general K electronic states via explicit verification of the condition MJM^T = J on the coadjoint orbit of the su(K) Lie-Poisson algebra.
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Krylov Dynamics and Operator Growth in Time-Dependent Systems via Lie Algebras
The paper establishes a Lie-algebraic framework for exact Krylov dynamics in time-dependent quantum systems and introduces a quantum speed limit for complexity growth that retains its time-independent form but saturates only when the Hamiltonian commutes with itself at different times.
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Cohomology of CR structures on compact Lie groups
Under a division condition, tangential CR cohomology on compact Lie groups with left-invariant CR structures is finite-dimensional and computable on maximal tori, with necessity shown for a class of structures.