On invariant subspace in quantum control systems and some concepts of integrable quantum systems

DOI10.1007/s10773-014-2498-6zbMath1330.81108OpenAlexW1965904284MaRDI QIDQ2634027

Grzegorz Pastuszak, Andrzej Jamiołkowski, Takeo Kamizawa

Publication date: 5 February 2016

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10773-014-2498-6

zbMATH Keywords

integrable systemcirculant matricesBrownian matricesMorris-Shore transformationquasi-diagonalisation

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Quantum control (81Q93)

Related Items (5)

On maps which preserve semipositivity and quantifier elimination theory for real numbers ⋮ On Some Algebraic Procedure for Block-Diagonal Decompositions of Open Dynamical Systems ⋮ Ascending chains of ideals in the polynomial ring ⋮ Quantifier elimination theory and maps which preserve semipositivity ⋮ On a Criterion for Simultaneous Block-Diagonalization of Normal Matrices

Cites Work

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• A non-commutative spectral theorem
• Simultaneous block triangularization and block diagonalization of sets of matrices
• Algebras of linear transformations
• Geometric phases in classical and quantum mechanics
• Generalized Shemesh criterion, common invariant subspaces and irreducible completely positive superoperators
• Design of quantum Fourier transforms and quantum algorithms by using circulant Hamiltonians
• A Theorem of Polynomial Identities
• Minimal Identities for Algebras
• \(C^*\)-algebras by example

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