Liouville space
From HandWiki
In the mathematical physics of quantum mechanics, Liouville space, also known as line space, is the space of operators on Hilbert space. Liouville space is itself a Hilbert space under the Hilbert-Schmidt inner product.[1][2] Abstractly, Liouville space is equivalent (isometrically isomorphic) to the tensor product of a Hilbert space with its dual.[1][3] A common computational technique to organize computations in Liouville space is vectorization.[2]
Liouville space underlies the density operator formalism and is a common computation technique in the study of open quantum systems.[2][3]
References
- ↑ 1.0 1.1 "Hilbert space". Uni Hamburg. https://www.chemie.uni-hamburg.de/nmr/insensitive/tutorial/en.lproj/hilbert_space.html.
- ↑ 2.0 2.1 2.2 Gyamfi, Jerryman A. (16 October 2020). "Fundamentals of quantum mechanics in Liouville space". European Journal of Physics 41 (6): 063002. doi:10.1088/1361-6404/ab9fdd.
- ↑ 3.0 3.1 Janos Polonyi; Rachid, Ines (forthcoming). "Elementary open quantum states". Symmetry.
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