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Liouville space

From Wikipedia, the free encyclopedia

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

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  1. ^ a b "Hilbert space". Uni Hamburg. Archived from the original on 29 Oct 2014. Retrieved 24 April 2022.
  2. ^ a b c Gyamfi, Jerryman A. (16 October 2020). "Fundamentals of quantum mechanics in Liouville space". European Journal of Physics. 41 (6): 063002. arXiv:2003.11472. Bibcode:2020EJPh...41f3002G. doi:10.1088/1361-6404/ab9fdd.
  3. ^ a b Janos Polonyi; Rachid, Ines (2021). "Elementary open quantum states". Symmetry. 13 (9): 1624. arXiv:2106.01443v2. Bibcode:2021Symm...13.1624P. doi:10.3390/sym13091624.