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Comonotonicity and Choquet integrals of Hermitian operators and their applications.
Publication Date
2016
End of Embargo
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© 2016 IOP. Reproduced in accordance with the publisher's self-archiving policy.
Peer-Reviewed
yes
Open Access status
openAccess
Accepted for publication
20th Jan 2016
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Abstract
In a quantum system with d-dimensional Hilbert space, the Q-function of a Hermitian positive
semide nite operator , is de ned in terms of the d2 coherent states in this system. The Choquet
integral CQ( ) of the Q-function of , is introduced using a ranking of the values of the Q-function,
and M obius transforms which remove the overlaps between coherent states. It is a gure of merit
of the quantum properties of Hermitian operators, and it provides upper and lower bounds to
various physical quantities in terms of the Q-function. Comonotonicity is an important concept
in the formalism, which is used to formalize the vague concept of physically similar operators.
Comonotonic operators are shown to be bounded, with respect to an order based on Choquet
integrals. Applications of the formalism to the study of the ground state of a physical system, are
discussed. Bounds for partition functions, are also derived.
Version
Accepted Manuscript
Citation
Vourdas, A (2016) Comonotonicity and Choquet integrals of Hermitian operators and their applications. Journal of Physics A: Mathematical and Theoretical. 49(14): 145002 (36pp).
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Article