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Published January 2016 | Submitted + Published
Journal Article Open

Non-commutative Nash inequalities

Abstract

A set of functional inequalities—called Nash inequalities—are introduced and analyzed in the context of quantum Markov process mixing. The basic theory of Nash inequalities is extended to the setting of non-commutative L_p spaces, where their relationship to Poincaré and log-Sobolev inequalities is fleshed out. We prove Nash inequalities for a number of unital reversible semigroups.

Additional Information

© 2016 AIP Publishing LLC. Received 11 August 2015; accepted 24 November 2015; published online 16 December 2015. M.J.K. was supported by the Carlsbergfond and the Villum foundation. K.T. was supported by the Institute for Quantum Information and Matter, a NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation (Grant Nos. PHY-0803371 and PHY-1125565).

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Published - 1.4937382.pdf

Submitted - 1508.02522v1.pdf

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Additional details

Created:
August 20, 2023
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October 17, 2023