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Title: 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{sub 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.

Authors:
 [1];  [2]
  1. NBIA, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen (Denmark)
  2. Institute for Quantum Information and Matter, California Institute of Technology, Pasadena California 91125 (United States)
Publication Date:
OSTI Identifier:
22479621
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MARKOV PROCESS; MATHEMATICAL SPACE; STATISTICS

Citation Formats

Kastoryano, Michael, and Temme, Kristan. Non-commutative Nash inequalities. United States: N. p., 2016. Web. doi:10.1063/1.4937382.
Kastoryano, Michael, & Temme, Kristan. Non-commutative Nash inequalities. United States. doi:10.1063/1.4937382.
Kastoryano, Michael, and Temme, Kristan. Fri . "Non-commutative Nash inequalities". United States. doi:10.1063/1.4937382.
@article{osti_22479621,
title = {Non-commutative Nash inequalities},
author = {Kastoryano, Michael and Temme, Kristan},
abstractNote = {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{sub 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.},
doi = {10.1063/1.4937382},
journal = {Journal of Mathematical Physics},
number = 1,
volume = 57,
place = {United States},
year = {Fri Jan 15 00:00:00 EST 2016},
month = {Fri Jan 15 00:00:00 EST 2016}
}
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