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Title: Non-commutative Nash inequalities

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