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We prove that the canonical sub-Laplacian on $SU(2)$ admits a uniform modified log-Sobolev inequality for all its matrix-valued functions, independent of the matrix dimension.
Dominique Bakry, Fabrice Baudoin, Michel Bonnefont, and Djalil Chafai, On gradient bounds for the heat kernel on the Heisenberg group , J. Funct. Anal. 255
1938
Earlier work this paper cites.
Lars Hörmander, Hypoelliptic second order differential equations , Acta Math. 119
1967
Earlier work this paper cites.
Elliott H. Lieb, Convex trace functions and the Wigner-Yanase-Dyson conjecture , Advances in Math. 11
1973
Earlier work this paper cites.
Leonard Gross, Hypercontractivity and logarithmic Sobolev inequalities for the Clifford Dirichlet form , Duke Math. J. 42
1975
Earlier work this paper cites.
by same author, Logarithmic Sobolev inequalities , Amer. J. Math. 97
1975
Earlier work this paper cites.
Vittorio Gorini, Andrzej Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N N -level systems , J. Mathematical Phys. 17
1976
Earlier work this paper cites.
G. Lindblad, On the generators of quantum dynamical semigroups , Comm. Math. Phys. 48
1976
Earlier work this paper cites.
D. Bakry and Michel Émery, Diffusions hypercontractives , Séminaire de probabilités, XIX, 1983/84, Lecture Notes in Math., vol. 1123, Springer, Berlin, 1985, pp. 177–206. MR 889476 (88j:60131)
1985
Earlier work this paper cites.
O. S. Rothaus, Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities , J. Funct. Anal. 64
1985
Earlier work this paper cites.
Robert S. Strichartz, Sub-Riemannian geometry , J. Differential Geom. 24
1986
Earlier work this paper cites.
by same author, Corrections to: “Sub-Riemannian geometry” [J. Differential Geom. 24
1989
Earlier work this paper cites.
Persi Diaconis and Laurent Saloff-Coste, Logarithmic sobolev inequalities for finite markov chains , The Annals of Applied Probability 6
1996
Earlier work this paper cites.
Dénes Petz, Monotone metrics on matrix spaces , Linear algebra and its applications 244
1996
Earlier work this paper cites.
Robert Olkiewicz and Bogusław Zegarlinski, Hypercontractivity in noncommutative L p L_{p} spaces , J. Funct. Anal. 161
1999
Earlier work this paper cites.
Richard Montgomery, A tour of subriemannian geometries, their geodesics and applications , Mathematical Surveys and Monographs, vol. 91, American Mathematical Society, Providence, RI, 2002. MR 1867362 (2002m:53045)
2002
Earlier work this paper cites.
Michel Ledoux, Spectral gap, logarithmic sobolev constant, and geometric bounds , Surveys in differential geometry 9
2004
Earlier work this paper cites.
Bruce K. Driver and Tai Melcher, Hypoelliptic heat kernel inequalities on the Heisenberg group , J. Funct. Anal. 221
2005
Earlier work this paper cites.
Hong-Quan Li, Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de heisenberg , Journal of Functional Analysis 236
2006
Cited alongside, same era.
P. Ługiewicz and B. Zegarliński, Coercive inequalities for Hörmander type generators in infinite dimensions , J. Funct. Anal. 247
2007
Cited alongside, same era.
Raffaella Carbone and Emanuela Sasso, Hypercontractivity for a quantum Ornstein-Uhlenbeck semigroup , Probab. Theory Related Fields 140
2008
Cited alongside, same era.
Tai Melcher, Hypoelliptic heat kernel inequalities on Lie groups , Stochastic Process. Appl. 118
2008
Cited alongside, same era.
Nicholas T Varopoulos, Laurent Saloff-Coste, and Thierry Coulhon, Analysis and geometry on groups , vol. 100, Cambridge university press, 2008
2008
Cited alongside, same era.
Eric A Carlen and Jan Maas, Gradient flow and entropy inequalities for quantum markov semigroups with detailed balance , Journal of Functional Analysis 273
2017
Later among the works it cites.
Dariusz Chruściński and Saverio Pascazio, A brief history of the GKLS equation , Open Syst. Inf. Dyn. 24
2017
Later among the works it cites.
by same author, A convergence to Brownian motion on sub-Riemannian manifolds , Trans. Amer. Math. Soc. 369
2017
Later among the works it cites.
2018
Later among the works it cites.
Salman Beigi, Nilanjana Datta, and Cambyse Rouzé, Quantum reverse hypercontractivity: its tensorization and application to strong converses , Communications in Mathematical Physics 376
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Fabrice Baudoin and Michel Bonnefont, The subelliptic heat kernel on SU ( 2 ) {\rm SU}(2) : representations, asymptotics and gradient bounds , Math. Z. 263
2009
Cited alongside, same era.
Marius Junge, Eric Ricard, and Dimitri Shlyahktenko, Noncommutative diffusion semigroups and free probability , unpublished notes, 2013
2013
Cited alongside, same era.
Michael J. Kastoryano and Kristan Temme, Quantum logarithmic Sobolev inequalities and rapid mixing , J. Math. Phys. 54
2013
Cited alongside, same era.
Dominique Bakry, Ivan Gentil, and Michel Ledoux, Analysis and geometry of Markov diffusion operators , Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 348, Springer, Cham, 2014. MR 3155209
2014
Cited alongside, same era.
Fabrice Baudoin, Michel Bonnefont, and Nicola Garofalo, A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality , Math. Ann. 358
2014
Cited alongside, same era.
by same author, Hypercontractivity, logarithmic sobolev inequalities, and applications: a survey of surveys , Diffusion, quantum theory, and radically elementary mathematics 47
2014
Cited alongside, same era.
Christopher King, Hypercontractivity for semigroups of unital qubit channels , Communications in Mathematical Physics 328
2014
Cited alongside, same era.
2020
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2020
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by same author, Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems , Journal of Statistical Physics 178
2020
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Nilanjana Datta and Cambyse Rouzé, Relating relative entropy, optimal transport and fisher information: A quantum hwi inequality , Annales Henri Poincaré, Springer, 2020, pp. 1–36
2020
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Li Gao, Marius Junge, and Nicholas LaRacuente, Fisher information and logarithmic Sobolev inequality for matrix-valued functions , Annales Henri Poincaré, vol. 21, Springer, 2020, pp. 3409–3478
2020
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2020
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Melchior Wirth and Haonan Zhang, Complete gradient estimates of quantum markov semigroups , arXiv preprint, 2020
2020
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2021
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Michael Brannan, Li Gao, and Marius Junge, Complete logarithmic sobolev inequality via ricci curvature bounded below ii , Journal of Topology and Analysis (2021), 1–54
2021
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2021
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2021
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by same author, Complete logarithmic Sobolev inequalities via Ricci curvature bounded below , Adv. Math. 394
2022
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