03463nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153072001500165072002300180072001400203245014500217250001800362264006900380300006200449336002600511337002600537338003600563347002400599490005800623505061600681520081601297650001702113650002702130650003502157650002902192650002002221650001702241650001402258650004702272650002902319700007202348700008102420700007802501700008202579710003402661773002602695776003602721776003602757776003602793830005802829856004602887978-3-031-50466-2DE-He21320251030113054.0cr nn 008mamaa240919s2024    sz |    s    |||| 0|eng d  a97830315046627 a10.1007/978-3-031-50466-22doi 4aQA1-939 7aPB2bicssc 7aMAT0000002bisacsh 7aPB2thema10aOptimal Transport on Quantum Structuresh[electronic resource] /cedited by Jan Maas, Simone Rademacher, Tamás Titkos, Dániel Virosztek.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aIX, 321 p. 8 illus., 2 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aBolyai Society Mathematical Studies,x2947-9460 ;v290 aPreface -- Chapter 1. An Introduction to Optimal Transport and Wasserstein Gradient Flows by Alessio Figalli -- Chapter 2. Dynamics and Quantum Optimal Transport:Three Lectures on Quantum Entropy and Quantum Markov Semigroups by Eric A. Carlen -- Chapter 3. Quantum Couplings and Many-body Problems by Francois Golse -- Chapter 4. Quantum Channels and Qubits by Giacomo De Palma and Dario Trevisan -- Chapter 5. Entropic Regularised Optimal Transport in a Noncommutative Setting by Lorenzo Portinale -- Chapter 6. Logarithmic Sobolev Inequalities for Finite Dimensional Quantum Markov Chains by Cambyse Rouzé.  aThe flourishing theory of classical optimal transport concerns mass transportation at minimal cost. This book introduces the reader to optimal transport on quantum structures, i.e., optimal transportation between quantum states and related non-commutative concepts of mass transportation. It contains lecture notes on classical optimal transport and Wasserstein gradient flows dynamics and quantum optimal transport quantum couplings and many-body problems quantum channels and qubits These notes are based on lectures given by the authors at the "Optimal Transport on Quantum Structures" School held at the Erdös Center in Budapest in the fall of 2022. The lecture notes are complemented by two survey chapters presenting the state of the art in different research areas of non-commutative optimal transport. 0aMathematics. 0aMathematical analysis. 0aGlobal analysis (Mathematics). 0aManifolds (Mathematics). 0aMeasure theory.14aMathematics.24aAnalysis.24aGlobal Analysis and Analysis on Manifolds.24aMeasure and Integration.1 aMaas, Jan.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt1 aRademacher, Simone.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt1 aTitkos, Tamás.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt1 aVirosztek, Dániel.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303150465508iPrinted edition:z978303150467908iPrinted edition:z9783031504686 0aBolyai Society Mathematical Studies,x2947-9460 ;v2940uhttps://doi.org/10.1007/978-3-031-50466-2