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100   $a20161201d2017      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aLieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory /$fby J.-B. Bru, W. de Siqueira Pedra
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017.
215   $a1 online resource (VII, 109 p.) 
225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v13
311   $a3-319-45783-7 
311   $a3-319-45784-5 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- Algebraic Quantum Mechanics -- Algebraic Setting for Interacting Fermions on the Lattice -- Lieb?Robinson Bounds for Multi?Commutators -- Lieb?Robinson Bounds for Non?Autonomous Dynamics -- Applications to Conductivity Measures.
330   $aLieb-Robinson bounds for multi-commutators are effective mathematical tools to handle analytic aspects of infinite volume dynamics of non-relativistic quantum particles with short-range, possibly time-dependent interactions. In particular, the existence of fundamental solutions is shown for those (non-autonomous) C*-dynamical systems for which the usual conditions found in standard theories of (parabolic or hyperbolic) non-autonomous evolution equations are not given. In mathematical physics, bounds on multi-commutators of an order higher than two can be used to study linear and non-linear responses of interacting particles to external perturbations. These bounds are derived for lattice fermions, in view of applications to microscopic quantum theory of electrical conduction discussed in this book. All results also apply to quantum spin systems, with obvious modifications. In order to make the results accessible to a wide audience, in particular to students in mathematics with little Physics background, basics of Quantum Mechanics are presented, keeping in mind its algebraic formulation. The C*-algebraic setting for lattice fermions, as well as the celebrated Lieb-Robinson bounds for commutators, are explained in detail, for completeness.
410  0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v13
606   $aPhysics
606   $aMathematical physics
606   $aFunctional analysis
606   $aCondensed matter
606   $aQuantum computers
606   $aSpintronics
606   $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013
606   $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aCondensed Matter Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P25005
606   $aQuantum Information Technology, Spintronics$3https://scigraph.springernature.com/ontologies/product-market-codes/P31070
615  0$aPhysics.
615  0$aMathematical physics.
615  0$aFunctional analysis.
615  0$aCondensed matter.
615  0$aQuantum computers.
615  0$aSpintronics.
615 14$aMathematical Methods in Physics.
615 24$aMathematical Physics.
615 24$aFunctional Analysis.
615 24$aCondensed Matter Physics.
615 24$aQuantum Information Technology, Spintronics.
676   $a530.12
700   $aBru$b J.-B$4aut$4http://id.loc.gov/vocabulary/relators/aut$0950325
702   $ade Siqueira Pedra$b W$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910155320803321
996   $aLieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory$92148677
997   $aUNINA