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101 0 $aeng
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181   $ctxt$2rdacontent
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200 10$aLinear response theory $ean analytic-algebraic approach /$fby Giuseppe De Nittis, Max Lein
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017.
215   $a1 online resource (X, 138 p.)
225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v21
311   $a3-319-56731-4 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- Setting, Hypotheses and Main Results -- Mathematical Framework -- A Unified Framework for Common Physical Systems -- Studying the Dynamics -- The Kubo Formula and its Adiabatic Limit -- Applications.
330   $aThis book presents a modern and systematic approach to Linear Response Theory (LRT) by combining analytic and algebraic ideas. LRT is a tool to study systems that are driven out of equilibrium by external perturbations. In particular the reader is provided with a new and robust tool to implement LRT for a wide array of systems. The proposed formalism in fact applies to periodic and random systems in the discrete and the continuum. After a short introduction describing the structure of the book, its aim and motivation, the basic elements of the theory are presented in chapter 2. The mathematical framework of the theory is outlined in chapters 3?5: the relevant von Neumann algebras, noncommutative $L^p$- and Sobolev spaces are introduced; their construction is then made explicit for common physical systems; the notion of isopectral perturbations and the associated dynamics are studied. Chapter 6 is dedicated to the main results, proofs of the Kubo and Kubo-Streda formulas. The book closes with a chapter about possible future developments and applications of the theory to periodic light conductors. The book addresses a wide audience of mathematical physicists, focusing on the conceptual aspects rather than technical details and making algebraic methods accessible to analysts.
410  0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v21
606   $aPhysics
606   $aMathematical physics
606   $aCondensed matter
606   $aFunctional analysis
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   $aCondensed Matter Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P25005
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
615  0$aPhysics.
615  0$aMathematical physics.
615  0$aCondensed matter.
615  0$aFunctional analysis.
615 14$aMathematical Methods in Physics.
615 24$aMathematical Physics.
615 24$aCondensed Matter Physics.
615 24$aFunctional Analysis.
676   $a512.5
700   $aDe Nittis$b Giuseppe$4aut$4http://id.loc.gov/vocabulary/relators/aut$0555451
702   $aLein$b Max$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
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906   $aBOOK
912   $a9910254572103321
996   $aLinear Response Theory$92182038
997   $aUNINA