Lieb-Robinson bounds for multi-commutators and applications to response theory

• 作者： Bru, J.-B., author.
• 其他作者：
  • Pedra, W. de Siqueira, author.
  • SpringerLink (Online service)
• 其他題名：
  • SpringerBriefs in mathematical physics ;
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： SpringerBriefs in mathematical physics,volume 13
• 主題： Quantum theory. , Physics. , Mathematical Methods in Physics. , Mathematical Physics. , Functional Analysis. , Condensed Matter Physics. , Quantum Information Technology, Spintronics.
• ISBN： 9783319457840 (electronic bk.) 、 9783319457833 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Introduction -- 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.
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• 摘要註: Lieb-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.
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