rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory
  name:
    name part: Bru, J.-B.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: de Siqueira Pedra, W.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2017
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VII, 109 p. online resource.
  abstract: 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.
  table of contents: 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.
  note: by J.-B. Bru, W. de Siqueira Pedra.
  subject:
    topic: Physics
  subject:
    topic: Functional analysis
  subject:
    topic: Mathematical physics
  subject:
    topic: Condensed matter
  subject:
    topic: Quantum computers
  subject:
    topic: Spintronics
  subject:
    topic: Physics
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Mathematical Physics
  subject:
    topic: Functional Analysis
  subject:
    topic: Condensed Matter Physics
  subject:
    topic: Quantum Information Technology, Spintronics
  classification: QC5.53
  classification: 530.15
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: SpringerBriefs in Mathematical Physics, 13
  identifier: 9783319457840
  identifier: http://dx.doi.org/10.1007/978-3-319-45784-0
  record info:
    record creation date: 161201
    record change date: 20161201113634.0
    record identifier: 978-3-319-45784-0