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Title: Dynamical error bounds for continuum discretisation via Gauss quadrature rules—A Lieb-Robinson bound approach

Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive error bounds on expectation values of system observables that have been time evolved under such discretised Hamiltonians. These bounds take on the form of a function of time and the number of discrete modes, where the discrete modes are chosen according to Gauss quadrature rules. The derivation makes use of tools from the field of Lieb-Robinson bounds and the theory of orthonormal polynomials.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. University College of London, Department of Physics and Astronomy, London WC1E 6BT (United Kingdom)
  2. (Singapore)
  3. (Netherlands)
  4. Institute für Theoretische Physik, Universität Ulm, D-89069 Ulm (Germany)
Publication Date:
OSTI Identifier:
22479627
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 2; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; ERRORS; EXPECTATION VALUE; HAMILTONIANS; OSCILLATORS; POLYNOMIALS; QUADRATURES; QUANTUM SYSTEMS; TIME DEPENDENCE