4.4 Article

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

Journal

JOURNAL OF MATHEMATICAL PHYSICS
Volume 57, Issue 2, Pages -

Publisher

AMER INST PHYSICS
DOI: 10.1063/1.4940436

Keywords

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Funding

  1. MOE Tier 3A [MOE2012-T3-1]
  2. Alexander von Humboldt Professorship
  3. ERC grant BioQ
  4. EU projects PAPETS
  5. SIQS

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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. (C) 2016 AIP Publishing LLC.

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