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Title: Symmetry and conservation laws in semiclassical wave packet dynamics

We formulate symmetries in semiclassical Gaussian wave packet dynamics and find the corresponding conserved quantities, particularly the semiclassical angular momentum, via Noether’s theorem. We consider two slightly different formulations of Gaussian wave packet dynamics; one is based on earlier works of Heller and Hagedorn and the other based on the symplectic-geometric approach by Lubich and others. In either case, we reveal the symplectic and Hamiltonian nature of the dynamics and formulate natural symmetry group actions in the setting to derive the corresponding conserved quantities (momentum maps). The semiclassical angular momentum inherits the essential properties of the classical angular momentum as well as naturally corresponds to the quantum picture.
Authors:
 [1]
  1. Department of Mathematical Sciences, The University of Texas at Dallas, 800 W Campbell Rd., Richardson, Texas 75080-3021 (United States)
Publication Date:
OSTI Identifier:
22403118
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 3; Other Information: (c) 2015 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; ANGULAR MOMENTUM; CONSERVATION LAWS; HAMILTONIANS; SEMICLASSICAL APPROXIMATION; SYMMETRY GROUPS; WAVE PACKETS