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Title: Quantum field theory of classically unstable Hamiltonian dynamics

We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic deviation equation of Jacobi, constructed with a second covariant derivative, is unitarily equivalent to that of a parametric harmonic oscillator, and we study the second quantization of this oscillator. The excitations of the Fock space modes correspond to the emission and absorption of quanta into the dynamical medium, thus associating unstable behavior of the dynamical system with calculable fluctuations in an ensemble with possible thermodynamic consequences.
Authors:
 [1] ;  [2] ;  [3] ;  [2] ;  [2] ;  [3] ;  [4]
  1. Department of Mathematics, Ben-Gurion University of the Negev, Be’er Sheva 8410501 (Israel)
  2. (Israel)
  3. Department of Physics, Ariel University, Ariel 4070000 (Israel)
  4. Department of Electrical and Electronic Engineering, Ariel 4070000 (Israel)
Publication Date:
OSTI Identifier:
22479701
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 7; 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; GEODESICS; HAMILTONIANS; HARMONIC OSCILLATORS; MATHEMATICAL SPACE; OSCILLATORS; QUANTUM FIELD THEORY; SECOND QUANTIZATION