Feynman formulas as a method of averaging random Hamiltonians



We propose a method for finding the mathematical expectation of random unbounded operators in a Hilbert space. The method is based on averaging random one-parameter semigroups by means of the Feynman-Chernoff formula. We also consider an application of this method to the description of various operations that assign quantum Hamiltonians to the classical Hamilton functions.


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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • Yu. N. Orlov
    • 1
  • V. Zh. Sakbaev
    • 2
  • O. G. Smolyanov
    • 3
  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia
  2. 2.Moscow Institute of Physics and Technology (State University)Dolgoprudnyi, Moscow oblastRussia
  3. 3.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

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