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Continuous Maassen kernels and the inverse oscillator

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1626)

Abstract

The quantum stochastic differential equation of the inverse oscillator in a heat bath of oscillators is solved by the means of a calculus of continuous and differentiable Maassen kernels. It is shown that the time development operator does not only map the Hilbert space of the problem into itself, but also vectors with finite moments into vectors with finite moments. The vacuum expectation of the occupancy numbers coincides for pyramidally ordered times with a classical Markovian birth process showing the avalanche character of the quantum process.

Keywords

  • Heat Bath
  • Rotate Wave Approximation
  • Heisenberg Equation
  • Real Physical System
  • Finite Moment

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Dedicated to P.A. Meyer to his 60th birthday

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© 1996 Springer-Verlag

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von Waldenfels, W. (1996). Continuous Maassen kernels and the inverse oscillator. In: Azéma, J., Yor, M., Emery, M. (eds) Séminaire de Probabilités XXX. Lecture Notes in Mathematics, vol 1626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094646

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  • DOI: https://doi.org/10.1007/BFb0094646

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61336-7

  • Online ISBN: 978-3-540-68463-3

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