Continuous Maassen kernels and the inverse oscillator
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.
KeywordsHeat Bath Rotate Wave Approximation Heisenberg Equation Real Physical System Finite Moment
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