A Probabilistic Representation of the Ground State Expectation of Fractional Powers of the Boson Number Operator

Details A Probabilistic Representation of the Ground State Expectation of Fractional Powers of the Boson Number Operator A Probabilistic Representation of the Ground State Expectation of Fractional Powers of the Boson Number Operator

2011-05-10

arxiv.org/abs/1105.1850v1

Physics

Mathematical Physics

Scientific paper

We give a formula in terms of a joint Gibbs measure on Brownian paths and the
measure of a random-time Poisson process of the ground state expectations of
fractional (in fact, any real) powers of the boson number operator in the
Nelson model. We use this representation to obtain tight two-sided bounds. As
applications, we discuss the polaron and translation invariant Nelson models.

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