A. Duncan, M. Niedermaier
We reexamine the Parisi-Klauder conjecture for quantum mechanical \phi^4 theories with a Wick rotation angle 0 <= \theta/2 < \pi/2 interpolating between the Euclidean and the Lorentzian signature path integrals. The moments are shown to admit a transfer operator representation for all angles and all times t, with a non-selfadjoint propagation kernel whose spectral representation is governed by Davies' spectral norms. The moments also admit an asymptotic expansion around t=0 which is shown to be Borel summable. A simple argument is presented that the moments evaluated with the real measure simulated by the stochastic Langevin equation have the same t -> 0 asymptotic expansion. Our main result is that the agreement breaks down for t larger than a finite t_c. The real equilibrium distribution as t goes to infinity is computed explicitly and its moments are verified to differ from those obtained with the complex measure.
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http://arxiv.org/abs/1205.0307
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