We calculate the large deviation functions characterizing the long-time
fluctuations of the occupation of drifted Brownian motion and show that these
functions have non-analytic points. This provides the first example of
dynamical phase transition that appears in a simple, homogeneous Markov process
without an additional low-noise, large-volume or hydrodynamic scaling limit.Comment: v1: 5 pages, 2 figures; v2: minor corrections, close to published
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