An analytic continuation via contour integrals gives the emptiness instanton and emptiness formation probability for all polytropic indices gamma > 1 in a 1D quantum gas.
Phase transitions in full counting statistics of free fermions and directed polymers
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abstract
We consider directed polymers in 1+1 spatial dimension under action of an external repulsive potential along a line. Using the exact mapping onto imaginary time evolution of free fermions we find that for sufficiently strong potential the system of polymers undergoes a continuous configurational phase transition. The transition corresponds to merging empty regions in the dominant limit shape.
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Emptiness Instanton in Quantum Polytropic Gas
An analytic continuation via contour integrals gives the emptiness instanton and emptiness formation probability for all polytropic indices gamma > 1 in a 1D quantum gas.