Finite-temperature free fermions and the Kardar-Parisi-Zhang equation at finite time.

  title={Finite-temperature free fermions and the Kardar-Parisi-Zhang equation at finite time.},
  author={D. Dean and Pierre Le Doussal and Satya N. Majumdar and Gr{\'e}gory Schehr},
  journal={Physical review letters},
  volume={114 11},
We consider the system of N one-dimensional free fermions confined by a harmonic well V(x)=mω(2)x(2)/2 at finite inverse temperature β=1/T. The average density of fermions ρ(N)(x,T) at position x is derived. For N≫1 and β∼O(1/N), ρ(N)(x,T) is given by a scaling function interpolating between a Gaussian at high temperature, for β≪1/N, and the Wigner semicircle law at low temperature, for β≫N(-1). In the latter regime, we unveil a scaling limit, for βℏω=bN(-1/3), where the fluctuations close to… 

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