• DOI:10.1103/PhysRevLett.114.110402
• Corpus ID: 6298011

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

@article{Dean2014FinitetemperatureFF,
  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},
  year={2014},
  volume={114 11},
  pages={
          110402
        }
}

• D. Dean, P. Le Doussal, +1 author G. Schehr
• Published 4 December 2014
• Physics
• Physical review letters

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 the edge of the support, at x∼±√[2ℏN/(mω)], are described by a limiting kernel K(b)(ff)(s,s') that depends continuously on b and is a generalization of the Airy kernel, found in the Gaussian unitary ensemble of random matrices. Remarkably, exactly the same kernel K(b)(ff)(s,s') arises in the exact solution of the Kardar-Parisi-Zhang equation in 1+1 dimensions at finite time t, with the correspondence t=b(3).