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
        }
}
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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References

SHOWING 1-10 OF 25 REFERENCES

Random Matrices

The elementary properties of random matrices are reviewed and widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles are discussed.

Log-Gases and Random Matrices (London

  • Mathematical Society monographs,
  • 2010

Random matrices and determinantal processes

We survey recent results on determinantal processes, random growth, random tilings and their relation to random matrix theory.

= 2 2/3 λ in terms of λ defined in

    Phys

    • Rev. A 85, 062104
    • 2012

    Phys

    • Rev. Lett. 112, 254101
    • 2014

    Promotion of Advanced Research under Project 4604-3 (SM and GS) and Labex-PALM

      We recall that, for a trace-class operator K(x, y) such that TrK = dxK(x, x) is well defined, det(I − K) = exp

        Comm

        • Pure and Appl. Math. 64, 466
        • 2011

        Phys

        • Lett. B 268, 21
        • 1991