Eldad Bettelheim et al 2008 J. Phys. A: Math. Theor. 41 392003 doi:10.1088/1751-8113/41/39/392003
Eldad Bettelheim1, Alexander G Abanov2 and Paul B Wiegmann3
Show affiliationsWe present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain are integrable equations. They generalize known nonlinear differential equations for correlation functions at equilibrium [1–4] and provide vital tools for studying non-equilibrium dynamics of electronic systems. The method we developed is based only on Wick's theorem and the hydrodynamic description of the Fermi gas. Differential equations appear directly in bilinear form.
03.75.Ss Degenerate Fermi gases
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
15A15 Determinants, permanents, other special matrix functions (See also 19B10, 19B14)
34A34 Nonlinear equations and systems, general
15A63 Quadratic and bilinear forms, inner products [See mainly 11Exx]
Issue 39 (3 October 2008)
Received 26 June 2008, in final form 7 August 2008
Published 2 September 2008
Eldad Bettelheim et al 2008 J. Phys. A: Math. Theor. 41 392003
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