Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas

Abstract

We 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 and provide vital tools to study 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.

10+ pages, appendix with some technical details is added

References in corpus (4)

• Temperature Correlations of Quantum Spins
• Fermi-Edge Resonance and Tunneling in Nonequilibrium Electron Gas
• Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas
• Correlations in the impenetrable electron gas

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• Quantum Shock Waves and Population Inversion in Collisions of Ultracold Atomic Clouds
• Quantum quench and thermalization of one-dimensional Fermi gas via phase space hydrodynamics
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• The Whitham approach to Generalized Hydrodynamics
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• Mobile impurity approach to the optical conductivity in the Hubbard chain
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• Nonlinear Luttinger liquid: Exact result for the Green function in terms of the fourth Painlevé transcendent
• Fermi Edge Resonances in Non-equilibrium States of Fermi Gases
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• Quantum Generalized Hydrodynamics of the Tonks-Girardeau gas: density fluctuations and entanglement entropy
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• Quantum fluctuating theory for one-dimensional shock waves