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• W1965857418 abstract "We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integrodifferential equation, whose only inputs are the one-particle density matrix and the pair-correlation function of the ground state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a Hermitian eigenvalue problem, which admits a complete set of orthonormal eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems." @default.
• W1965857418 created "2016-06-24" @default.
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• W1965857418 date "2010-05-07" @default.
• W1965857418 modified "2023-10-16" @default.
• W1965857418 title "Continuum mechanics for quantum many-body systems: Linear response regime" @default.
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• W1965857418 doi "https://doi.org/10.1103/physrevb.81.195106" @default.
• W1965857418 hasPublicationYear "2010" @default.
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