Continuum Mechanics for Quantum Many-Body Systems: The Linear Response Regime

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 integro-differential 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.

23 pages, 4 figures, 1 table, 6 Appendices This paper is a follow-up to PRL 103, 086401 (2009)

References in corpus (4)

• Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction
• Non-adiabatic electron dynamics in time-dependent density-functional theory
• Time-dependent deformation functional theory
• Linear Continuum Mechanics for Quantum Many-Body Systems

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