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Continuum Mechanics for Quantum Many-Body Systems: The Linear Response Regime by Gao, Xianlong; Tao, Jianmin; Vignale, G.; Tokatly, I. V. is a scholarly article available to read on EtoBox.

What is Continuum Mechanics for Quantum Many-Body Systems: The Linear Response Regime about?

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 form

Author

Gao, Xianlong; Tao, Jianmin; Vignale, G.; Tokatly, I. V.

Published

2010

Language

EN