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arXiv · 1511.03989

Local energy and power for many-particle quantum systems driven by an external electrical field

Guillermo Albareda·Fabio Lorenzo Traversa·Xavier Oriols
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Abstract

We derive expressions for the expectation values of the local energy and the local power transferred by an external electrical field to a many-particle system of interacting spinless electrons. In analogy with the definition of the (local) presence and current probability densities, we construct a local energy operator such that the time-rate of change of its expectation value provides information on the spatial distribution of power. Results are presented as functions of an arbitrarily small volume $Ω$, and physical insights are discussed by means of the quantum hydrodynamical representation of the wavefunction, which is proven to allow for a clear-cut separation into contributions with and without classical correspondence. Quantum features of the local power are mainly manifested through the presence of non-local sources/sinks of power and through the action of forces with no classical counterpart. Many-particle classical-like effects arise in the form of current-force correlations and through the inflow/outflow of energy across the boundaries of the volume $Ω$. Interestingly, such intriguing features are only reflected in the expression for the local power when the volume $Ω$ is finite. Otherwise, for closed systems with $Ω\to \infty$, we recover a classical-like single-particle expression.

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Guillermo Albareda, Fabio Lorenzo Traversa, Xavier Oriols. 2016-01-25. Local energy and power for many-particle quantum systems driven by an external electrical field. https://doi.org/10.1088/1742-5468%2F2016%2F05%2F054026

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