TL;DR
This paper reviews linear response theory in quantum liquids, connecting statistical mechanics and electrostatics, and explores how response properties depend on trap frequency in atomic Bose gases.
Contribution
It provides a comprehensive review of linear response in quantum liquids, including Coulomb systems and atomic gases, highlighting new connections and general results.
Findings
Connection between response functions and dielectric properties in Coulomb systems
Dependence of atomic Bose gas response on trap frequency
Unified framework for various quantum liquid responses
Abstract
We review the linear response theory in the horizontal quantum liquids framework spanning from Coulomb liquids to Atomic gases. There are several well known references about this subject, like the onset of the Kramers-Kronig relations and the fluctuation-dissipation theorem. For the Coulomb systems we show the connection between the linear response function and the dielectric function which settles a parallelism between statistical mechanics and electrostatic properties. For (very degenerate, dilute, trapped, two dimensional) Atomic (Bose) gases we will prove, in full generality, how the response properties of the gas depend from the frequency of the harmonic trap.
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