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We describe the dimensional crossover in a noninteracting Fermi gas in ananisotropic trap, obtained by populating various transverse modes of the trap.We study the dynamical structure factor and drag force. Starting from adimension $d$, the $(\!d\!+\!1\!)$-dimensional case is obtained to a goodapproximation with relatively few modes. We show that the dynamical structurefactor of a gas in a $d$-dimensional harmonic trap simulates an effective$2d$-dimensional box trap. We focus then on the experimentally relevantsituation when only a portion of the gas in harmonic confinement is probed andgive a condition to obtain the behavior of a $d$-dimensional gas in a box.Finally, we propose a generalized Tomonaga-Luttinger model for the multimodeconfiguration and compare the dynamical structure factor in the 2D limit withthe exact result, finding that it is accurate in the backscattering region andat low energy.

Dimensional crossover in a Fermi gas from one to effective six dimensions and a cross-dimensional Tomonaga-Luttinger model