We analyze the macroscopic dynamics of a Bose gas axially confined in anoptical lattice with a superimposed harmonic trap, taking into account weaktunneling effect. Our results show that upon transition to thequasi-two-dimensional (2D) regime of the trapped gas, the 3D equation of stateand equilibrium density profile acquire corrections from 2D many-body effects.The corresponding frequency shift in the transverse breathing mode isaccessible within current facilities, suggesting a direct observation ofdimensional effects. Comparisons with other relevant effects are alsopresented.
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