Anisotropic collective excitations of Bose gases in modified Newtonian dynamics
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Abstract
Collective excitations are fundamental in quantum many-body physics, yet their spectra have traditionally been studied within Newtonian dynamics. In this paper, we investigate collective excitations in Bose gases under Modified Newtonian Dynamics (MOND). We derive an anisotropic excitation spectrum in the MOND regime. This anisotropy arises directly from the intrinsic nonlinear structure of the MOND Poisson equation, forming a distinctive signature of the modified gravitational response. We then analyze the Jeans instability, obtaining analytic expressions for the direction-dependent critical wavelength and mass. These results advance our understanding of collective behavior in quantum systems under modified dynamics and establish clear theoretical signatures for testing MOND-like effects in quantum simulators.