Anisotropic Collective Excitations of Bose Gases in Modified Newtonian Dynamics

Abstract

Collective excitations are fundamental in quantum many-body physics, yet their spectra have traditionally been studied within Newtonian dynamics. In this Letter, 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.

Figures (3)

• Figure 1: Squared frequency $\tilde{\omega}^2$ versus angle $\theta$ for fixed wavenumbers $\tilde{k} = 0.5$ (dashed), $\tilde{k} = 1.0$ (dot-dashed), and $\tilde{k} = 1.5$ (solid), with $\chi = 1$ and $\eta = 0.1$.
• Figure 2: Contour plot of the squared frequency $\tilde{\omega}^2$ in the $\tilde{k}$-$\theta$ plane for $\chi = 1$, $\eta = 0.1$. The red dashed line indicates the stability boundary $\tilde{\omega}^2 = 0$, separating the stable (right) and unstable (left) regions.
• Figure 3: Polar plot of the normalized Jeans mass $\widetilde{M}_J(\theta)$. The radial coordinate is $\widetilde{M}_J(\theta)$; the dashed circle indicates the isotropic Newtonian limit (normalized to $1$). Parameters are the same as in Fig. \ref{['fig:omega_theta']}.