Shohei Watabe, Yusuke Kato
The Landau's criterion for superfluids gives the critical velocity where superfluidity disappears at a large velocity. Actually, in the presence of impurities, the dissipation appears at smaller velocity, where solitons or quantized vortices are emitted dependently on the shape of an impurity potential barrier and the dimensionality of the system. This instability is categorized as the bifurcation. Therefore, in the present paper, we propose a universal stability criterion for superfluids that is applicable to Landau's instability and also to soliton or vortex emission instability. For that, we study the local density spectral function ${\mathcal I}_{n}({\bf r}, \omega)$ and the autocorrelation function $C_{n} ({\bf r},t)$ in uniform and inhomogeneous systems. According to results from the Bogoliubov theory and the Feynman's single-mode approximation beyond the mean-field theory, we find a universal feature in the local density spectral function and in the autocorrelation function. When superfluids flow below a threshold, we find in the $d$-dimensional system, ${\mathcal I}_{n}({\bf r}, \omega) \propto \omega^{d}$ holds in the low-energy regime and $C_{n} ({\bf r},t) \propto 1/t^{d+1}$ holds in the long-time regime. When superfluids flow with the critical current, on the other hand, we find ${\mathcal I}_{n}({\bf r}, \omega) \propto \omega^{\beta}$ in the low-energy regime and $C_{n} ({\bf r},t) \propto 1/t^{\beta+1}$ in the long-time regime with $\beta < d$.
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http://arxiv.org/abs/1305.6984
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