Observation of fast sound in two-dimensional dusty plasma liquids

Equilibrium molecular dynamics simulations are performed to study two-dimensional (2D) dusty plasma liquids. Based on the stochastic thermal motion of simulated particles, the longitudinal and transverse phonon spectra are calculated, and used to determine the corresponding dispersion relations. From there, the longitudinal and transverse sound speeds of 2D dusty plasma liquids are obtained. It is discovered that, for wavenumbers beyond the hydrodynamic regime, the longitudinal sound speed of a 2D dusty plasma liquid exceeds its adiabatic value, i.e., the so-called fast sound. This phenomenon appears at roughly the same length scale of the cutoff wavenumber for transverse waves, confirming its relation to the emergent solidity of liquids in the nonhydrodynamic regime. Using the thermodynamic and transport coefficients extracted from the previous studies, and relying on the Frenkel theory, the ratio of the longitudinal to the adiabatic sound speeds is derived analytically, providing the optimal conditions for fast sound, which are in quantitative agreement with the current simulation results.

Figure 1

Longitudinal (a) and transverse (b) phonon spectra of the 2D dust plasma liquid for $\kappa =1$ and $\mathrm{\Gamma }/{\mathrm{\Gamma }}_m=0.95$, calculated from equilibrium MD simulations. Circle and triangular symbols on the phonon spectra correspond respectively to ${\omega }_0\left(k\right)$ and ${\omega }_0\left(k\right)\pm {\gamma }_0\left(k\right)$ as defined in the DHO model, Eq. (9).

Figure 2

Longitudinal (a) and transverse (b) dispersion relations of the 2D dusty plasma liquid with $\kappa =1$ and $\mathrm{\Gamma }/{\mathrm{\Gamma }}_m=0.95$, as extracted from the data in Fig. 1. The dashed line indicates the linear dispersion $\omega =v_{s}k$, where the value of the adiabatic sound speed $v_s$ is derived from the combination of the current conditions with the equation of state for 2D Yukawa liquids [91].

Figure 3

Longitudinal (a) and transverse (b) phonon spectra of the 2D dusty plasma liquid under $\kappa =2.5$ and $\mathrm{\Gamma }/{\mathrm{\Gamma }}_m=0.95$ calculated from equilibrium MD simulations.

Figure 4

Longitudinal (a) and transverse (b) dispersion relations of a 2D dusty plasma liquid under the conditions of $\kappa =1$ and $\mathrm{\Gamma }/{\mathrm{\Gamma }}_m=0.95$ extracted from the data in Fig. 3. The dashed line indicates the hydrodynamic dispersion $\omega =v_{s}k$, where $v_s$ is the adiabatic speed of sound.

Figure 5

Obtained longitudinal sound speed $v_L^{\prime }=\omega /k$ from the dispersion relation data points in Fig. 4, normalized by the adiabatic sound speed $v_s$, for the 2D dusty plasma liquid for $\kappa =2.5$ and $\mathrm{\Gamma }/{\mathrm{\Gamma }}_m=0.95$.

Figure 6

Theoretical derived ratio of the longitudinal sound speed $v_L^{\prime }$ to the adiabatic sound speed $v_s$ for 2D Yukawa liquids. The locations of the cross and the star symbols correspond to the parameters in Fig. 2 and Fig. 4, respectively.