Anomalous Phonon Dispersion Research Articles

Anomalous Phonon Dispersion of an Ultracold $$^6\mathrm{{Li}}$$ 6 Li – $$^{40}\mathrm{{K}}$$ 40 K Mixture in a Square Optical Lattice

A necessary condition for the damping of the long-wavelength excitations of the superfluid phase (referred to as superfluid phonons) due to the three-particle process is to have an anomalous phonon dispersion. The existence of anomalous phonon dispersion has been confirmed in superfluid \(^4\mathrm {He}\). There are no experimental data suggesting that this phenomenon exists in superfluid Fermi gases. To the best of our knowledge, the existence of anomalous dispersion has been theoretically predicted only in atomic spin balanced Fermi gas close to the unitarity limit. The numerical results reported here suggest that the anomalous long-wavelength dispersion can be realized in mass and spin imbalanced atomic Fermi gases away from the unitary limit. In particular, the numerical solution of the Bethe–Salpeter equation in a weak-coupling regime shows that the long-wavelength part of the collective-mode dispersion of the superfluid Fulde–Ferrell phase of a mixture of population-imbalanced Lithium-6 and Potassium-40 atoms in a square lattice at some values of polarization, interacting strength and temperature initially bends upward before bending over.

Angular distribution of phonons from a planar heater in superfluidHe4: Pressure and power dependence

We have measured the angular distribution of phonons propagating in liquid $^{4}\mathrm{He}$ which are created by a planar heater. The angular distribution varies considerably with pressure in the range $0--20\phantom{\rule{0.3em}{0ex}}\text{bars}$. At small angles to the heater normal, the angular distribution shows a mesa shape at $P=0$. At $6<P<12\phantom{\rule{0.3em}{0ex}}\text{bars}$ a large cusplike peak replaces the mesa shape and the peak gradually disappears at higher pressures. At larger angles to the heater normal, the signal is very small at $P=0$ and grows slowly until $P\ensuremath{\sim}15\phantom{\rule{0.3em}{0ex}}\text{bars}$ when it grows rapidly. At $P>19\phantom{\rule{0.3em}{0ex}}\text{bars}$ the overall angular distribution is cosinelike. The behavior is explained in terms of phonon interactions amongst the injected phonons, that take place in the liquid helium when there is anomalous phonon dispersion. The interactions change the energy of the phonons and this is detected by the phonon-energy sensitive bolometer. Modeling of the results indicates that at small angles to the heater normal, there is thermalization of the low energy phonons and the creation of high energy phonons, which decreases in the range $7.5<P<15\phantom{\rule{0.3em}{0ex}}\text{bars}$. At larger angles to the heater normal, $>20\ifmmode^\circ\else\textdegree\fi{}$, phonons with energy below the pressure-dependent critical energy only spontaneously decay. We find that the injected phonon spectrum can be approximately characterized by a Bose-Einstein spectrum with a temperature $\ensuremath{\sim}0.6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which is nearly independent of heater power.

Anyon superfluidity in the framework of nonrelativistic-current algebra.

Anyon superfluidity is studied by using nonrelativistic currents and densities as coordinates. The excitation spectrum, obtained by solving the equation of motion of a suitably constructed excitation operator, reveals the importance of vortex-type excitations and predicts an anomalous phonon dispersion in the long-wavelength limit.

Liquid helium at negative pressures: Nucleation of bubbles and anomalous phonon dispersion

We calculate the rate at which bubbles nucleate in4He when the liquid is at negative pressure. Previous calculations have predicted that at low temperatures (T≤0.3 K) the nucleation rate remains low until a pressure of roughly −15 bar is reached. We show that this result is incorrect, and that at a critical pressure Pc (≃−9 bar) the liquid becomes macroscopically unstable. We have made a calculation of the nucleation rate allowing for this effect. It is shown that the effect of quantum nucleation is small and probably hard to observe experimentally. Finally, we demonstrate that one can understand the pressure dependence of the phonon dispersion relation by a simple model. This model uses a parameter which also enters into the nucleation calculation.

Covalent and metallic bonding within the quasi-ion approach.

A recently proposed theory of a quasi-ion description of solids is used to discuss simultaneously the dynamics of bonding and its relation to the phonon dispersion in crystals. The theory can be applied in principle to all types of bonding and allows a rigorous separation into ``two-center'' forces and proper many-body interactions. Applications for this separation are provided with respect to the metallic and covalent bonding type. In particular it is shown, using Si as an example, how angular rigidity of the covalent bond can be described by relative rotations of the quasi ions. In case of metallic bonding, special many-body effects leading to an anomalous phonon dispersion are investigated within a simple model.

Specific heat and phonon dispersion of liquidHe4

The specific heat of liquid $^{4}\mathrm{He}$ was measured with high precision in the temperature range from 65 to 850 mK and at sixteen molar volumes corresponding to the pressure range from vapor pressure to 25 bars. Several different analyses performed on these data yield quantitative information concerning the magnitude of the anomalous phonon dispersion as a function of pressure. The findings are generally in good agreement with the results indirectly derived from sound-propagation measurements. The specific heat data also provide precise values of the roton parameters as a function of pressure. There is an unexplained discrepancy between these values and those resulting from neutron scattering measurements.

Elastic constants and Debye temperature of bccHe3

Measurements of the longitudinal, the fast-transverse, and the slow-transverse sound velocities have been made in single crystals of bcc $^{3}\mathrm{He}$ at 24.45 ${\mathrm{cm}}^{3}$/mole and at 0.4 K. The quality and orientation of the crystals were determined using x rays. The reduced elastic constants, in units of ${10}^{9}$ ${\mathrm{cm}}^{2}$/${\mathrm{sec}}^{2}$, $\frac{{C}_{11}}{\ensuremath{\rho}}=1.634\ifmmode\pm\else\textpm\fi{}0.020$, $\frac{{C}_{12}}{\ensuremath{\rho}}=1.356\ifmmode\pm\else\textpm\fi{}0.033$, and $\frac{{C}_{44}}{\ensuremath{\rho}}=0.753\ifmmode\pm\else\textpm\fi{}0.010$ resulted from a least-squares fitting of the data. These constants yield a compressibility which is in agreement with the results of thermodynamic measurements and a Debye temperature which is consistent with ${\ensuremath{\Theta}}_{D}^{max}$, the maximum value of the temperature-dependent calorimetric Debye temperature. Existing sound-velocity data at 21.66 ${\mathrm{cm}}^{3}$/mole were reanalyzed with the results, in units of ${10}^{9}$ ${\mathrm{cm}}^{2}$/${\mathrm{sec}}^{2}$: $\frac{{C}_{11}}{\ensuremath{\rho}}=2.727\ifmmode\pm\else\textpm\fi{}0.033$, $\frac{{C}_{12}}{\ensuremath{\rho}}=2.477\ifmmode\pm\else\textpm\fi{}0.058$, and $\frac{{C}_{44}}{\ensuremath{\rho}}=1.422\ifmmode\pm\else\textpm\fi{}0.021$. These constants also yield a compressibility in agreement with thermodynamic measurements. Only ${C}_{12}$ is significantly different (4%) from the constants previously reported. As an important consequence, however, $\frac{({C}_{11}\ensuremath{-}{C}_{12})}{2\ensuremath{\rho}}$, the modulus corresponding to the slow-transverse velocity in the $〈110〉$ direction, is considerably larger. The Debye temperature calculated using these constants is not inconsistent with ${\ensuremath{\Theta}}_{D}^{max}$. This result is contrary to that previously reported. At neither density is there evidence to suggest that any of the anomalous specific heat must be due to an anomalous phonon dispersion.

Numerical Solution of the Transport Equation for Sound Propagation in He II

Assuming an anomalous phonon dispersion, the velocity shift and the attenuation of ultrasound in liquid ${\mathrm{He}}^{4}$ below 0.5 K are calculated by a direct numerical solution of the Boltzmann equation for the phonon distribution function. In order to account for the hydrodynamic regime the collision invariants are treated separately. The results are in qualitative agreement with the experiments and show a nonmonotonic increase of the velocity shift as a function of the applied frequency, but they are different from an approximate solution using relaxation times. The method developed to solve the Boltzmann equation can also be applied directly to calculate transport properties of phonons in solids.