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تسجيل مستخدم جديدEntanglement area law in superfluid $^4$He
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Area laws were first discovered by Bekenstein and Hawking, who found that the entropy of a black hole grows proportional to its surface area, and not its volume. Entropy area laws have since become a fundamental part of modern physics, from the holographic principle in quantum gravity to ground state wavefunctions of quantum matter, where entanglement entropy is generically found to obey area law scaling. As no experiments are currently capable of directly probing the entanglement area law in naturally occurring many-body systems, evidence of its existence is based on studies of simplified theories. Using new exact microscopic numerical simulations of superfluid $^4$He, we demonstrate for the first time an area law scaling of entanglement entropy in a real quantum liquid in three dimensions. We validate the fundamental principles underlying its physical origin, and present an entanglement equation of state showing how it depends on the density of the superfluid.
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We calculate the effect of a heat current on transporting $^3$He dissolved in superfluid $^4$He at ultralow concentration, as will be utilized in a proposed experimental search for the electric dipole moment of the neutron (nEDM). In this experiment,
a phonon wind will generated to drive (partly depolarized) $^3$He down a long pipe. In the regime of $^3$He concentrations $tilde < 10^{-9}$ and temperatures $sim 0.5$ K, the phonons comprising the heat current are kept in a flowing local equilibrium by small angle phonon-phonon scattering, while they transfer momentum to the walls via the $^4$He first viscosity. On the other hand, the phonon wind drives the $^3$He out of local equilibrium via phonon-$^3$He scattering. For temperatures below $0.5$ K, both the phonon and $^3$He mean free paths can reach the centimeter scale, and we calculate the effects on the transport coefficients. We derive the relevant transport coefficients, the phonon thermal conductivity and the $^3$He diffusion constants from the Boltzmann equation. We calculate the effect of scattering from the walls of the pipe and show that it may be characterized by the average distance from points inside the pipe to the walls. The temporal evolution of the spatial distribution of the $^3$He atoms is determined by the time dependent $^3$He diffusion equation, which describes the competition between advection by the phonon wind and $^3$He diffusion. As a consequence of the thermal diffusivity being small compared with the $^3$He diffusivity, the scale height of the final $^3$He distribution is much smaller than that of the temperature gradient. We present exact solutions of the time dependent temperature and $^3$He distributions in terms of a complete set of normal modes.
We conducted series of experiments on observing a Stark-type effect in superfluid $^4$He in presence of relative laminar flows of the normal and superfluid components. It is designed a measurement cell which allows us to simultaneously create hydrody
namic flows in the liquid and to carry out high-frequency radio-measurements at external electric field. We used a dielectric disk resonator that made possible to cover a wide frequency range. In our experiments it was registered the spectrum of the dielectric disk resonator modes, as well as narrow lines of absorption of a microwave radiation in He II on its background and in different conditions. We discovered that having in the liquid helium a relative motion of the normal and superfluid fractions in the temperature range of 1.4$div$2.17 K the narrow line of absorption/radiation is observed in the EM spectrum, the frequency of which - 180 GHz - corresponds to the roton minimum. This line splits in a constant electric field. Note that in a weak electric field the value of splitting depends linearly on the electric field strength, i.e. the linear Stark effect is detected. It is found that with the external electric field increasing both split lines are displaced towards more low frequencies side. The obtained data set could be described by an empirical formula, taking into account as the linear part of the Stark effect, as well as a quadratic addition, related to the polarization part. The data point out on having particles or excitations in the liquid helium with the dipole moment $sim 10^{-4}$ D, that in four order less of the characteristic dipole moment of polar molecules. The comparison of our findings to values of the electric dipole moment (EDM) of elementary particles and nuclei is also performed. We sum up with brief discussion of extensions of the known theoretical models and possible mechanisms of the EDM production.
We study numerically nonuniform quantum turbulence of coflow in a square channel by the vortex filament model. Coflow means that superfluid velocity $bm{v}_s$ and normal fluid velocity $bm{v}_n$ flow in the same direction. Quantum turbulence for ther
mal counterflow has been long studied theoretically and experimentally. In recent years, experiments of coflow are performed to observe different features from thermal counterflow. By supposing that $bm{v}_s$ is uniform and $bm{v}_n$ takes the Hagen-Poiseiulle profile, our simulation finds that quantized vortices are distributed inhomogeneously. Vortices like to accumulate on the surface of a cylinder with $bm{v}_s simeq bm{v}_n$. Consequently, the vortex configuration becomes degenerate from three-dimensional to two-dimensional.
Motivated by a proposed experimental search for the electric dipole moment of the neutron (nEDM) utilizing neutron-$^3$He capture in a dilute solution of $^3$He in superfluid $^4 $He, we derive the transport properties of dilute solutions in the regi
me where the $^3$He are classically distributed and rapid $^3$He-$^3$He scatterings keep the $^3$He in equilibrium. Our microscopic framework takes into account phonon-phonon, phonon-$^3$He, and $^3$He-$^3$He scatterings. We then apply these calculations to measurements by Rosenbaum et al. [J.Low Temp.Phys. {bf 16}, 131 (1974)] and by Lamoreaux et al. [Europhys.Lett. {bf 58}, 718 (2002)] of dilute solutions in the presence of a heat flow. We find satisfactory agreement of theory with the data, serving to confirm our understanding of the microscopics of the helium in the future nEDM experiment.
We study the coupled dynamics of normal and superfluid components of the superfluid $^4$He in the channel considering the counterflow turbulence with laminar normal component. In particular, we calculated profiles of the normal velocity, the mutual f
riction, the vortex line density and other flow properties and compared them to the case when the dynamic of the normal component is frozen. We have found that the coupling between the normal and superfluid components leads to flattening of the normal velocity profile, increasingly more pronounced with temperature, as the mutual friction, and therefore coupling, becomes stronger. The commonly measured flow properties also change when the coupling between two components is taken into account.
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