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Transition to Turbulence for a Quartz Tuning Fork in Superfluid 4He

“…There is much interest in the behaviour of vibrating objects immersed in the quantum fluids 3 He and 4 He. The recent expansion in activity has been largely inspired by developments in the study of turbulence, with several groups investigating oscillating wires [1][2][3][4][5][6][7][8][9][10][11][12], grids [13][14][15][16][17][18], spheres [19][20][21][22][23][24][25] and quartz tuning forks [26][27][28][29][30][31][32][33]. Mechanical probes give much information about the dynamics of superfluids and their excitations.…”

Pendulum in a Fermi Liquid

“…We show that the Fermi liquid acts like an elastic medium, which can increase the restoring force and thus lead to increased frequency of oscillation. We show that this effect is important in explaining oscillator experiments made in liquid mixtures of 3 He and 4 He [4,5]. Moreover, this fermion-boson mixture allows a deep insight into the Fermi-liquid theory.…”

“…Here ρ is the liquid density and G−1 = O(a/b) 2 is a small correction caused by a finite chamber dimension b. In the experimental case [4] Z ideal /an F p F = −0.50. With increasing the viscosity of the liquid becomes important.…”

“…We also use the Fermi-liquid theory adapted to the simultaneous presence of bosonic superfluid, as formulated by Khalatnikov [19]. Besides being applicable to mixtures of 3 He and 4 He, this has the advantage that some basic properties of the Fermi-liquid theory are more easily visible [20]. A noninteracting Fermi system has plane-wave states with momenta p and energy p = p 2 /2m where m is the mass of a fermion.…”

“…The Landau force leads to increased effective mass of any objects, including ions [21], aerogel [22] and deformations of the surface of the liquid [23], which effect has not been explored yet. The case of negative F 0 is realized in mixtures of 3 He and 4 He. Below we calculate in detail the case of a circular cylinder oscillating transverse to its axis.…”