Critical behavior of the free surface of liquid 4He near the λ point

Wong, V. K.

doi:10.1007/bf00116990

J Low Temp Phys

1979

DOI: 10.1007/bf00116990

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Critical behavior of the free surface of liquid 4He near the λ point

V. K. Wong

Abstract: The noncriticality of the free surface of liquid 4He near the h point and the finite-size scaling postulate are combined to show that the surface tension can have two singularities, one due to rounding and another due to shifting. The rounding singularity can be reduced, via a further scaling assumption, to that previously suggested by Sobvanin and Hohenberg. Results from calculations based on continuous symmetry models and experiments on topologically 2D 4He films are used to argue that the shift singularity … Show more

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1983

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Relation between the condensate fraction and the surface tension of superfluidHe4

Campbell¹

1983

Phys. Rev. B

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The variation of the superfluid order parameter at the liquid surface contributes to the surface tension in proportion to the condensate density. This yields a prediction of the condensate fraction as a function of temperature when proper account is taken of the temperature dependence of the normal components of the surface tension, the largest of which is due to surface modes of vibration. Good agreement is obtained with recent values of the condensate fraction from neutron and x-ray scattering measurements.where m is the mass of a 4He atom, distances are in units of g, and @ = P/ Jpp. The surface energy o. , associated with Eq. (1) for a half space, where~P~1in the interior and $ = 0 on the planar boundary, is known to be'By now it is established that a fundamental characterization of superfluidity is the breaking of a gauge symmetry for temperatures T ( T&. ' In the case of superfluid 4He (and superconductors) this occurs through the appearance of a complex scalar order parameter P which, for He, is identified with the macroscopic occupation of a single-particle state, so that~P~' is the density of particles po in the so-called condensate state. A very general description of such systems is provided by gauge theory plus the Higgs mechanism for broken symmetry. '~T he simplest Higgs potential gives rise to the well-known o (and formally equivalent) Ginzburg-Landau and GrossPitaevskii (GP) 9'o equations, whose predictions, for instance, of quantized vorticity' are completely verified in the superconducting and superfluid states.Because a first-principles derivation of the GP equation does not exist for 4He, we justify its use here on the basis of its general origin from gauge symmetry as outlined above. The associated Higgs energy then contributes an additional term at the boundary of superfluid regions that is proportional to the condensate fraction no = po/p, where p is the total density. As shown below, this permits no to be evaluated in terms of the experimental surface tension o. " the superfluid coherence length g, and theoretical estimates of the nonsuperfluid contribution to the temperature dependence of a, (T) between T=0 and T = T".The physical state of interest here is static and has a fixed gauge so it is sufficient to employ the Higgs energy with only the scalar field:This is the superfluid component of the surface energy, i.e. , the component due to variation of the order parameter at the boundary. In addition, there remains the nonsuperfluid component 0-", so Oe =~s +~nŨ sing o,(T&) =0, Eqs. (2) and (3) imply no(T) = -i~,(T) -o, (Tg) 3 m g(T) 2 )r p +o.(T~) -o.(T)] . (4)Therefore, if f(T) and o"(Tq) -a"(T) are known, the condensate fraction can be found from measurements of the surface energy.

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Relation between the condensate fraction and the surface tension of superfluidHe4

Campbell¹

1983

Phys. Rev. B

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Critical behavior of the free surface of liquid 4He near the λ point

Cited by 1 publication

References 18 publications

Relation between the condensate fraction and the surface tension of superfluidHe4

Relation between the condensate fraction and the surface tension of superfluidHe4

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