Second sound very near T?

Goldner, Lori S.; Mulders, N.; Ahlers, Guenter

doi:10.1007/bf00682285

Cited by 88 publications

(70 citation statements)

References 61 publications

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“…23) and α = −0.0115 are consistent with the hyperscaling relation α = 2−3ν. Measurements for films over a wide range of L support this expected scaling behaviour up to the neighbourhood of the specific-heat maximum.…”

Section: Figure 1 | the Confinement Cellsupporting

confidence: 75%

Coupling and proximity effects in the superfluid transition in 4He dots

et al. 2010

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The superfluid transition in 4 He is associated with the onset of an order parameter that is a macroscopic wavefunction. This is similar to the onset of superconductivity in metals and alloys. Yet, some of the hallmark phenomena that are associated with wavefunctions, and are evident in superconductors, have not been identified in 4 He. Here we report proximity effects on the specific heat and superfluid density of a thin 4 He film in equilibrium with an array of larger boxes of 4 He. Comparison with previous data also enables us, by scaling, to deduce an excess specific heat associated with a collective behaviour of weakly coupled boxes. These effects should be relevant to the understanding of experiments where helium has been studied when confined in packed powders, porous materials or other inhomogeneous confinements, where proximity and collective effects must be present but not readily quantifiable 1,2 . Our work also forms a point of comparison and contrast with the case of superconductors 3,4 , and is relevant to studies of Josephson effects in superfluids, coupling effects in arrays of Bose-condensed atoms 5,6 , and magnetic systems where, because of chemical composition, two separate but interacting ordering transitions take place 7,8 .In the case of superconductors, coupling and proximity effects have been well understood for many years. The large correlationlength amplitude ξ 0 makes coupling between two superconductors easy to achieve. Weak links with dimensions of the order of ξ 0 , which can be a metal, an insulator or another superconductor, enable measurements of the familiar Josephson effects (see for instance ref. 9). With 4 He these effects are much more difficult to achieve because ξ 0 is of the order of interatomic dimensions. Furthermore, weak links and coupling between two regions of 4 He cannot be achieved through any material other than 4 He. We can, however, take advantage of the growth of the correlation length with temperature T and critical exponent ν, ξ = ξ 0 |1 − T /T λ | −ν ≡ ξ 0 t −ν near the transition temperature T λ and construct apertures whereby analogous Josephson effects can be realized 10,11 .We are unaware of any theory that describes the effects on thermodynamic properties of a 'grain' or dot of helium due to a coupling to another dot through a weak link, or, for that matter, how this coupling is affected by the geometry or 'strength' of this link. This question arose while attempting to verify finite-size scaling for zero-dimensional crossover 12 . We had measured the heat capacity of helium in arrays of (1 µm) 3 and (2 µm) 3 boxes linked by channels of 1 µm × 1 µm × 0.019 µm and 2 µm × 2 µm × 0.010 µm respectively. These data did not scale anywhere in the critical region 13 . The lack of scaling is unexpected, because for both twoand one-dimensional crossover, at least for T > T λ , other data do scale 14 . More significantly, an analysis of the zero-dimensional data suggested that the smaller boxes had a higher heat capacity than expected 13 . This might result from ...

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Section: Figure 1 | the Confinement Cellsupporting

confidence: 75%

Coupling and proximity effects in the superfluid transition in 4He dots

et al. 2010

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“…All the curves dT U 2 ( ) observed at different pressures and temperatures in our studies look much the same. Similar saturation effects at high W were reported in [15,16]. A detailed discussion of the reasons for the saturation lies beyond the scope of the present paper, but one reason could be the attenuation of the propagating second sound wave by vortices in the bulk of the He II [17].…”

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confidence: 79%

Nonlinear and shock waves in superfluid He II

Kolmakov

Efimov

Ganshin

et al. 2006

Low Temperature Physics

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We review studies of the generation and propagation of nonlinear and shock sound waves in He II (the superfluid phase of 4 He), both under the saturated vapor pressure (SVP) and at elevated pressures. The evolution in shape of second and first sound waves excited by a pulsed heater has been investigated for increasing power W of the heat pulse. It has been found that, by increasing the pressure P from SVP up to 25 atm, the temperature T a , at which the nonlinearity coefficient a of second sound reverse its sign, is decreased from 1.88 to 1.58 K. Thus at all pressures there exists a wide temperature range below T l where a is negative, so that the temperature discontinuity (shock front) should be formed at the center of a propagating bipolar pulse of second sound. Numerical estimates show that, with rising pressure, the amplitude ratio of linear first and second sound waves generated by the heater at small W should increase significantly. This effect has allowed us to observe at P = 13 3. atm a linear wave of heating (rarefaction) in first sound, and its transformation to a shock wave of cooling (compression). Measurements made at high W for pressures above and below the critical pressure in He II, P cr = 22 . atm, suggest that the main reason for initiation of the first sound compression wave is strong thermal expansion of a layer of He I (the normal phase) created at the heater-He II interface when W exceeds a critical value. Experiments with nonlinear second sound waves in a high-quality resonator show that, when the driving amplitude of the second sound is sufficiently high, multiple harmonics of second sound waves are generated over a wide range of frequencies due to nonlinearity. At sufficiently high frequencies the nonlinear transfer of the wave energy to sequentially higher wave numbers is terminated by the viscous damping of the waves.

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“…The purity of liquid helium together with the stability of temperature control and the accuracy of specific-heat measurements at low temperatures means that the limiting factor in approaching the critical singularities is the rounding due to the Earth's gravitational field. 2 To overcome gravitational rounding, space-based microgravity experiments have been devised 3 that achieve foursignificant-digit accuracy for the specific-heat exponent ␣. These experimental results seemingly do not agree with either analytical or numerical calculations.…”

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confidence: 99%

High-precision measurement of the thermal exponent for the three-dimensionalXYuniversality class

et al. 2006

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Simulation results are reported for the critical point of the two-component 4 field theory. The correlationlength exponent is measured to high precision with the result = 0.6717͑3͒. This value is in agreement with recent simulation results ͓Campostrini et al., Phys. Rev. B 63, 214503 ͑2001͔͒ and marginally agrees with the most recent space-based measurements of the superfluid transition in 4 Universality at critical points is among the most beautiful and powerful ideas to emerge from statistical physics. 1 The unversality hypothesis asserts that critical exponents and some other asymptotic properties of critical points are independent of microscopic details and depend on only a few properties such as the symmetry of the order parameter and spatial dimensionality. Universality permits the calculation of critical exponents for experimental systems using simplified and optimized model systems with the same symmetries. The theory of critical phenomena also predicts relationships among critical exponents. Among these relations are the hyperscaling relation ␣ =2−d between the specific-heat exponent ␣, the correlation-length exponent , and the dimensionality d and the Josephson relation = ͑d −2͒ for the superfluid-stiffness exponent . Improvements in experiments, theory, and computer simulations have led to increasingly strict tests of universality and scaling relations. By far the most accurate experimental measurements of critical exponents are for the superfluid transition in 4 He, which is in the O͑2͒ or XY universality class. The purity of liquid helium together with the stability of temperature control and the accuracy of specific-heat measurements at low temperatures means that the limiting factor in approaching the critical singularities is the rounding due to the Earth's gravitational field. 2 To overcome gravitational rounding, space-based microgravity experiments have been devised 3 that achieve foursignificant-digit accuracy for the specific-heat exponent ␣. These experimental results seemingly do not agree with either analytical or numerical calculations. The experimental value itself has evolved with time due to the reanalysis of the data ͑see Refs. 3-5͒, the most recent reported value being exp = 0.6709͑1͒, as inferred from the measured value of ␣ via the hyperscaling relation.A number of recent analytical and numerical calculations were aimed at high-precision determinations of for the XY universality class. The vortex-loop calculations by Williams 6 yield = 0.6717. Török and Hasenbusch 8 studied the twocomponent 4 model via Monte Carlo simulations. This model has a parameter that adjusts the softness of the potential-constraining-amplitude fluctuations of the order parameter. These authors took advantage of this freedom to suppress the leading corrections to scaling. This study resulted in = 0.6723͑3͒͑8͒ ͑the statistical and systematic errors are given in the first and second parentheses, respectively͒. Later the effort was advanced by Campostrini et al. 7 who combined Monte Carlo simulations with a...

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Second sound very near T?

Cited by 88 publications

References 61 publications

Coupling and proximity effects in the superfluid transition in 4He dots

Coupling and proximity effects in the superfluid transition in 4He dots

Nonlinear and shock waves in superfluid He II

High-precision measurement of the thermal exponent for the three-dimensionalXYuniversality class

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