Excitations in Liquid Helium: Thermodynamic Calculations

Bendt, P.J.; Cowan, Robert D.; Yarnell, J. L.

doi:10.1103/physrev.113.1386

Cited by 128 publications

(17 citation statements)

References 25 publications

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“…The specific heat of liquid helium was calculated using the Landau theory [1,2]; the results agree well with experimental data near zero temperature. However, the calculated values differ greatly from the experimental data obtained near the λ point.…”

Section: Introductionsupporting

confidence: 62%

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Logarithmic Singularity of Specific Heat in Liquid Helium II at the λ Point

Sasaki

2007

J Low Temp Phys

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The experimental width of the second sound peak in Brillouin scattering is less than the instrumental width. It is also less than the width of the first sound peak near the λ point. The theoretical width of the second sound peak becomes infinitely large at the λ point in the traditional viewpoint. This discrepancy suggests that the second sound peak detected in Brillouin scattering is an elementary excitation. We calculate the specific heat of liquid helium near the λ point by considering the second sound peak. The calculated temperature-dependence of the specific heat has a logarithmic divergence at the λ point. Furthermore, the calculated values of the specific heat agree well with data derived from experiments.

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Section: Introductionsupporting

confidence: 62%

“…However, the calculated values differ greatly from the experimental data obtained near the λ point. Bendt et al [1] and Brooks and Donnelly [2] calculated the specific heat and other thermodynamic functions of superfluid helium on the basis of the Landau theory. Their result for specific heat has no logarithmic divergence at the λ point.…”

Section: Introductionmentioning

confidence: 99%

Logarithmic Singularity of Specific Heat in Liquid Helium II at the λ Point

Sasaki

2007

J Low Temp Phys

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“…A. Donnelly, and R. N. Hills thermodynamic analysis, made by a piecewise approximation to the dispersion curve, seemed unusually encouraging. 4 In spite of at least one warning from a theoretician s and the somewhat disconcerting discovery that the Landau parameters are both temperature and pressure dependent, it appeared possible to think of trying to unify the neutron scattering and dispersion data over the whole temperature-pressure (T, P) plane. Such an effort was begun by Donnelly and Brooks in 1971 and is continuing at the University of Oregon.…”

Section: Introductionmentioning

confidence: 99%

Specific heat and dispersion curve for helium II

1981

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The dispersion curve for elementary excitations in He H at low temperatures and at the vapor pressure is evaluated using inelastic neutron scattering data. It is found that this dispersion curve is consistent with recent specific heat measurements of high resolution. We represent the dispersion curve by means of cubic splines, and emphasize the need for further neutron scattering studies at low momentum transfer.

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“…This scattering is consistent with a "two-dimensional roton," predicted to occur at the solid-liquid interface and inferred from measurements of the heat capacity and superfluid fraction. Superfluid helium is a model system whose microscopic excitations explain the macroscopic thermodynamic and transport properties of the liquid [1]. The superfluid excitation spectrum at low momentum transfers ͑Q , 2.4 Å 21 ͒ is well defined, clearly showing the quantum nature of the liquid via the long-lived excited states.…”

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confidence: 99%

Localized Collective Excitations in Superfluid Helium in Vycor

et al. 1998

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Inelastic neutron scattering has been used to probe the collective excitations of superfluid helium in porous Vycor glass for 0.5 # T͑K͒ # 1.9. The confined roton displays a temperature dependence similar to that of the bulk roton but with larger widths. Additional scattering has been observed near the roton minimum but with a substantially lower energy than the bulk roton. This scattering is consistent with a "two-dimensional roton," predicted to occur at the solid-liquid interface and inferred from measurements of the heat capacity and superfluid fraction. [S0031-9007(98)08080-6] PACS numbers: 61.12.Ex Superfluid helium is a model system whose microscopic excitations explain the macroscopic thermodynamic and transport properties of the liquid [1]. The superfluid excitation spectrum at low momentum transfers ͑Q , 2.4 Å 21 ͒ is well defined, clearly showing the quantum nature of the liquid via the long-lived excited states. The dominant excitations, which determine the thermodynamics of the liquid, are the phonons at low Q ͑Q , 0.9 Å 21 ͒ and the rotons at higher Q ͑Q Ӎ 1.9 Å 21 ͒. At low temperatures ͑T , 0.7 K͒ the liquid can be treated as a noninteracting gas of phonons, and above 1 K the liquid can be treated as an ideal gas of rotons.Confinement can have dramatic effects on the macroscopic properties of superfluid helium, especially near the superfluid transition temperature. For instance, confinement in aerogel glass results in only a slight decrease in the transition temperature T l but dramatically changes the critical exponent [2]. Alternatively, confinement in porous Vycor glass results in a substantial decrease in the transition temperature ͑T l Ӎ 1.95 K͒ but no change in critical exponents. Recently studies of the microscopic dynamics of helium confined in aerogel have reported [3,4] a crossover behavior of the roton energy from a low temperature regime ͑T , 1.9 K͒ with a weak temperature dependence to a high temperature regime, where it exhibits a strong temperature dependence. This anomalous temperature dependence can be understood in terms of a competition between the temperature-dependent roton mean free path and a temperature-independent length scale set by the porous media.In this Letter we report neutron inelastic scattering measurements of the collective excitation spectrum of superfluid helium confined in porous Vycor glass. We observe a strong excitation similar to the roton observed in the bulk liquid which we shall refer to as the three-dimensional (3D) roton. We also observe additional scattering around the bulk roton minimum but lower in energy. This additional intensity is consistent with a two-dimensional (2D) roton which is confined to the higher density liquid layer near the pore wall [5]. The properties of this 2D roton, which have previously been observed directly (via inelastic neutron scattering) on crystalline substrates such as pyrolytic graphite [6][7][8], and indirectly (via third sound measurements) on amorphous substrates [9], are consistent with the thermodynamic data ...

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Excitations in Liquid Helium: Thermodynamic Calculations

Cited by 128 publications

References 25 publications

Logarithmic Singularity of Specific Heat in Liquid Helium II at the λ Point

Logarithmic Singularity of Specific Heat in Liquid Helium II at the λ Point

Specific heat and dispersion curve for helium II

Localized Collective Excitations in Superfluid Helium in Vycor

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