Generation efficiencies for propagating modes in a supersolid

Sears, Matthew R.; Saslow, Wayne M.

doi:10.1103/physrevb.82.094519

Cited by 3 publications

(7 citation statements)

References 32 publications

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“…These propagating modes, in the presence of a finite P a , and their generation by transducers and heaters, have been considered in Ref. 43. We also find a rather complex additional mode, not considered in Ref.…”

Section: Discussionsupporting

confidence: 55%

Andreev-Lifshitz hydrodynamics applied to an ordinary solid under pressure

Sears

Saslow

2010

Phys. Rev. B

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We have applied the Andreev-Lifshitz hydrodynamic theory of supersolids to an ordinary solid. This theory includes an internal pressure P , distinct from the applied pressure Pa and the stress tensor λ ik . Under uniform static Pa, we have λ ik = (P −Pa)δ ik . For Pa = 0, Maxwell relations imply that P ∼ P 2 a . The theory also permits vacancy diffusion but treats vacancies as conserved. It gives three sets of propagating elastic modes; it also gives two diffusive modes, one largely of entropy density and one largely of vacancy density (or, more generally, defect density). For the vacancy diffusion mode (or, equivalently, the lattice diffusion mode) the vacancies behave like a fluid within the solid, with the deviations of internal pressure associated with density changes nearly canceling the deviations of stress associated with strain. We briefly consider pressurization experiments in solid 4 He at low temperatures in light of this lattice diffusion mode, which for small Pa has diffusion constant DL ∼ P 2 a . The general principles of the theory -that both volume and strain should be included as thermodynamic variables, with the result that both P and λ ik appear -should apply to all solids under pressure, especially near the solid-liquid transition. The lattice diffusion mode provides an additional degree of freedom that may permit surfaces with different surface treatments to generate different responses in the bulk.

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Section: Discussionsupporting

confidence: 55%

Andreev-Lifshitz hydrodynamics applied to an ordinary solid under pressure

Sears

Saslow

2010

Phys. Rev. B

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“…Although the elastic modes of a supersolid had previously been found for P a = 0, 1,26,27 Ref. 29 explicitly finds the elastic modes for nonzero P a (recall that a P a 25 bars is necessary to solidify 4 He). A summary of the results and convenient notation are provided here.…”

Section: A Elastic Modesmentioning

confidence: 99%

“…Two other modes also form a degenerate pair, corresponding to fourth sound, with the superfluid component in motion and the normal component essentially at rest. 29,31,32 The ninth and final mode is diffusive, with v ′ n and v ′ s in opposing directions, and nearly constant chemical potential and stress.…”

Section: Normal Modes In a Supersolidmentioning

confidence: 99%

“…23 Ref. 29 shows that for P a ≪ K we have c 2 1 ≫ c 2 ≫ c 2 0 and strain w (0) ll ≪ 1. It is also convenient to define the "fluid-like" and "solid-like" velocities c lL and c lS , which satisfy 23…”

Section: Longitudinal Elastic Modesmentioning

confidence: 99%

“…Ref. 29 calculates the effect of P a on the propagating elastic modes of a supersolid, as well as the efficiency with which a heater or a transducer generates these modes. The present work considers the effect of P a on the diffusive mode of a supersolid.…”

Section: Introductionmentioning

confidence: 99%

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Andreev-Lifshitz supersolid hydrodynamics including the diffusive mode

Sears

Saslow

2010

Phys. Rev. B

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We have re-examined the Andreev-Lifshitz theory of supersolids. This theory implicitly neglects uniform bulk processes that change the vacancy number, and assumes an internal pressure P in addition to lattice stress λ ik . Each of P and λ ik takes up a part of an external, or applied, pressure Pa (necessary for solid 4 He). The theory gives four pairs of propagating elastic modes, of which one corresponds to a fourth-sound mode, and a single diffusive mode, which has not been analyzed previously. The diffusive mode has three distinct velocities, with the superfluid velocity much larger than the normal fluid velocity, which in turn is much larger than the lattice velocity. The mode structure depends on the relative values of certain kinetic coefficients and thermodynamic derivatives. We consider pressurization experiments in solid 4 He at low temperatures in light of this diffusion mode and a previous analysis of modes in a normal solid with no superfluid component.

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Effects of $^3$He Impurity on Solid $^4$He Studied by Compound Torsional Oscillator

Gumann,

Keiderling,

Ruffner

et al. 2011

Preprint

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Frequency shifts and dissipations of a compound torsional oscillator induced by solid 4 He samples containing 3 He impurity concentrations (x3 = 0.3, 3, 6, 12 and 25 in units of 10 −6 ) have been measured at two resonant mode frequencies (f1 = 493 and f2 = 1164 Hz) at temperatures (T ) between 0.02 and 1.1 K. The fractional frequency shifts of the f1 mode were much smaller than those of the f2 mode. The observed frequency shifts continued to decrease as T was increased above 0.3 K, and the conventional non-classical rotation inertia fraction was not well defined in all samples with x3 ≥ 3 ppm. Temperatures where peaks in dissipation of the f2 mode occurred were higher than those of the f1 mode in all samples. The peak dissipation magnitudes of the f1 mode was greater than those of the f2 mode in all samples. The activation energy and the characteristic time (τ0) were extracted for each sample from an Arrhenius plot between mode frequencies and inverse peak temperatures. The average activation energy among all samples was 430 mK, and τ0 ranged from 2×10 −7 s to 5×10 −5 s in samples with x3 = 0.3 to 25 ppm. The characteristic time increased in proportion to x 2/3 3 . Observed temperature dependence of dissipation were consistent with those expected from a simple Debye relaxation model if the dissipation peak magnitude was separately adjusted for each mode. Observed frequency shifts were greater than those expected from the model. The discrepancies between the observed and the model frequency shifts increased at the higher frequency mode.

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Generation efficiencies for propagating modes in a supersolid

Cited by 3 publications

References 32 publications

Andreev-Lifshitz hydrodynamics applied to an ordinary solid under pressure

Andreev-Lifshitz hydrodynamics applied to an ordinary solid under pressure

Andreev-Lifshitz supersolid hydrodynamics including the diffusive mode

Effects of $^3$He Impurity on Solid $^4$He Studied by Compound Torsional Oscillator

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