Critical thermal boundary resistance of4He above and belowT ?: Renormalization-group theory

Singularity in the Thermal Boundary Resistance between SuperfluidH4eand a Solid Surface

“…1). The theoretical prediction [8] of R b , after vertical shifts which cause agreement with the data near t = 10 −4 , is given by the solid lines in the figure. Obviously the agreement is not good.…”

“…where x b = ν − x λ ≃ 0.24 [6]. A renormalization-grouptheoretical calculation of R b carried out by Frank and Dohm (FD) [7,8] agrees with this qualitative picture and is expected to give the behavior of R b (t) quantitatively. The singular boundary resistance is particularly interesting because it is a direct consequence of the boundary conditions (BC) which are relevant at the solid-liquid interface.…”

“…Using their tabulated values [23], we evaluated δR th b numerically from the equations given in Ref. [8] and t 0 = 0.05. In Fig.…”

“…1, but that the resulting values of x b are close to 0.18 and thus significantly smaller than the theoreticallyexpected value x th b ≃ 0.24. Alternatively, a reasonable fit of the function predicted by the theory [8] to the data can be obtained if this function is multiplied by a factor which is significantly less than one and, for three of the cells, close to 0.53. Although a detailed theoretical explanation of this problem may be required, we believe that this discrepancy may be indicative of a need to consider modifications of the DBC which have been assumed in the theory not only of R b , but also of finite-size effects on the specific heat [11].…”

“…The calculation of Frank and Dohm [8] gives the difference δR th b = R th b (t) − R th b (t 0 ) and thus the values of R th b are determined only to within an additive constant. The theoretical result has the form…”