The superfluid transition in helium clusters

Abstract

We address cluster size effects on the λ temperature (Tλ) for the rounded-off transition for the Bose–Einstein condensation and for the onset of superfluidity in (4He)N clusters of radius R0=aN1/3, where a=3.5 Å is the constituent radius. The phenomenological Ginsburg–Pitaevskii–Sobaynin theory for the order parameter of the second-order phase transition, in conjunction with the free-surface boundary condition, results in a scaling law for the cluster size dependence of Tλ, which is defined by the maximum of the specific heat and/or from the onset of the finite fraction of the superfluid density. This size scaling law (Tλ0−Tλ)/Tλ0∝R0−1/ν∝N−1/3ν, where ν (=0.67) is the critical exponent for the superfluid fraction and for the correlation length for superfluidity in the infinite bulk system, implies the depression of the finite system Tλ relative to the bulk value of Tλ0. The quantum path integral molecular dynamics simulations of Sindzingre, Ceperley, and Klein [Phys. Rev. Lett. 63, 1601 (1989)] for N=64, 128, together with experimental data for specific heat of He4 in porous gold and in other confined systems [J. Yoon and M. H. W. Chan, Phys. Rev. Lett. 78, 4801 (1997); G. M. Zahssenhaus and J. D. Reppy, ibid. 83, 4800 (1999)], are accounted for in terms of the cluster size scaling theory (Tλ0−Tλ)/Tλ0=(πξ0/a)3/2N−1/2, where ξ0=1.7±0.3 Å is the “critical” amplitude for the correlation length in the bulk. The phenomenological theory relates Tλ for the finite system to the correlation length ξ(T) for superfluidity in the infinite bulk system, with the shift (Tλ0−Tλ) being determined by the ratio R0/ξ(T), in accord with the theory of finite-size scaling.

Electron bubbles in helium clusters. II. Probing superfluidity

“…15 The ͑ 4 He͒ N cluster sizes employed in the experiments of Toennies and co-workers 3,[6][7][8]17,18 and of Northby and co-workers, 4,5 i.e., N Ӎ 10 4 -10 7 , are considerably larger than N min . In this large cluster size domain the point temperature depression is small, 14,15 i.e., ͑T − T 0 ͒ / T 0 Ӎ 2 ϫ 10 −2 -2ϫ 10 −3 for N =10 4 -10 7 . Thus for the current experimentally accessible temperature of 0.4 K, the large ͑ 4 He͒ N − clusters ͑N =10 4 -10 7 ͒ studied by Toennies and co-workers 3,[6][7][8]17,18 are superfluid.…”

“…9-11͒ and, on the basis of quantum path integral simulations, 12,13 were theoretically predicted to undergo a rounded-off superfluid phase transition. A theory of cluster size effects on the temperature T in a ͑ 4 He͒ N cluster 14,15 of radius R resulted in the finite size scaling relation ͑T 0 − T ͒ / T 0 ϰ R −1/ ϰ N −1/3 for the reduction of T relative to the bulk value T 0 = 2.17 K, with = 0.67 being the critical exponent for the superfluid fraction and for the correlation length in the infinite bulk system. 16 The superfluidity transition and/or Bose-Einstein condensation is exhibited at surprisingly small cluster sizes, i.e., N min =8-70, 15 where the threshold cluster size N min is property dependent.…”

The absorption spectrum of the (1,0), (3,1) and (4,2) bands in the c3Σg+–a3Σu+ system of He2 eximer

“…[9] This work Ref. [9] T t a 12369.50264 (89) 6 6.5887 6.5887 6.5887 6.5887 r 0.0020 0.0037 0.0034 a The energy of t = 0 level in the a 3 R u + state is set to 0. b Numbers in parentheses denote one standard deviation in unit of the last quoted digit. If the numbers are missing, the values are fixed at those of Ref.…”

“…It is the simplest but the most studied exemplary both in experiments and in theory. The He 2 molecule plays a significant role in the fields of chemical bond formation [1][2][3], the mechanism of low-temperature discharge plasma [4,5] and the spectroscopic study of superfluid helium nano-droplets [6,7].…”

REFLECTIONS ON PHYSICAL CHEMISTRY: Science and Scientists

“…So, the field of dynamics of large finite systems encompasses ultrafast (fs) dynamics of cluster explosion and ultraslow (ms) dynamics expansion of ultracold optical molasses. The latter studies, together with the exploration of superfluidity of helium-4 boson clusters (128), which can be interrogated by spectroscopic probes (143) and by electron tunneling from electron bubbles in these clusters (65), open up a new research area of the dynamics of ultracold large finite quantum systems.…”