Zero-point motion and superfluid helium
We propose that He II exhibits macroscopic (sigma/sub P//Napprox.O(1)) quantum zero-point motion in momentum space, i.e., that a nonzero root-mean-square superfluid velocity exists even in an equilibrium superfluid system at rest. At absolute zero, using coherent states, we relate the uncertainty sigma/sub P//N in the total momentum P (per particle) to the long-range-order (LRO) part of the phase gradient correlation function, which is proposed as an order parameter. The local equilibrium equation for the superfluid velocity potential derived by Biswas and Rama Rao yields, in the strict equilibrium limit, the equation determining this order parameter in terms of fluctuation correlations that remain to be determined. The order parameter is interaction dependent, nonzero at T=0 if mu-tilde (0)-rho/sub 0/V/sub 0/>0, and can vanish at some transition temperature T/sub lambda/when fluctuation terms become comparable to the T=0 value. (Here V/sub 0/ rho/sub 0/, and mu-tilde (0) are the uniform parts of the potential, density, and chemical potential with shifted zero of energy, respectively.) A characteristic length ..lambda.. (T), diverging at T=T/sub lambda/appears naturally, with its defining relation reducing to a macroscopic uncertainty relation sigma/sub P//N) ..lambda.. (0) =h/2 at T=0. With certain assumptions it is shown that at T=0, LRO in the phase gradient correlation function is incompatible with off-diagonal long-range order (ODLRO) in the correlation function, and with nonzero condensate function.
- Research Organization:
- Institute of Physics, Bhubaneswar, India
- OSTI ID:
- 7287623
- Journal Information:
- J. Low Temp. Phys.; (United States), Vol. 28:3
- Country of Publication:
- United States
- Language:
- English
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