Quantum momentum distribution and kinetic energy in solid 4He.
We present measurements of neutron scattering from solid 4He at high momentum transfer. The solid is held close to the melting line at molar volume 20.87 cm3/mol and temperature T=1.6 K. From the data, we determine the shape of the momentum distribution, n(k), of atoms in the solid and the leading final state contribution to the scattering. We show that n(k) in this highly anharmonic, quantum solid differs significantly from a Gaussian. The n(k) is more sharply peaked with larger occupation of low momentum states than in a Maxwell-Boltzmann distribution, as found in liquid 4He and predicted qualitatively by path integral Monte Carlo calculations. The atomic kinetic energy is =(24.25+/-0.30) K. If n(k) is assumed to be Gaussian, as is usually the practice, a 10% smaller is obtained.
Bose-Einstein Condensation Measurements and Superflow in Condensed Helium
We review the formulation and measurement of Bose-Einstein condensation (BEC) in liquid and solid helium. BEC is defined for a Bose gas and subsequently for interacting systems via the one-body density matrix (OBDM) valid for both uniform and non-uniform systems. The connection between the phase coherence created by BEC and superflow is made. Recent measurements show that the condensate fraction in liquid 4He drops from 7.25±0.75 % at saturated vapor pressure (p≈0) to 2.8±0.2 % at pressure p=24 bars near the solidification pressure (p=25.3 bar). Extrapolation to solid densities suggests a condensate fraction in the solid of 1 % or less, assuming a frozen liquid structure such as an amorphous solid. Measurements in the crystalline solid have not been able to detect a condensate with an upper limit set at n0≤0.3 %. Opportunities to observe BEC directly in liquid 4He confined in porous media, where BEC is localized to patches by disorder, and in amorphous solid helium is discussed.
Experimental observation of a strange nonchaotic attractor.
Evidence is presented for the existence of a strange nonchaotic attractor in a two-frequency quasi-periodically driven, buckled, magnetoelastic ribbon experiment. Scaling behavior in the Fourier amplitude spectrum is observed in agreement with predicted scaling behavior for strange nonchaotic attractors. Dimension measurements also support the existence of a strange nonchaotic attractor