Velocity dependent interactions and a new sum rule in bcc He

Recent neutron scattering experiments [PRL,{\bf 88},p.195301 (2002)] on solid $^4$He, discovered a new optic-like mode in the bcc phase. This excitation was predicted by a recently proposed model that describes the correlated atomic zero-point motion in bcc Helium in terms of dynamic electric dipole moments. Modulations of the relative phase of these dipoles between different atoms describes the anomalously soft T$_1$(110) phonon and two new optic-like modes, one of which was recently found in the neutron scattering experiments. In this work we show that the correlated dipolar interactions can be written as a velocity dependent interaction. This then results in a modified f-sum rule for the T$_1$(110) phonon, in good agreement with the recent experimental data.Comment: 5 pages, 3 figure

Imaginary Squashing Mode Spectroscopy of Helium Three B

We have made precision measurements of the frequency of a collective mode of the superfluid 3He-B order parameter, the J=2- imaginary squashing mode. Measurements were performed at multiple pressures using interference of transverse sound in an acoustic cavity. Transverse waves propagate in the vicinity of this order parameter mode owing to off-resonant coupling. At the crossing of the sound mode and the order parameter mode, the sound wave is strongly attenuated. We use both velocity and attenuation measurements to determine precise values of the mode frequency with a resolution between 0.1% and 0.25%.Comment: 6 pages, 4 figures, submitted to proceedings of Quantum Fluids and Solids (QFS) Conference 2006; revised 9/26/0

Calculation of NMR Properties of Solitons in Superfluid 3He-A

Superfluid 3He-A has domain-wall-like structures, which are called solitons. We calculate numerically the structure of a splay soliton. We study the effect of solitons on the nuclear-magnetic-resonance spectrum by calculating the frequency shifts and the amplitudes of the soliton peaks for both longitudinal and transverse oscillations of magnetization. The effect of dissipation caused by normal-superfluid conversion and spin diffusion is calculated. The calculations are in good agreement with experiments, except a problem in the transverse resonance frequency of the splay soliton or in magnetic-field dependence of reduced resonance frequencies.Comment: 15 pages, 10 figures, updated to the published versio

Elastic Wave Transmission at an Abrupt Junction in a Thin Plate, with Application to Heat Transport and Vibrations in Mesoscopic Systems

The transmission coefficient for vibrational waves crossing an abrupt junction between two thin elastic plates of different widths is calculated. These calculations are relevant to ballistic phonon thermal transport at low temperatures in mesoscopic systems and the Q for vibrations in mesoscopic oscillators. Complete results are calculated in a simple scalar model of the elastic waves, and results for long wavelength modes are calculated using the full elasticity theory calculation. We suggest that thin plate elasticty theory provide a useful and tractable approximation to the full three dimensional geometry.Comment: 35 pages, including 12 figure

Preliminary Heat Capacity and Vapor Pressure Measurements of 2D 4He on ZYX Graphite

We report preliminary heat capacity and vapor pressure measurements of the first and second layers of 4He adsorbed on ZYX graphite. ZYX is known to have much better crystallinity than Grafoil, the most commonly-used exfoliated graphite substrate, such as a ten-times larger platelet size. This allows us to distinguish different phases in 2D helium-4 much more clearly and may provide qualitatively different insights into this system. We found a significantly asymmetric density-dependence of the heat-capacity peak associated with the 1/3 phase formation comparing with that obtained with Grafoil. The 2nd-layer promotion density is determined as 11.8+-0.3 nm-2 from the heat-capacity measurement of low density samples in the 2nd layer and vapor pressure measurement.Comment: 7 pages, 7 figures, accepted for publication in JLTP - QFS201

Local Dynamics and Strong Correlation Physics I: 1D and 2D Half-filled Hubbard Models

We report on a non-perturbative approach to the 1D and 2D Hubbard models that is capable of recovering both strong and weak-coupling limits. We first show that even when the on-site Coulomb repulsion, U, is much smaller than the bandwith, the Mott-Hubbard gap never closes at half-filling in both 1D and 2D. Consequently, the Hubbard model at half-filling is always in the strong-coupling non-perturbative regime. For both large and small U, we find that the population of nearest-neighbour singlet states approaches a value of order unity as $T\to 0$ as would be expected for antiferromagnetic order. We also find that the double occupancy is a smooth monotonic function of U and approaches the anticipated non-interacting limit and large U limits. Finally, in our results for the heat capacity in 1D differ by no more than 1% from the Bethe ansatz predictions. In addition, we find that in 2D, the heat capacity vs T for different values of U exhibits a universal crossing point at two characteristic temperatures as is seen experimentally in a wide range of strongly-correlated systems such as $^3He$, $UBe_3$, and $CeCu_{6-x}Al_x$. The success of this method in recovering well-established results that stem fundamentally from the Coulomb interaction suggests that local dynamics are at the heart of the physics of strongly correlated systems.Comment: 10 pages, 16 figures included in text, Final version for publication with a reference added and minor corrections. Phys. Rev. B, in pres