Spin-Echo Measurements for an Anomalous Quantum Phase of 2D Helium-3

Previous heat-capacity measurements of our group had shown the possible existence of an anomalous quantum phase containing the zero-point vacancies (ZPVs) in 2D $^{3}$He. The system is monolayer $^{3}$He adsorbed on graphite preplated with monolayer $^{4}$He at densities ($\rho$) just below the 4/7 commensurate phase ($0.8\leq \rho /\rho_{4/7}\leq 1$). We carried out pulsed-NMR measurements in order to examine the microscopic and dynamical nature of this phase. The measured decay of spin echo signals shows the non-exponential behaviour. The decay curve can be fitted with the double exponential function, but the relative intensity of the component with a longer time constant is small (5%) and does not depend on density and temperature, which contradicts the macroscopic fluid and 4/7 phase coexistence model. This slowdown is likely due to the mosaic angle spread of Grafoil substrate and the anisotropic spin-spin relaxation time $T_{2}$ in 2D systems with respect to the magnetic field direction. The inverse $T_2$ value deduced from the major echo signal with a shorter time constant, which obeys the single exponential function, decreases linearly with decreasing density from $n=1$, supporting the ZPV model.Comment: 4 pages, 6 figure

Divergence of the orbital nuclear magnetic relaxation rate in metals

We analyze the nuclear magnetic relaxation rate $(1/T_1)_{orb}$ due to the coupling of nuclear spin to the orbital moment of itinerant electrons in metals. In the clean non--interacting case, contributions from large--distance current fluctuations add up to cause a divergence of $(1/T_1)_{orb}$. When impurity scattering is present, the elastic mean free time $\tau$ cuts off the divergence, and the magnitude of the effect at low temperatures is controlled by the parameter $\ln(\mu \tau)$, where $\mu$ is the chemical potential. The spin--dipolar hyperfine coupling, while has the same spatial variation $1/r^3$ as the orbital hyperfine coupling, does not produce a divergence in the nuclear magnetic relaxation rate.Comment: 11pages; v4: The analysis of the normal state is more compelete now, including a comparison with other hyperfine interactions and a detailed discussion of the effect in representative metals. The superconducting state is excluded from consideration in this pape

Surface tension in an intrinsic curvature model with fixed one-dimensional boundaries

A triangulated fixed connectivity surface model is investigated by using the Monte Carlo simulation technique. In order to have the macroscopic surface tension \tau, the vertices on the one-dimensional boundaries are fixed as the edges (=circles) of the tubular surface in the simulations. The size of the tubular surface is chosen such that the projected area becomes the regular square of area A. An intrinsic curvature energy with a microscopic bending rigidity b is included in the Hamiltonian. We found that the model undergoes a first-order transition of surface fluctuations at finite b, where the surface tension \tau discontinuously changes. The gap of \tau remains constant at the transition point in a certain range of values A/N^\prime at sufficiently large N^\prime, which is the total number of vertices excluding the fixed vertices on the boundaries. The value of \tau remains almost zero in the wrinkled phase at the transition point while \tau remains negative finite in the smooth phase in that range of A/N^\prime.Comment: 12 pages, 8 figure

Initial Data for General Relativity with Toroidal Conformal Symmetry

A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no isometries, but a $U(1)\times U(1)$ group of conformal isometries. After decomposing the Lichnerowicz conformal factor in a double Fourier series on the group orbits, the solutions are given in terms of a countable family of uncoupled ODEs on the orbit space.Comment: REVTEX, 9 pages, ESI Preprint 12

Dynamics of a Brownian circle swimmer

Self-propelled particles move along circles rather than along a straight line when their driving force does not coincide with their propagation direction. Examples include confined bacteria and spermatozoa, catalytically driven nanorods, active, anisotropic colloidal particles and vibrated granulates. Using a non-Hamiltonian rate theory and computer simulations, we study the motion of a Brownian "circle swimmer" in a confining channel. A sliding mode close to the wall leads to a huge acceleration as compared to the bulk motion, which can further be enhanced by an optimal effective torque-to-force ratio.Comment: v2: changed title from "The fate of a Brownian circle swimmer"; mainly changes of introduction and conclusion

Phase transitions of an intrinsic curvature model on dynamically triangulated spherical surfaces with point boundaries

An intrinsic curvature model is investigated using the canonical Monte Carlo simulations on dynamically triangulated spherical surfaces of size upto N=4842 with two fixed-vertices separated by the distance 2L. We found a first-order transition at finite curvature coefficient \alpha, and moreover that the order of the transition remains unchanged even when L is enlarged such that the surfaces become sufficiently oblong. This is in sharp contrast to the known results of the same model on tethered surfaces, where the transition weakens to a second-order one as L is increased. The phase transition of the model in this paper separates the smooth phase from the crumpled phase. The surfaces become string-like between two point-boundaries in the crumpled phase. On the contrary, we can see a spherical lump on the oblong surfaces in the smooth phase. The string tension was calculated and was found to have a jump at the transition point. The value of \sigma is independent of L in the smooth phase, while it increases with increasing L in the crumpled phase. This behavior of \sigma is consistent with the observed scaling relation \sigma \sim (2L/N)^\nu, where \nu\simeq 0 in the smooth phase, and \nu=0.93\pm 0.14 in the crumpled phase. We should note that a possibility of a continuous transition is not completely eliminated.Comment: 15 pages with 10 figure

The Momentum Constraints of General Relativity and Spatial Conformal Isometries

Transverse-tracefree (TT-) tensors on $({\bf R}^3,g_{ab})$, with $g_{ab}$ an asymptotically flat metric of fast decay at infinity, are studied. When the source tensor from which these TT tensors are constructed has fast fall-off at infinity, TT tensors allow a multipole-type expansion. When $g_{ab}$ has no conformal Killing vectors (CKV's) it is proven that any finite but otherwise arbitrary set of moments can be realized by a suitable TT tensor. When CKV's exist there are obstructions -- certain (combinations of) moments have to vanish -- which we study.Comment: 16 page

Evidence for a Self-Bound Liquid State and the Commensurate-Incommensurate Coexistence in 2D 3^3He on Graphite

We made heat-capacity measurements of two dimensional (2D) $^3$He adsorbed on graphite preplated with monolayer $^4$He in a wide temperature range (0.1 $\leq T \leq$ 80 mK) at densities higher than that for the 4/7 phase (= 6.8 nm$^{-2}$). In the density range of 6.8 $\leq \rho \leq$ 8.1 nm$^{-2}$, the 4/7 phase is stable against additional $^3$He atoms up to 20% and they are promoted into the third layer. We found evidence that such promoted atoms form a self-bound 2D Fermi liquid with an approximate density of 1 nm$^{-2}$ from the measured density dependence of the $\gamma$-coefficient of heat capacity. We also show evidence for the first-order transition between the commensurate 4/7 phase and the ferromagnetic incommensurate phase in the second layer in the density range of 8.1 $\leq \rho \leq$ 9.5 nm$^{-2}$.Comment: 6 pages, 4 figure

A Triplectic Bi-Darboux Theorem and Para-Hypercomplex Geometry

We provide necessary and sufficient conditions for a bi-Darboux Theorem on triplectic manifolds. Here triplectic manifolds are manifolds equipped with two compatible, jointly non-degenerate Poisson brackets with mutually involutive Casimirs, and with ranks equal to 2/3 of the manifold dimension. By definition bi-Darboux coordinates are common Darboux coordinates for two Poisson brackets. We discuss both the Grassmann-even and the Grassmann-odd Poisson bracket case. Odd triplectic manifolds are, e.g., relevant for Sp(2)-symmetric field-antifield formulation. We demonstrate a one-to-one correspondence between triplectic manifolds and para-hypercomplex manifolds. Existence of bi-Darboux coordinates on the triplectic side of the correspondence translates into a flat Obata connection on the para-hypercomplex side.Comment: 31 pages, LaTeX. v2: Changed title; Added references. v3: Minor reorganization of pape