Exact Analysis of Entanglement in Gapped Quantum Spin Chains

We investigate the entanglement properties of the valence-bond-solid states with generic integer-spin $S$. Using the Schwinger boson representation of the valence-bond-solid states, the entanglement entropy, the von Neumann entropy of a subsystem, is obtained exactly and its relationship with the usual correlation function is clarified. The saturation value of the entanglement entropy, $2 \log_2 (S+1)$, is derived explicitly and is interpreted in terms of the edge-state picture. The validity of our analytical results and the edge-state picture is numerically confirmed. We also propose a novel application of the edge state as a qubit for quantum computation.Comment: 4 pages, 2 figure

Ultrasonographic observation of the healing process in the gap after a Ponseti-type Achilles tenotomy for idiopathic congenital clubfoot at two-year follow-up

AbstractBackgroundPonseti management usually requires Achilles tenotomy during the final stage of serial casting. However, we lack a good understanding of the sequential tendon healing process after tenotomy in the Ponseti bracing protocol. The purpose of this study was to clarify the ultrasonographic process of tendon healing in the gap for up to twoyears after Ponseti-type Achilles tenotomy in patients with clubfeet.MethodsWe conducted an ultrasonographic study to clarify the sequential changes in gap healing for up to twoyears after tenotomy. The subjects were 23 patients with 33 clubfeet. Achilles tenotomy was performed at mean 10.4 (8–16) weeks after birth. Dynamic and static ultrasonography was performed before tenotomy and at 1, 2, 3, 4, 6, 8, and 12weeks as well as at 4, 6, 12, 18, and 24months after tenotomy.ResultsContinuity and gliding were noted within fourweeks. The united portion continued to thicken for up to threemonths after tenotomy. Starting from the fourth month, the healed portion began to lose its thickness, and this process continued into the sixth month. At oneyear, the thickness of the tendon did not differ much from that of the tendon on the opposing foot. In cases where patients had clubfoot on both feet and underwent simultaneous tenotomies, measurement of the tendons could not be accurately compared. At twoyears after tenotomy, slight irregularity of the internal structure persisted when compared with the unaffected foot. In addition, clinical and X-ray findings were evaluated simultaneously, and no recurrence was confirmed.ConclusionsTo our knowledge, our results are the first to describe the process of gap healing in the tendon after tenotomy up to and beyond twoyears, as recommended in the Ponseti bracing protocol.Level of evidence IV

Static and dynamic properties of frictional phenomena in a one-dimensional system with randomness

Static and dynamic frictional phenomena at the interface with random impurities are investigated in a two-chain model with incommensurate structure. Static frictional force is caused by the impurity pinning and/or by the pinning due to the regular potential, which is responsible for the breaking of analyticity transition for impurity-free cases. It is confirmed that the static frictional force is always finite in the presence of impurities, in contrast to the impurity-free system. The nature of impurity pinning is discussed in connection with that in density waves. The kinetic frictional force of a steady sliding state is also investigated numerically. The relationship between the sliding velocity dependence of the kinetic frictional force and the strength of impurity potential is discussed.Comment: RevTex, 14 pages, 6 PostScript figures, to appear in Phys. Rev.

Anomalous pinning behavior in an incommensurate two-chain model of friction

Pinning phenomena in an incommensurate two-chain model of friction are studied numerically. The pinning effect due to the breaking of analyticity exists in the present model. The pinning behavior is, however, quite different from that for the breaking of analyticity state of the Frenkel-Kontorova model. When the elasticity of chains or the strength of interchain interaction is changed, pinning force and maximum static frictional force show anomalously complicated behavior accompanied by a successive phase transition and they vanish completely under certain conditions.Comment: RevTex, 9 pages, 19 figures, to appear in Phys. Rev. B58 No.23(1998

Dynamical frictional phenomena in an incommensurate two-chain model

Dynamical frictional phenomena are studied theoretically in a two-chain model with incommensurate structure. A perturbation theory with respect to the interchain interaction reveals the contributions from phonons excited in each chain to the kinetic frictional force. The validity of the theory is verified in the case of weak interaction by comparing with numerical simulation. The velocity and the interchain interaction dependences of the lattice structure are also investigated. It is shown that peculiar breaking of analyticity states appear, which is characteristic to the two-chain model. The range of the parameters in which the two-chain model is reduced to the Frenkel-Kontorova model is also discussed.Comment: RevTex, 9 pages, 7 PostScript figures, to appear in Phys. Rev.

Astrometric VLBI observations of H2_2O masers in an extreme OH/IR star candidate NSV17351

Results of astrometric very long baseline interferometry (VLBI) observations towards an extreme OH/IR star candidate NSV17351 are presented. We used the VERA (VLBI Exploration of Radio Astrometry) VLBI array to observe 22\,GHz H$_2$O masers of NSV17351. We derived an annual parallax of 0.247$\pm$0.035 mas which corresponds to a distance of 4.05$\pm$0.59 kpc. By averaging the proper motions of 15 maser spots, we obtained the systemic proper motion of NSV17351 to be ($\mu_{\alpha}\cos{\delta}, \mu_{\delta}$)$^{\mathrm{avg}}$ $=$ ($-$1.19 $\pm$ 0.11, 1.30 $\pm$ 0.19) mas\,yr$^{-1}$. The maser spots spread out over a region of 20 mas $\times$ 30 mas, which can be converted to a spatial distribution of $\sim$80 au $\times$ $\sim$120 au at the source distance. Internal motions of the maser spots suggest an outward moving maser region with respect to the estimated position of the central star. From single dish monitoring of the H$_2$O maser emission, we estimate the pulsation period of NSV17351 to be 1122$\pm$24 days. This is the first report of the periodic activity of NSV17351, indicating that NSV17351 could have a mass of $\sim$4\,M$_{\odot}$. We confirmed that the time variation of H$_2$O masers can be used as a period estimator of variable OH/IR stars. Furthermore, by inspecting dozens of double-peaked H$_2$O maser spectra from the last 40 years, we detected a long-term acceleration in the radial velocity of the circumstellar matter to be $0.17\pm0.03$ km\,s$^{-1}$\,yr$^{-1}$ Finally, we determined the position and kinematics of NSV17351 in the Milky Way Galaxy and found that NSV17351 is located in an interarm region between the Outer and Perseus arms. We note that astrometric VLBI observations towards extreme OH/IR stars are useful samples for studies of the Galactic dynamics.Comment: Published in the Publications of the Astronomical Society of Japa

Block Spin Density Matrix of the Inhomogeneous AKLT Model

We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outside the block. It is diagonalized and shown to be a projector onto a subspace. We prove that for large block the density matrix behaves as the identity in the subspace. The von Neumann entropy coincides with Renyi entropy and is equal to the saturated value.Comment: 20 page