Analytic Expression for Exact Ground State Energy Based on an Operator Method for a Class of Anharmonic Potentials

A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic expressions for the exact ground state energy have also been derived specifically for a large class of the one-dimensional oscillator with cubic-quartic anharmonic terms. Our analytical results can be used to check the accuracy of existing numerical methods, for instance the method of state-dependent diagonalization. Our results also agree with the asymptotic behavior in the divergent pertubative expansion of quartic harmonic oscillator.Comment: LaTeX with six figure (gif) files; Submitted to Phys. Rev.

Hydrostatic and uniaxial pressure dependence of superconducting transition temperature of KFe2As2 single crystals

We present heat capacity, c-axis thermal expansion and pressure dependent, low field, temperature dependent magnetization for pressures up to ~ 12 kbar, data for KFe2As2 single crystals. Tc decreases under pressure with dTc/dP ~ -0.10 K/kbar. The inferred uniaxial, c-axis, pressure derivative is positive, dTc/dpc ~ 0.11 K/kbar. The data are analyzed in comparison with those for overdoped Fe-based superconductors. Arguments are presented that superconductivity in KFe2As2 may be different from the other overdoped, Fe-based materials in the 122 family

A unified approach for exactly solvable potentials in quantum mechanics using shift operators

We present a unified approach for solving and classifying exactly solvable potentials. Our unified approach encompasses many well-known exactly solvable potentials. Moreover, the new approach can be used to search systematically for a new class of solvable potentials.Comment: RevTex, 8 page

Quantum and Classical Spins on the Spatially Distorted Kagome Lattice: Applications to Volborthite

In Volborthite, spin-1/2 moments form a distorted Kagom\'e lattice, of corner sharing isosceles triangles with exchange constants $J$ on two bonds and $J'$ on the third bond. We study the properties of such spin systems, and show that despite the distortion, the lattice retains a great deal of frustration. Although sub-extensive, the classical ground state degeneracy remains very large, growing exponentially with the system perimeter. We consider degeneracy lifting by thermal and quantum fluctuations. To linear (spin wave) order, the degeneracy is found to stay intact. Two complementary approaches are therefore introduced, appropriate to low and high temperatures, which point to the same ordered pattern. In the low temperature limit, an effective chirality Hamiltonian is derived from non-linear spin waves which predicts a transition on increasing $J'/J$, from $\sqrt 3\times \sqrt 3$ type order to a new ferrimagnetic {\em striped chirality} order with a doubled unit cell. This is confirmed by a large-N approximation on the O($n$) model on this lattice. While the saddle point solution produces a line degeneracy, $O(1/n)$ corrections select the non-trivial wavevector of the striped chirality state. The quantum limit of spin 1/2 on this lattice is studied via exact small system diagonalization and compare well with experimental results at intermediate temperatures. We suggest that the very low temperature spin frozen state seen in NMR experiments may be related to the disconnected nature of classical ground states on this lattice, which leads to a prediction for NMR line shapes.Comment: revised, section V about exact diagonalization is extensively rewritten, 17 pages, 11 figures, RevTex 4, accepted by Phys. Rev.

Pinning modes and interlayer correlation in high magnetic field bilayer Wigner solids

We report studies of pinning mode resonances in the low total Landau filling (\nu) Wigner solid of a series of bilayer hole samples with negligible interlayer tunneling, and with varying interlayer separation d. Comparison of states with equal layer densities (p,p) to single layer states (p,0) produced {in situ} by biasing, indicates that there is interlayer quantum correlation in the solid at small d. Also, the resonance frequency at small d is decreased just near \nu=1/2 and 2/3, indicating the importance in the solid of correlations related to those in the fractional quantum Hall effects

Increasing β-catenin/Wnt3A activity levels drive mechanical strain-induced cell cycle progression through mitosis.

Mechanical force and Wnt signaling activate β-catenin-mediated transcription to promote proliferation and tissue expansion. However, it is unknown whether mechanical force and Wnt signaling act independently or synergize to activate β-catenin signaling and cell division. We show that mechanical strain induced Src-dependent phosphorylation of Y654 β-catenin and increased β-catenin-mediated transcription in mammalian MDCK epithelial cells. Under these conditions, cells accumulated in S/G2 (independent of DNA damage) but did not divide. Activating β-catenin through Casein Kinase I inhibition or Wnt3A addition increased β-catenin-mediated transcription and strain-induced accumulation of cells in S/G2. Significantly, only the combination of mechanical strain and Wnt/β-catenin activation triggered cells in S/G2 to divide. These results indicate that strain-induced Src phosphorylation of β-catenin and Wnt-dependent β-catenin stabilization synergize to increase β-catenin-mediated transcription to levels required for mitosis. Thus, local Wnt signaling may fine-tune the effects of global mechanical strain to restrict cell divisions during tissue development and homeostasis