Spin-one bosons in low dimensional Mott insulating states

We analyze the strong coupling limit of spin-one bosons in low dimensional Mott insulating states. In 1D lattices, for an odd number of bosons per site ($N_0$), the ground state is a dimerized valence bond crystal state with a two-fold degeneracy; the low lying elementary spin excitations carry spin one. For an even number of bosons per site, the ground state is a nondegenerate spin singlet Mott state. We also argue that in a square lattice in a quantum disordered limit the ground states should be dimerized valence bond crystals for an odd integer $N_0$. Finally, we briefly report results for non-integer numbers of bosons per site in one-dimensional lattices.Comment: 5 pages; discussions on non-integer case have been shortene

Random Walk over Basins of Attraction to Construct Ising Energy Landscapes

An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal averages over each basin of attraction. It is applied to the SK spin glass Hamiltonian where existing methods have difficulties even for a moderate number of spins. Finite-size results are used to make predictions in the thermodynamic limit that match theoretical approximations and recent findings on the free energy landscapes of SK spin glasses.Comment: 2 Figures and 1 Table. To be published in Physical Review Letter

Surface-wave group-delay and attenuation kernels

We derive both 3-D and 2-D Fréchet sensitivity kernels for surface-wave group-delay and anelastic attenuation measurements. A finite-frequency group-delay exhibits 2-D off-ray sensitivity either to the local phase-velocity perturbation δc/c or to its dispersion ω(∂/∂ω)(δc/c) as well as to the local group-velocity perturbation δC/C. This dual dependence makes the ray-theoretical inversion of measured group delays for 2-D maps of δC/C a dubious procedure, unless the lateral variations in group velocity are extremely smooth

Resolvable Mendelsohn designs and finite Frobenius groups

We prove the existence and give constructions of a $(p(k)-1)$-fold perfect resolvable $(v, k, 1)$-Mendelsohn design for any integers $v > k \ge 2$ with $v \equiv 1 \mod k$ such that there exists a finite Frobenius group whose kernel $K$ has order $v$ and whose complement contains an element $\phi$ of order $k$, where $p(k)$ is the least prime factor of $k$. Such a design admits $K \rtimes \langle \phi \rangle$ as a group of automorphisms and is perfect when $k$ is a prime. As an application we prove that for any integer $v = p_{1}^{e_1} \ldots p_{t}^{e_t} \ge 3$ in prime factorization, and any prime $k$ dividing $p_{i}^{e_i} - 1$ for $1 \le i \le t$, there exists a resolvable perfect $(v, k, 1)$-Mendelsohn design that admits a Frobenius group as a group of automorphisms. We also prove that, if $k$ is even and divides $p_{i} - 1$ for $1 \le i \le t$, then there are at least $\varphi(k)^t$ resolvable $(v, k, 1)$-Mendelsohn designs that admit a Frobenius group as a group of automorphisms, where $\varphi$ is Euler's totient function.Comment: Final versio

Lepton flavor-changing Scalar Interactions and Muon g−2g-2

A systematic investigation on muon anomalous magnetic moment and related lepton flavor-violating process such as \m\to e\g, \t\to e\g and \t\to \m\g is made at two loop level in the models with flavor-changing scalar interactions. The two loop diagrams with double scalar exchanges are studied and their contributions are found to be compatible with the ones from Barr-Zee diagram. By comparing with the latest data, the allowed ranges for the relevant Yukawa couplings $Y_{ij}$ in lepton sector are obtained. The results show a hierarchical structure of Y_{\m e, \t e} \ll Y_{\m \t} \simeq Y_{\m\m} in the physical basis if $\Delta a_{\mu}$ is found to be $>50\times 10^{-11}$. It deviates from the widely used ansatz in which the off diagonal elements are proportional to the square root of the products of related fermion masses. An alternative Yukawa coupling matrix in the lepton sector is suggested to understand the current data. With such a reasonable Yukawa coupling ansatz, the decay rate of \t\to \m\g is found to be near the current experiment upper bound.Comment: 15 pages, Revtex, 9 figures, published version in EPJ