Lower Bounds on the Ground State Entropy of the Potts Antiferromagnet on Slabs of the Simple Cubic Lattice

We calculate rigorous lower bounds for the ground state degeneracy per site, $W$, of the $q$-state Potts antiferromagnet on slabs of the simple cubic lattice that are infinite in two directions and finite in the third and that thus interpolate between the square (sq) and simple cubic (sc) lattices. We give a comparison with large-$q$ series expansions for the sq and sc lattices and also present numerical comparisons.Comment: 7 pages, late

Quantal interferometry with dissipative internal motion

In presence of dissipation, quantal states may acquire complex-valued phase effects. We suggest a notion of dissipative interferometry that accommodates this complex-valued structure and that may serve as a tool for analyzing the effect of certain kinds of external influences on quantal interference. The concept of mixed-state phase and concomitant gauge invariance is extended to dissipative internal motion. The resulting complex-valued mixed-state interference effects lead to well-known results in the unitary limit and in the case of dissipative motion of pure quantal states. Dissipative interferometry is applied to fault-tolerant geometric quantum computation.Comment: Slight revision, journal reference adde

Shaped nozzles for cryogenic buffer gas beam sources

Cryogenic buffer gas beams are important sources of cold molecules. In this work we explore the use of a converging-diverging nozzle with a buffer-gas beam. We find that, under appropriate circumstances, the use of a nozzle can produce a beam with improved collimation, lower transverse temperatures, and higher fluxes per solid angle

Spin freezing and dynamics in Ca_{3}Co_{2-x}Mn_{x}O_{6} (x ~ 0.95) investigated with implanted muons: disorder in the anisotropic next-nearest neighbor Ising model

We present a muon-spin relaxation investigation of the Ising chain magnet Ca_{3}Co_{2-x}Mn_{x}O_{6} (x~0.95). We find dynamic spin fluctuations persisting down to the lowest measured temperature of 1.6 K. The previously observed transition at around T ~18 K is interpreted as a subtle change in dynamics for a minority of the spins coupling to the muon that we interpret as spins locking into clusters. The dynamics of this fraction of spins freeze below a temperature T_{SF}~8 K, while a majority of spins continue to fluctuate. An explanation of the low temperature behavior is suggested in terms of the predictions of the anisotropic next-nearest-neighbor Ising model.Comment: 4 pages, 2 figure

Bounding and approximating parabolas for the spectrum of Heisenberg spin systems

We prove that for a wide class of quantum spin systems with isotropic Heisenberg coupling the energy eigenvalues which belong to a total spin quantum number S have upper and lower bounds depending at most quadratically on S. The only assumption adopted is that the mean coupling strength of any spin w.r.t. its neighbours is constant for all N spins. The coefficients of the bounding parabolas are given in terms of special eigenvalues of the N times N coupling matrix which are usually easily evaluated. In addition we show that the bounding parabolas, if properly shifted, provide very good approximations of the true boundaries of the spectrum. We present numerical examples of frustrated rings, a cube, and an icosahedron.Comment: 8 pages, 3 figures. Submitted to Europhysics Letter

Approximating Spectral Impact of Structural Perturbations in Large Networks

Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as synchronization and cascading processes on networks. Here we develop a theory for estimating the change of the largest eigenvalue of the adjacency matrix or the extreme eigenvalues of the graph Laplacian when small but arbitrary set of links are added or removed from the network. We demonstrate the effectiveness of our approximation schemes using both real and artificial networks, showing in particular that we can accurately obtain the spectral ranking of small subgraphs. We also propose a local iterative scheme which computes the relative ranking of a subgraph using only the connectivity information of its neighbors within a few links. Our results may not only contribute to our theoretical understanding of dynamical processes on networks, but also lead to practical applications in ranking subgraphs of real complex networks.Comment: 9 pages, 3 figures, 2 table

Determination of characteristic muon precession and relaxation signals in FeAs and FeAs2, possible impurity phases in pnictide superconductors

We report muon-spin relaxation measurements of highly homogeneous samples of FeAs and FeAs2, both previously found as impurity phases in some samples of recently synthesized pnictide superconductors. We observe well defined muon precession in the FeAs sample with two precession frequencies of 38.2(3) and 22.7(9) MHz at 7.5 K, with the majority of the amplitude corresponding to the lower frequency component. In FeAs2 we confirm previous measurements showing that no long-ranged magnetic order occurs above 2 K and measure the muon spin relaxation rate, which increases on cooling. Our results exclude the possibility that previous muon-spin relaxation measurements of pnictide superconductors have been measuring the effect of these possible impurities.Comment: 4 pages, 3 figures, corrected Figure

Non-linear Microwave Surface Impedance of Epitaxial HTS Thin Films in Low DC Magnetic Fields

We have carried out non-linear microwave (8 GHz) surface impedance measurements of three YBaCuO thin films in dc magnetic fields $H_{dc}$ (parallel to c axis) up to 12 mT using a coplanar resonator technique. In zero dc field the three films, deposited by the same method, show a spread of low-power residual surface resistance, $R_{res}$ and penetration depth, $\lambda$ (T=15 K) within a factor of 1.9. However, they exhibit dramatically different microwave field, $H_{rf}$ dependences of the surface resistance, $R_s$, but universal $X_s(H_{rf})$ dependence. Application of a dc field was found to affect not only absolute values of $R_s$ and $X_s$, but the functional dependences $R_s(H_{rf})$ and $X_s(H_{rf})$ as well. For some of the samples the dc field was found to decrease $R_s$ below its zero-field low-power value.Comment: 4 pages, 4 figures. To be published in IEEE Trans. Appl. Supercond., June 199