Acyclic orientations on the Sierpinski gasket

We study the number of acyclic orientations on the generalized two-dimensional Sierpinski gasket $SG_{2,b}(n)$ at stage $n$ with $b$ equal to two and three, and determine the asymptotic behaviors. We also derive upper bounds for the asymptotic growth constants for $SG_{2,b}$ and $d$-dimensional Sierpinski gasket $SG_d$.Comment: 20 pages, 8 figures and 6 table

Chiral Vertex Operators in Off-Conformal Theory: The Sine-Gordon Example

We study chiral vertex operators in the sine-Gordon [SG] theory, viewed as an off-conformal system. We find that these operators, which would have been primary fields in the conformal limit, have interesting and, in some ways, unexpected properties in the SG model. Some of them continue to have scale- invariant dynamics even in the presence of the non-conformal cosine interaction. For instance, it is shown that the Mandelstam operator for the bosonic representation of the Fermi field does {\it not} develop a mass term in the SG theory, contrary to what the real Fermi field in the massive Thirring model is expected to do. It is also shown that in the presence of the non-conformal interactions, some vertex operators have unique Lorentz spins, while others do not.Comment: 32 pages, Univ. of Illinois Preprint # ILL-(TH)-93-1

Anomalous Rabi oscillations in multilevel quantum systems

We show that the excitation probability of a state within a manifold of levels undergoes Rabi oscillations with frequency determined by the energy difference between the states and not by the pulse area for sufficiently strong pulses. The observed dynamics can be used as a procedure for robust state preparation as an alternative to adiabatic passage and as a useful spectroscopic method.Comment: 9 pages, 3 figure

Stabilizing the forming process in unipolar resistance switching using an improved compliance current limiter

The high reset current IR in unipolar resistance switching now poses major obstacles to practical applications in memory devices. In particular, the first IR-value after the forming process is so high that the capacitors sometimes do not exhibit reliable unipolar resistance switching. We found that the compliance current Icomp is a critical parameter for reducing IR-values. We therefore introduced an improved, simple, easy to use Icomp-limiter that stabilizes the forming process by drastically decreasing current overflow, in order to precisely control the Icomp- and subsequent IR-values.Comment: 15 pages, 4 figure

Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

Predictability of reset switching voltages in unipolar resistance switching

In unipolar resistance switching of NiO capacitors, Joule heating in the conducting channels should cause a strong nonlinearity in the low resistance state current-voltage (I-V) curves. Due to the percolating nature of the conducting channels, the reset current IR, can be scaled to the nonlinear coefficient Bo of the I-V curves. This scaling relationship can be used to predict reset voltages, independent of NiO capacitor size; it can also be applied to TiO2 and FeOy capacitors. Using this relation, we developed an error correction scheme to provide a clear window for separating reset and set voltages in memory operations