Lyapunov Spectra in SU(2) Lattice Gauge Theory

We develop a method for calculating the Lyapunov characteristic exponents of lattice gauge theories. The complete Lyapunov spectrum of SU(2) gauge theory is obtained and Kolmogorov-Sinai entropy is calculated. Rapid convergence with lattice size is found.Comment: 7pp, DUKE-TH-93-5

Temperature Dependent Empirical Pseudopotential Theory For Self-Assembled Quantum Dots

We develop a temperature dependent empirical pseudopotential theory to study the electronic and optical properties of self-assembled quantum dots (QDs) at finite temperature. The theory takes the effects of both lattice expansion and lattice vibration into account. We apply the theory to the InAs/GaAs QDs. For the unstrained InAs/GaAs heterostructure, the conduction band offset increases whereas the valence band offset decreases with increasing of the temperature, and there is a type-I to type-II transition at approximately 135 K. Yet, for InAs/GaAs QDs, the holes are still localized in the QDs even at room temperature, because the large lattice mismatch between InAs and GaAs greatly enhances the valence band offset. The single particle energy levels in the QDs show strong temperature dependence due to the change of confinement potentials. Because of the changes of the band offsets, the electron wave functions confined in QDs increase by about 1 - 5%, whereas the hole wave functions decrease by about 30 - 40% when the temperature increases from 0 to 300 K. The calculated recombination energies of exciton, biexciton and charged excitons show red shifts with increasing of the temperature, which are in excellent agreement with available experimental data

Hamiltonian Dynamics of Yang-Mills Fields on a Lattice

We review recent results from studies of the dynamics of classical Yang-Mills fields on a lattice. We discuss the numerical techniques employed in solving the classical lattice Yang-Mills equations in real time, and present results exhibiting the universal chaotic behavior of nonabelian gauge theories. The complete spectrum of Lyapunov exponents is determined for the gauge group SU(2). We survey results obtained for the SU(3) gauge theory and other nonlinear field theories. We also discuss the relevance of these results to the problem of thermalization in gauge theories.Comment: REVTeX, 51 pages, 20 figure

A 1.3 cm Line Survey toward Orion KL

Orion KL has served as a benchmark for spectral line searches throughout the (sub)millimeter regime. The main goal is to systematically study spectral characteristics of Orion KL in the 1.3 cm band. We carried out a spectral line survey (17.9 GHz to 26.2 GHz) with the Effelsberg-100 m telescope towards Orion KL. We find 261 spectral lines, yielding an average line density of about 32 spectral features per GHz above 3$\sigma$. The identified lines include 164 radio recombination lines (RRLs) and 97 molecular lines. A total of 23 molecular transitions from species known to exist in Orion KL are detected for the first time in the interstellar medium. Non-metastable 15NH3 transitions are detected in Orion KL for the first time. Based on the velocity information of detected lines and the ALMA images, the spatial origins of molecular emission are constrained and discussed. A narrow feature is found in SO2 ($8_{1,7}-7_{2,6}$), possibly suggesting the presence of a maser line. Column densities and fractional abundances relative to H2 are estimated for 12 molecules with LTE methods. Rotational diagrams of non-metastable 14NH3 transitions with J=K+1 to J=K+4 yield different results; metastable 15NH3 is found to have a higher excitation temperature than non-metastable 15NH3, indicating that they may trace different regions. Elemental and isotopic abundance ratios are estimated: 12C/13C=63+-17, 14N/15N=100+-51, D/H=0.0083+-0.0045. The dispersion of the He/H ratios derived from H$\alpha$/He$\alpha$ pairs to H$\delta$/He$\delta$ pairs is very small, which is consistent with theoretical predictions that the departure coefficients bn factors for hydrogen and helium are nearly identical. Based on a non-LTE code neglecting excitation by the infrared radiation field and a likelihood analysis, we find that the denser regions have lower kinetic temperature, which favors an external heating of the Hot Core.Comment: 70 pages, 26 figures, 12 tables, accepted for publication in A&A. Figs. 1, 2, 8, 9 have been downsize

Numerical evidences of spin-1/2 chain approaching spin-1 chain

In this article, we study the one dimensional Heisenberg spin-1/2 alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and density matrix renormalization groups (DMRG) method, we discuss how the system approaches to the AF uniform spin-1 chain under certain condition. When the ratio of AF to FM coupling strength}$\alpha$ $(\alpha=J_{AF}/J_{F})$ \textit{is very small, the physical quantities of the alternating bond chain such as the spin-spin correlation, the string correlation function and the spin density coincide with that of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with small}$\alpha$\textit{limit. In addition, the Haldane gap of the AF uniform spin-1 chain is 4-times of the gap of the system considered.Comment: 9pages,8page

Quantifying the complexity of random Boolean networks

We study two measures of the complexity of heterogeneous extended systems, taking random Boolean networks as prototypical cases. A measure defined by Shalizi et al. for cellular automata, based on a criterion for optimal statistical prediction [Shalizi et al., Phys. Rev. Lett. 93, 118701 (2004)], does not distinguish between the spatial inhomogeneity of the ordered phase and the dynamical inhomogeneity of the disordered phase. A modification in which complexities of individual nodes are calculated yields vanishing complexity values for networks in the ordered and critical regimes and for highly disordered networks, peaking somewhere in the disordered regime. Individual nodes with high complexity are the ones that pass the most information from the past to the future, a quantity that depends in a nontrivial way on both the Boolean function of a given node and its location within the network.Comment: 8 pages, 4 figure

Towards the Equation of State of Classical SU(2) Lattice Gauge Theory

We determine numerically the full complex Lyapunov spectrum of SU(2) Yang-Mills fields on a 3-dimensional lattice from the classical chaotic dynamics. The equation of state, S(E), is determined from the Kolmogorov-Sinai entropy extrapolated to the large size limit.Comment: 12 pages, 8 PS figures, LaTe