Piecewise-linear maps with heterogeneous chaos

Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic invariant set is heterogeneous when arbitrarily close to each point of the set there are different periodic points with different numbers of unstable dimensions. We call such dynamics heterogeneous chaos (or hetero-chaos), While we believe it is common for physical systems to be hetero-chaotic, few explicit examples have been proved to be hetero-chaotic. Here we present two more explicit dynamical systems that are particularly simple and tractable with computer. It will give more intuition as to how complex even simple systems can be. Our maps have one dense set of periodic points whose orbits are 1D unstable and another dense set of periodic points whose orbits are 2D unstable. Moreover, they are ergodic relative to the Lebesgue measure.Comment: 16 pages, 9 figure

Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two- dimensionalcorrelation spectroscopy

We theoretically investigate an electron transfer (ET) process in a dissipative environment by means of two-dimensional (2D) correlation spectroscopy. We extend the reduced hierarchy equations of motion approach to include both overdamped Drude and underdamped Brownian modes. While the overdamped mode describes the inhomogeneity of a system in the slow modulation limit, the underdamped mode expresses the primary vibrational mode coupled with the electronic states. We outline a procedure for calculating 2D correlation spectrum that incorporates the ET processes. The present approach has the capability of dealing with system-bath coherence under an external perturbation, which is important to calculate nonlinear response functions for non-Markovian noise. The calculated 2D spectrum exhibits the effects of the ET processes through the presence of ET transition peaks along the $\Omega_1$ axis, as well as the decay of echo signals.Comment: 28 pages, 8 figures; J. Chem. Phys. 137 (2012

Molecular-dynamics simulations of glass formation and crystallization in binary liquid metals: Cu-Ag and Cu-Ni

We used molecular dynamics (MD) to obtain an atomistic description of the melting, glass formation, and crystallization processes in metal alloys. These studies use the quantum Sutton-Chen many-body potentials for Cu, Ni, and Ag to examine the Cu4Ag6 and CuNi alloys. Using cooling rates in the range of 2×10^12 to 4×10^14 K/s, we find that CuNi and pure Cu always form a face-centered-cubic (fcc) crystal while Cu4Ag6 always forms a glass (with Tg decreasing as the quench rate increases). The crystal formers have radius ratios of 1.025 (CuNi) and 1.00 (Cu) while the glass former (CuAg) has a ratio of 1.13, confirming the role of size mismatch in biasing toward glass formation

A Field-Theoretic Approach to Connes' Gauge Theory on M4×Z2M_4\times Z_2

Connes' gauge theory on $M_4\times Z_2$ is reformulated in the Lagrangian level. It is pointed out that the field strength in Connes' gauge theory is not unique. We explicitly construct a field strength different from Connes' one and prove that our definition leads to the generation-number independent Higgs potential. It is also shown that the nonuniqueness is related to the assumption that two different extensions of the differential geometry are possible when the extra one-form basis $\chi$ is introduced to define the differential geometry on $M_4\times Z_2$. Our reformulation is applied to the standard model based on Connes' color-flavor algebra. A connection between the unimodularity condition and the electric charge quantization is then discussed in the presence or absence of $\nu_R$.Comment: LaTeX file, 16 page

Correlated fluctuations in the exciton dynamics and spectroscopy of DNA

The absorption of ultraviolet light creates excitations in DNA, which subsequently start moving in the helix. Their fate is important for an understanding of photo damage, and is determined by the interplay of electronic couplings between bases and the structure of the DNA environment. We model the effect of dynamical fluctuations in the environment and study correlation, which is present when multiple base pairs interact with the same mode in the environment. We find that the correlations strongly affect the exciton dynamics, and show how they are observed in the decay of the anisotropy as a function of a coherence and a population time in a non-linear optical experiment