Gregory Levine

Integrating the nonintegrable: analytic structure of the Lorenz system revisited

Abstract A study of the complex time analytic structure of the Lorenz system in nonintegrable parameter regimes reveals the special sets of parameter values for which one (time-dependent) integral of motion exists. Furthermore, the analysis yields the exact form of the part of the integral with the highest homogeneous weight and a method to construct the rest of the integral. Recursive clustering of singularities in the chaotic regimes of the system is observed in computer studies and explained by a simple analytic argument. The analytic techniques used in these studies, a systematic resummation of a logarithmic psi-series, appears to be quite general and can provide explicit representations of a solution-even in the chaotic regimes-in the neighborhood of a given movable singularity. Furthermore, we suggest that this technique provides a type of renormalization program to study a wide class of nonintegrable systems.

Entanglement entropy in a boundary impurity model.

Boundary impurities are known to dramatically alter certain bulk properties of (1+1)-dimensional strongly correlated systems. The entanglement entropy of a zero temperature Luttinger liquid bisected by a single impurity is computed using a novel finite size scaling or bosonization scheme. For a Luttinger liquid of length 2L and UV cutoff epsilon, the boundary impurity correction (deltaSimp) to the logarithmic entanglement entropy (Sent proportional, variant lnL/epsilon scales as deltaSimp approximately yrlnL/epsilon, where yr is the renormalized backscattering coupling constant. In this way, the entanglement entropy within a region is related to scattering through the regions boundary. In the repulsive case (g<1), deltaSimp diverges (negatively) suggesting that the entropy vanishes. Our results are consistent with the recent conjecture that entanglement entropy decreases irreversibly along renormalization group flow.

Entanglement of a qubit with a single oscillator mode

We solve a model of a qubit strongly coupled to a massive environmental oscillator mode where the qubit back action is treated exactly. Using a Ginzburg-Landau formalism, we derive an effective action for this well-known localization transition. An entangled state emerges as an instanton in the collective qubit-environment degree of freedom and the resulting model is shown to be formally equivalent to a fluctuating gap model of a disordered Peierls chain. Below the transition, spectral weight is transferred to an exponentially small energy scale, leaving the qubit coherent but damped. Unlike the spin-boson model, coherent and effectively localized behaviors may coexist.

Photoluminescence of chemically deposited CdSe nanocrystallites: Effects of crystallite polydispersity

CdSe nanocrystalline films were prepared by chemical solution deposition. Photoluminescence (PL) spectroscopy was utilized to characterize the prepared films. We observed that the PL peak position of the films gradually shifts from ∼595 to ∼670 nm as the deposition time increases. Also, the PL spectra become broadened with the increase of deposition time. The data indicate that as the deposition time increases, the crystal size increases; but once the crystal size reaches a critical volume, crystal growth terminates. We used the effective mass approximation to analyze the effects of crystallite polydispersity upon the shape of the PL spectra.

Topological entropy of realistic quantum Hall wave functions

The entanglement entropy of the incompressible states of a realistic quantum Hall system are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is believed to carry information about topologic order in the ground state, was extracted for filling factors 1/3, 1/5 and 5/2. The results for 1/3 and 1/5 are consistent with the topological entanglement entropy for the Laughlin wave function. The 5/2 state exhibits a topological entanglement entropy consistent with the Moore-Read wave function.

Full counting statistics in a disordered free fermion system

The Full Counting Statistics (FCS) is studied for a one-dimensional system of non-interacting fermions with and without disorder. For two unbiased

Linear and nonlinear susceptibilities of a decoherent two-level system

L

Entanglement entropy of random fractional quantum Hall systems

site lattices connected at time

TOPOLOGICAL ENTANGLEMENT ENTROPY IN THE SECOND LANDAU LEVEL

t=0

QUANTUM EFFECT ON SHOT NOISE SUPPRESSION IN TRANSPORT THROUGH MICROSTRUCTURES

, the charge variance increases as the natural logarithm of