Graphical description of local Gaussian operations for continuous-variable weighted graph states

The form of a local Clifford (LC, also called local Gaussian (LG)) operation for the continuous-variable (CV) weighted graph states is presented in this paper, which is the counterpart of the LC operation of local complementation for qubit graph states. The novel property of the CV weighted graph states is shown, which can be expressed by the stabilizer formalism. It is distinctively different from the qubit weighted graph states, which can not be expressed by the stabilizer formalism. The corresponding graph rule, stated in purely graph theoretical terms, is described, which completely characterizes the evolution of CV weighted graph states under this LC operation. This LC operation may be applied repeatedly on a CV weighted graph state, which can generate the infinite LC equivalent graph states of this graph state. This work is an important step to characterize the LC equivalence class of CV weighted graph states.Comment: 5 pages, 6 figure

Scaling in the time-dependent failure of a fiber bundle with local load sharing

We study the scaling behaviors of a time-dependent fiber-bundle model with local load sharing. Upon approaching the complete failure of the bundle, the breaking rate of fibers diverges according to $r(t)\propto (T_f-t)^{-\xi}$, where $T_f$ is the lifetime of the bundle, and $\xi \approx 1.0$ is a quite universal scaling exponent. The average lifetime of the bundle $$ scales with the system size as $N^{-\delta}$, where $\delta$ depends on the distribution of individual fiber as well as the breakdown rule.Comment: 5 pages, 4 eps figures; to appear in Phys. Rev.

Single-particle subband structure of Quantum Cables

We proposed a model of Quantum Cable in analogy to the recently synthesized coaxial nanocable structure [Suenaga et al. Science, 278, 653 (1997); Zhang et al. ibid, 281, 973 (1998)], and studied its single-electron subband structure. Our results show that the subband spectrum of Quantum Cable is different from either double-quantum-wire (DQW) structure in two-dimensional electron gas (2DEG) or single quantum cylinder. Besides the double degeneracy of subbands arisen from the non-abelian mirrow reflection symmetry, interesting quasicrossings (accidental degeneracies), anticrossings and bundlings of Quantum Cable energy subbands are observed for some structure parameters. In the extreme limit (barrier width tends to infinity), the normal degeneracy of subbands different from the DQW structure is independent on the other structure parameters.Comment: 12 pages, 9 figure

Giant circular dichroism of a molecule in a region of strong plasmon resonances between two neighboring gold nanocrystals

We report on giant circular dichroism (CD) of a molecule inserted into a plasmonic hot spot. Naturally occurring molecules and biomolecules have typically CD signals in the UV range, whereas plasmonic nanocrystals exhibit strong plasmon resonances in the visible spectral interval. Therefore, excitations of chiral molecules and plasmon resonances are typically off-resonant. Nevertheless, we demonstrate theoretically that it is possible to create strongly-enhanced molecular CD utilizing the plasmons. This task is doubly challenging since it requires both creation and enhancement of the molecular CD in the visible region. We demonstrate this effect within the model which incorporates a chiral molecule and a plasmonic dimer. The associated mechanism of plasmonic CD comes from the Coulomb interaction which is greatly amplified in a plasmonic hot spot.Comment: Manuscript: 4+pages, 4 figures; Supplemental_Material: 10 pages, 7 figure