Symmetry protected fractional Chern insulators and fractional topological insulators

In this paper we construct fully symmetric wavefunctions for the spin-polarized fractional Chern insulators (FCI) and time-reversal-invariant fractional topological insulators (FTI) in two dimensions using the parton approach. We show that the lattice symmetry gives rise to many different FCI and FTI phases even with the same filling fraction $\nu$ (and the same quantized Hall conductance $\sigma_{xy}$ in FCI case). They have different symmetry-protected topological orders, which are characterized by different projective symmetry groups. We mainly focus on FCI phases which are realized in a partially filled band with Chern number one. The low-energy gauge groups of a generic $\sigma_{xy}=1/m\cdot e^2/h$ FCI wavefunctions can be either $SU(m)$ or the discrete group $Z_m$, and in the latter case the associated low-energy physics are described by Chern-Simons-Higgs theories. We use our construction to compute the ground state degeneracy. Examples of FCI/FTI wavefunctions on honeycomb lattice and checkerboard lattice are explicitly given. Possible non-Abelian FCI phases which may be realized in a partially filled band with Chern number two are discussed. Generic FTI wavefunctions in the absence of spin conservation are also presented whose low-energy gauge groups can be either $SU(m)\times SU(m)$ or $Z_m\times Z_m$. The constructed wavefunctions also set up the framework for future variational Monte Carlo simulations.Comment: 24 pages, 13 figures, published versio

A General SU(2) Formulation for Quantum Searching with Certainty

A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching condition relating the phase rotations in the algorithm, (2) a concise formula for evaluating the required number of iterations for the search, and (3) the final state after the search, with a phase angle in its amplitude of unity modulus. Moreover, the optimal choices and modifications of the phase angles in the Grover kernel is also studied.Comment: 8 pages, 2 figure

A General Phase Matching Condition for Quantum Searching Algorithm

A general consideration on the phase rotations in quantum searching algorithm is taken in this work. As four phase rotations on the initial state, the marked states, and the states orthogonal to them are taken account, we deduce a phase matching condition for a successful search. The optimal options for these phase are obtained consequently.Comment: 3 pages, 3 figure

Mitochondrial heat-shock protein hsp60 is essential for assembly of proteins imported into yeast mitochondria

A nuclear encoded mitochondrial heat-shock protein hsp60 is required for the assembly into oligomeric complexes of proteins imported into the mitochondrial matrix. hsp60 is a member of the 'chaperonin' class of protein factors, which include the Escherichia coli groEL protein and the Rubisco subunit-binding protein of chloroplast

Absorption cross sections of HCl and DCl at 135-232 nanometers: implications for photodissociation on Venus

Cross sections for photoabsorption of HCl and DCl are determined in the spectral region of 135-232 nm using radiation from a synchrotron light source. At wavelengths near the onset of absorption (λ > 200 nm), cross sections of HCl are approximately 5-10 times larger than those of DCl. These data are used to calculate rates of photodissociation of HCl and DCl in the Venusian atmosphere. For the entire wavelength region measured, the rate of photodissociation of DCl is only 16% that of HCl. The difference in rates of photodissociation contributes to the exceptionally large [D]/[H] ratio of the Venusian atmosphere

Non-Abelian Quantum Hall States and their Quasiparticles: from the Pattern of Zeros to Vertex Algebra

In the pattern-of-zeros approach to quantum Hall states, a set of data {n;m;S_a|a=1,...,n; n,m,S_a in N} (called the pattern of zeros) is introduced to characterize a quantum Hall wave function. In this paper we find sufficient conditions on the pattern of zeros so that the data correspond to a valid wave function. Some times, a set of data {n;m;S_a} corresponds to a unique quantum Hall state, while other times, a set of data corresponds to several different quantum Hall states. So in the latter cases, the patterns of zeros alone does not completely characterize the quantum Hall states. In this paper, We find that the following expanded set of data {n;m;S_a;c|a=1,...,n; n,m,S_a in N; c in R} provides a more complete characterization of quantum Hall states. Each expanded set of data completely characterize a unique quantum Hall state, at least for the examples discussed in this paper. The result is obtained by combining the pattern of zeros and Z_n simple-current vertex algebra which describes a large class of Abelian and non-Abelian quantum Hall states \Phi_{Z_n}^sc. The more complete characterization in terms of {n;m;S_a;c} allows us to obtain more topological properties of those states, which include the central charge c of edge states, the scaling dimensions and the statistics of quasiparticle excitations.Comment: 42 pages. RevTeX

Enhancement of deuterated ethane on Jupiter

We report laboratory measurements of cross sections of CH_3D and C_2H_5D in the extreme ultraviolet. The results are incorporated in a photochemical model for the deuterated hydrocarbons up to C_2 in the upper atmosphere of Jupiter, taking into account the fast reactions for exchanging H and D atoms between H_2 and CH_4, H + HD ↔ D + H_2, CH_3 + D ↔ CH_2D + H. Since there is no reliable kinetics measurement for the reaction, CH_2D + H → CH_3 + D, we use Yung et al.'s estimate for its rate constant. The strong temperature dependence for this reaction leads to large isotopic fractionation for CH_3D and C_2H_5D in the upper atmosphere of Jupiter, where their production rates depend on the abundance of deuterated methyl radical. The model predicts that the D/H ratio in deuterated ethane is about 15 times that of the bulk atmosphere. A confirmation of this result would provide a sensitive test of the photochemistry of hydrocarbons in the atmosphere of Jupiter