Efficient Schemes for Reducing Imperfect Collective Decoherences

We propose schemes that are efficient when each pair of qubits undergoes some imperfect collective decoherence with different baths. In the proposed scheme, each pair of qubits is first encoded in a decoherence-free subspace composed of two qubits. Leakage out of the encoding space generated by the imperfection is reduced by the quantum Zeno effect. Phase errors in the encoded bits generated by the imperfection are reduced by concatenation of the decoherence-free subspace with either a three-qubit quantum error correcting code that corrects only phase errors or a two-qubit quantum error detecting code that detects only phase errors, connected with the quantum Zeno effect again.Comment: no correction, 3 pages, RevTe

First passage time for random walks in heterogeneous networks

The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous networks, is not yet fully understood. Here, we study, both analytically and numerically, the scaling behavior of the FPT distribution to a given target node, averaged over all starting nodes. We find that random walks arrive quickly at a local hub, and therefore, the FPT distribution shows a crossover with respect to time from fast decay behavior (induced from the attractive effect to the hub) to slow decay behavior (caused by the exploring of the entire system). Moreover, the mean FPT is independent of the degree of the target node in the case of compact exploration. These theoretical results justify the necessity of using a random jump protocol (empirically used in search engines) and provide guidelines for designing an effective network to make information quickly accessible.Comment: 5 pages, 3 figure

Conserved cosmological structures in the one-loop superstring effective action

A generic form of low-energy effective action of superstring theories with one-loop quantum correction is well known. Based on this action we derive the complete perturbation equations and general analytic solutions in the cosmological spacetime. Using the solutions we identify conserved quantities characterizing the perturbations: the amplitude of gravitational wave and the perturbed three-space curvature in the uniform-field gauge both in the large-scale limit, and the angular-momentum of rotational perturbation are conserved independently of changing gravity sector. Implications for calculating perturbation spectra generated in the inflation era based on the string action are presented.Comment: 5 pages, no figure, To appear in Phys. Rev.

Compressibility of graphene

We develop a theory for the compressibility and quantum capacitance of disordered monolayer and bilayer graphene including the full hyperbolic band structure and band gap in the latter case. We include the effects of disorder in our theory, which are of particular importance at the carrier densities near the Dirac point. We account for this disorder statistically using two different averaging procedures: first via averaging over the density of carriers directly, and then via averaging in the density of states to produce an effective density of carriers. We also compare the results of these two models with experimental data, and to do this we introduce a model for inter-layer screening which predicts the size of the band gap between the low-energy conduction and valence bands for arbitary gate potentials applied to both layers of bilayer graphene. We find that both models for disorder give qualitatively correct results for gapless systems, but when there is a band gap at charge neutrality, the density of states averaging is incorrect and disagrees with the experimental data.Comment: 10 pages, 7 figures, RevTe