Partition function loop series for a general graphical model: free energy corrections and message-passing equations

A loop series expansion for the partition function of a general statistical model on a graph is carried out. If the auxiliary probability distributions of the expansion are chosen to be a fixed point of the belief-propagation equation, the first term of the loop series gives the Bethe-Peierls free energy functional at the replica-symmetric level of the mean-field spin glass theory, and corrections are contributed only by subgraphs that are free of dangling edges. This result generalize the early work of Chertkov and Chernyak on binary statistical models. If the belief-propagation equation has multiple fixed points, a loop series expansion is performed for the grand partition function. The first term of this series gives the Bethe-Peierls free energy functional at the first-step replica-symmetry-breaking (RSB) level of the mean-field spin-glass theory, and corrections again come only from subgraphs that are free of dangling edges, provided that the auxiliary probability distributions of the expansion are chosen to be a fixed point of the survey-propagation equation. The same loop series expansion can be performed for higher-level partition functions, obtaining the higher-level RSB Bethe-Peierls free energy functionals (and the correction terms) and message-passing equations without using the Bethe-Peierls approximation.Comment: 12 pages with 1 figure included. Extensive revision on structure of the paper (no change in results). Accepted by Journal of Physica

Multipartite entanglement, quantum coherence, and quantum criticality in triangular and Sierpi\'nski fractal lattices

We investigate the quantum phase transitions of the transverse-field quantum Ising model on the triangular lattice and Sierpi\'nski fractal lattices by employing multipartite entanglement and quantum coherence along with the quantum renormalization group method. It is shown that the quantum criticalities of these high-dimensional models closely relate to the behaviors of the multipartite entanglement and quantum coherence. As the thermodynamic limit is approached, the first derivatives of multipartite entanglement and quantum coherence exhibit singular behaviors and the consistent finite-size scaling behaviors for each lattice are also obtained from the first derivatives. The multipartite entanglement and quantum coherence are demonstrated to be good indicators for detecting the quantum phase transitions in the triangular lattice and Sierpi\'nski fractal lattices. Furthermore, the factors that determine the relations between the critical exponents and the correlation length exponents for these models are diverse. For the triangular lattice, the decisive factor is the spatial dimension, while for the Sierpi\'nski fractal lattices, it is the Hausdorff dimension.Comment: 12 pages; 12 figure

Linear temperature behavior of thermopower and strong electron-electron scattering in thick F-doped SnO2_{2} films

Both the semi-classical and quantum transport properties of F-doped SnO$_2$ thick films ($\sim$1\,$\mu$m) were investigated experimentally. It is found that the resistivity caused by the thermal phonons obeys Bloch-Gr\"{u}neisen law from $\sim$90 to 300\,K, while only the diffusive thermopower, which varies linearly with temperature from 300 down to 10\,K, can be observed.The phonon-drag thermopower is completely suppressed due to the long electron-phonon relaxation time in the compound. These observations, together with the temperature independent characteristic of carrier concentration, indicate that the conduction electron in F-doped SnO$_2$ films behaves essentially like a free electron. At low temperatures, the electron-electron scattering dominates over the electron-phonon scattering and governs the inelastic scattering process. The theoretical predicated scattering rates for both large- and small-energy-transfer electron-electron scattering processes, which are negligibly weak in three-dimensional disordered conventional conductors, are quantitatively tested in this lower carrier concentration and free-electron-like highly degenerate semiconductor

Measuring Contextual Relationships in Temporal Social Networks by Circle Link

Network science has released its talents in social network analysis based on the information of static topologies. In reality social contacts are dynamic and evolve concurrently in time. Nowadays they can be recorded by ubiquitous information technologies, and generated into temporal social networks to provide new sights in social reality mining. Here, we define \emph{circle link} to measure contextual relationships in three empirical social temporal networks, and find that the tendency of friends having frequent continuous interactions with their common friend prefer to be close, which can be considered as the extension of Granovetter's hypothesis in temporal social networks. Finally, we present a heuristic method based on circle link to predict relationships and acquire acceptable results.Comment: 5 pages, 3 figure

Quantum Cryptography Using Einstein-Podolsky-Rosen Correlations of Continuous Variables

Quantum cryptography with the predetermined key was experimentally realized using Einstein-Podolsky-Rosen(EPR) correlations of continuously bright optical beams. Only one of two EPR correlated beams is transmitted with the signals modulated on quadrature phases and amplitudes, and the other one is retained by the authorized receiver. The modulated small signals are totally submerged in the large quantum noise of the signal beam, therefore nobody except the authorized receiver can decode the signals. Usability of imperfect quantum correlation, high transmission and detection efficiencies, and security provided by quantum mechanics are the favorable features of the presented scheme.Comment: 8 pages, 3 figures, 1 tabl

Spin relaxation via exchange with donor impurity-bound electrons

At low temperatures, electrons in semiconductors are bound to shallow donor impurity ions, neutralizing their charge in equilibrium. Inelastic scattering of other externally-injected conduction electrons accelerated by electric fields can excite transitions within the manifold of these localized states. Promotion of the bound electron into highly spin-orbit-mixed excited states drives a strong spin relaxation of the conduction electrons via exchange interactions, reminiscent of the Bir-Aronov-Pikus process where exchange occurs with valence band hole states. Through low-temperature experiments with silicon spin transport devices and complementary theory, we reveal the consequences of this previously unknown spin depolarization mechanism both below and above the impact ionization threshold

Local field modulated entanglment among three distant atoms

We extend the scheme for that proposed by S. Mancini and S. Bose (Phys. Rev. A \QTR{bf}{70}, 022307(2004)) to the case of triple-atom. Under mean field approximation, we obtain an effective Hamiltonian of triple-body Ising-model interaction. Furthermore, we stress on discussing the influence of the existence of a third-atom on the two-atom entanglement and testing the modulation effects of locally applied optical fields and fiber on the entanglement properties of our system.Comment: 10 pages, 4 figure

Quantum Entanglement transfer between spin-pairs

We investigate the transfer of entanglement from source particles (SP) to target particles (TP) in the Heisenberg interaction $H=\vec s_{1} \cdot \vec s_{2}$. In our research, TP are two qubits and SP are two qubits or qutrits. When TP are two qubits, we find that no matter what state the TP is initially prepared in, at the specific time $t=\pi$, the entanglement of TP can attain to 1 after interaction with SP which stay on the maximally entangled state. For the TP are two qutrits, we find that the maximal entanglement of TP after interaction is relative to the initial state of TP and always cannot attain to 1 to almost all of initial states of TP. But we discuss an iterated operation which can make the TP to the maximal entangled state.Comment: 6 pages; 4 figs. Accepted for publication in International Journal of Quantum Informatio

A position dependent atom-atom entanglement in real-time Cavity QED system

We study a special two-atom entanglement case in assumed Cavity QED experiment in which only one atom effectively exchanges a single photon with a cavity mode. We compute diatom entanglement under position-dependent atomic resonant dipole-dipole interaction (RDDI) for large interatomic separation limit. We show that the RDDI, even which is much smaller than the maximal atomic Rabi frequency, can induce distinct diatom entanglement. The peak entanglement (PE) reaches a maximum when RDDI strength can compare with the Rabi frequency of an atom

Field tuned atom-atom entanglement via diople-dipole interaction

We propose a simple scheme, in which only one atom couples to a cavity field, to entangle two two-level atoms. We connect two atoms with dipole-dipole interaction since one of them can move around the cavity. The results show that the peak entanglment does not depend on dipole-dipole interaction strength but on field density at a certain controlling time. So the field density can act as a switch for maximum entanglement (ME) generation.Comment: 7 pages, 5 figure