Does solitary wave solution persist for the long wave equation with small perturbations?

In this paper, persistence of solitary wave solutions of the regularized long wave equation with small perturbations are investigated by the geometric singular perturbation theory. Two different kinds of the perturbations are considered in this paper: one is the weak backward diffusion and dissipation, the other is the Marangoni effects. Indeed, the solitary wave persists under small perturbations. Furthermore, the different perturbations do affect the proper wave speed ensuring the persistence of the solitary waves. Finally, numerical simulations are utilized to confirm the theoretical results

Electric-field control of magnetic ordering in the tetragonal BiFeO3

We propose a way to use electric-field to control the magnetic ordering of the tetragonal BiFeO3. Based on systematic first-principles studies of the epitaxial strain effect on the ferroelectric and magnetic properties of the tetragonal BiFeO3, we find that there exists a transition from C-type to G-type antiferromagnetic (AFM) phase at in-plane constant a ~ 3.905 {\AA} when the ferroelectric polarization is along [001] direction. Such magnetic phase transition can be explained by the competition between the Heisenberg exchange constant J1c and J2c under the influence of biaxial strain. Interestingly, when the in-plane lattice constant enlarges, the preferred ferroelectric polarization tends to be canted and eventually lies in the plane (along [110] direction). It is found that the orientation change of ferroelectric polarization, which can be realized by applying external electric-field, has significant impact on the Heisenberg exchange parameters and therefore the magnetic orderings of tetragonal BiFeO3. For example, at a ~ 3.79 {\AA}, an electric field along [111] direction with magnitude of 2 MV/cm could change the magnetic ordering from C-AFM to G-AFM. As the magnetic ordering affects many physical properties of the magnetic material, e.g. magnetoresistance, we expect such strategy would provide a new avenue to the application of multiferroic materials.Comment: 4 pages, 4 figure

Effects of Zeeman spin splitting on the modular symmetry in the quantum Hall effect

Magnetic-field-induced phase transitions in the integer quantum Hall effect are studied under the formation of paired Landau bands arising from Zeeman spin splitting. By investigating features of modular symmetry, we showed that modifications to the particle-hole transformation should be considered under the coupling between the paired Landau bands. Our study indicates that such a transformation should be modified either when the Zeeman gap is much smaller than the cyclotron gap, or when these two gaps are comparable.Comment: 8 pages, 4 figure

An experimental study on Γ\Gamma(2) modular symmetry in the quantum Hall system with a small spin-splitting

Magnetic-field-induced phase transitions were studied with a two-dimensional electron AlGaAs/GaAs system. The temperature-driven flow diagram shows the features of the $\Gamma$(2) modular symmetry, which includes distorted flowlines and shiftted critical point. The deviation of the critical conductivities is attributed to a small but resolved spin splitting, which reduces the symmetry in Landau quantization. [B. P. Dolan, Phys. Rev. B 62, 10278.] Universal scaling is found under the reduction of the modular symmetry. It is also shown that the Hall conductivity could still be governed by the scaling law when the semicircle law and the scaling on the longitudinal conductivity are invalid. *corresponding author:[email protected]: The revised manuscript has been published in J. Phys.: Condens. Matte

Security proof of a three-state quantum key distribution protocol without rotational symmetry

Standard security proofs of quantum key distribution (QKD) protocols often rely on symmetry arguments. In this paper, we prove the security of a three-state protocol that does not possess rotational symmetry. The three-state QKD protocol we consider involves three qubit states, where the first two states, |0_z> and |1_z>, can contribute to key generation and the third state, |+>=(|0_z>+|1_z>)/\sqrt{2}, is for channel estimation. This protocol has been proposed and implemented experimentally in some frequency-based QKD systems where the three states can be prepared easily. Thus, by founding on the security of this three-state protocol, we prove that these QKD schemes are, in fact, unconditionally secure against any attacks allowed by quantum mechanics. The main task in our proof is to upper bound the phase error rate of the qubits given the bit error rates observed. Unconditional security can then be proved not only for the ideal case of a single-photon source and perfect detectors, but also for the realistic case of a phase-randomized weak coherent light source and imperfect threshold detectors. Our result on the phase error rate upper bound is independent of the loss in the channel. Also, we compare the three-state protocol with the BB84 protocol. For the single-photon source case, our result proves that the BB84 protocol strictly tolerates a higher quantum bit error rate than the three-state protocol; while for the coherent-source case, the BB84 protocol achieves a higher key generation rate and secure distance than the three-state protocol when a decoy-state method is used.Comment: 10 pages, 3 figures, 2 column

Spin-dependent thermoelectric transport through double quantum dots

We study thermoelectric transport through double quantum dots system with spin-dependent interdot coupling and ferromagnetic electrodes by means of the non-equilibrium Green function in the linear response regime. It is found that the thermoelectric coefficients are strongly dependent on the splitting of interdot coupling, the relative magnetic configurations and the spin polarization of leads. In particular, the thermoelectric efficiency can achieve considerable value in parallel configuration when the effective interdot coupling and tunnel coupling between QDs and the leads for spin-down electrons are small. Moreover, the thermoelectric efficiency increases with the intradot Coulomb interactions increasing and can reach very high value at an appropriate temperature. In the presence of the magnetic field, the spin accumulation in leads strongly suppresses the thermoelectric efficiency and a pure spin thermopower can be obtained.Comment: 5 figure

Quantum Hacking: Experimental demonstration of time-shift attack against practical quantum key distribution systems

Quantum key distribution (QKD) systems can send signals over more than 100 km standard optical fiber and are widely believed to be secure. Here, we show experimentally for the first time a technologically feasible attack, namely the time-shift attack, against a commercial QKD system. Our result shows that, contrary to popular belief, an eavesdropper, Eve, has a non-negligible probability (~4%) to break the security of the system. Eve's success is due to the well-known detection efficiency loophole in the experimental testing of Bell inequalities. Therefore, the detection efficiency loophole plays a key role not only in fundamental physics, but also in technological applications such as QKD.Comment: 5 pages, 3 figures. Substantially revised versio

Experimental Studies of Low-field Landau Quantization in Two-dimensional Electron Systems in GaAs/AlGaAs Heterostructures

By applying a magnetic field perpendicular to GaAs/AlGaAs two-dimensional electron systems, we study the low-field Landau quantization when the thermal damping is reduced with decreasing the temperature. Magneto-oscillations following Shubnikov-de Haas (SdH) formula are observed even when their amplitudes are so large that the deviation to such a formula is expected. Our experimental results show the importance of the positive magneto-resistance to the extension of SdH formula under the damping induced by the disorder.Comment: 9 pages, 3 figure

Tunnel splitting and quantum phase interference in biaxial ferrimagnetic particles at excited states

The tunneling splitting in biaxial ferrimagnetic particles at excited states with an explicit calculation of the prefactor of exponent is obtained in terms of periodic instantons which are responsible for tunneling at excited states and is shown as a function of magnetic field applied along an arbitrary direction in the plane of hard and medium axes. Using complex time path-integral we demonstrate the oscillation of tunnel splitting with respect to the magnitude and the direction of the magnetic field due to the quantum phase interference of two tunneling paths of opposite windings . The oscillation is gradually smeared and in the end the tunnel splitting monotonously increases with the magnitude of the magnetic field when the direction of the magnetic field tends to the medium axis. The oscillation behavior is similar to the recent experimental observation with Fe$_8$ molecular clusters. A candidate of possible experiments to observe the effect of quantum phase interference in the ferrimagnetic particles is proposed.Comment: 15 pages, 5 figures, acceptted to be pubblished in Physical Review

Rigidity of compact Riemannian spin Manifolds with Boundary

In this article, we prove new rigidity results for compact Riemannian spin manifolds with boundary whose scalar curvature is bounded from below by a non-positive constant. In particular, we obtain generalizations of a result of Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake \cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy