Topological Characterization of Extended Quantum Ising Models

We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.Comment: 5 pages, 3 figure

A pairwise maximum entropy model describes energy landscape for spiral wave dynamics of cardiac fibrillation

Heart is an electrically-connected network. Spiral wave dynamics of cardiac fibrillation shows chaotic and disintegrated patterns while sinus rhythm shows synchronized excitation patterns. To determine functional interactions between cardiomyocytes during complex fibrillation states, we applied a pairwise maximum entropy model (MEM) to the sequential electrical activity maps acquired from the 2D computational simulation of human atrial fibrillation. Then, we constructed energy landscape and estimated hierarchical structure among the different local minima (attractors) to explain the dynamic properties of cardiac fibrillation. Four types of the wave dynamics were considered: sinus rhythm; single stable rotor; single rotor with wavebreak; and multiple wavelet. The MEM could describe all types of wave dynamics (both accuracy and reliability>0.9) except the multiple random wavelet. Both of the sinus rhythm and the single stable rotor showed relatively high pairwise interaction coefficients among the cardiomyocytes. Also, the local energy minima had relatively large basins and high energy barrier, showing stable attractor properties. However, in the single rotor with wavebreak, there were relatively low pairwise interaction coefficients and a similar number of the local minima separated by a relatively low energy barrier compared with the single stable rotor case. The energy landscape of the multiple wavelet consisted of a large number of the local minima separated by a relatively low energy barrier, showing unstable dynamics. These results indicate that the MEM provides information about local and global coherence among the cardiomyocytes beyond the simple structural connectivity. Energy landscape analysis can explain stability and transitional properties of complex dynamics of cardiac fibrillation, which might be determined by the presence of 'driver' such as sinus node or rotor.Comment: Presented at the 62nd Biophysical Society Annual Meeting, San Francisco, California, 201

Gaussian enveloped decoherence of the atomic states in quantum cavity

We revisit the decoherence of the atomic state in the resonant Jaynes-Cummings model with the field initially being in a coherent state. We show that the purity of the atom exhibits oscillating Gaussian dependence on the time with a width independent of the initial atomic state. It is also shown that when the atom and the coherent state match each other in phase, the atomic decoherence is Gaussian time dependence.Comment: 8 pages, 2 figure

A Study of S doped ZnSb

We report on S-doping of ZnSb for S concentrations ranging from 0.02 at% to 2.5 at%. There are no previous reports on S-doping. ZnSb is a thermoelectric material with some advantages for the temperature range 400 K - 600 K. The solid solubility of S in ZnSb was estimated to be lower than 0.1% from observations of precipitates by scanning microscopy. Hall and Seebeck measurements were performed as a function of temperature from 6K to 623 K. The temperature dependence of the electrical properties suggests that S introduces neutral scattering centers for holes in the p-type material. An increase in hole concentration by S is argued by defect reactions involving Zn vacancies

How to Evolve Safe Control Strategies

Autonomous space vehicles need adaptive control strategies that can accommodate unanticipated environmental conditions. The evaluation of new strategies can often be done only by actually trying them out in the real physical environment. Consequently, a candidate control strategy must be deemed safe--i.e., it won't damage any systems--prior to being tested online. How to do this efficiently has been a challenging problem. We propose using evolutionary programming in conjunction with a formal verification technique (called model checking) to evolve candidate control strategies that are guaranteed to be safe for implementation and evaluation.Comment: 3 pages, 1 figur

Quantum-state transfer between atom and cavity field in Jaynes-Cummings model

We present a scheme for transferring quantum state between atom and cavity field in Jaynes-Cummings model. It is based on the fact that the atom in a cavity can induce the generation of modified coherent states, which can be shown to be macroscopically distinguishable. The application on two-cavity system provides an alternative scheme for preparation of non-local superpositions of quasi-classical light states. Numerical simulation shows that the proposed schemes are efficient.Comment: 14 pages, 5 figure

Application of the Complex Monge-Ampere equation to the study of proper holomorphic mappings of strictly pseudoconvex domains

We construct a special plurisubharmonic defining function for a smoothly bounded strictly pseudoconvex domain so that the determinant of the complex Hessian vanishes to high order on the boundary. This construction, coupled with regularity of solutions of complex Monge-Ampere equation and the reflection principle, enables us to give a new proof of the Fefferman mapping theorem

Measurement of the Geometrical Decay of the Spin Hall Effect in Fe(CsAu) Multi Layers

The anomalous Hall effect of Fe(CsAu) is investigated. Electrons with spin up and down experience a different degree of specular reflection at the FeCs interface. This yields a different mean free path for the two spin orientations. In the presence of an electric field parallel to the film plane one obtains a spin current in addition to the charge current. If one introduces impurities with a large spin-orbit scattering into the Cs host then the combination of spin current and spin-orbit scattering yields an anomalous Hall effect. By building in situ multi layers of CsAu (5nm of Cs and 0.04 atomic layers of Au) on top of an Fe film one can measure the relative magnitude of the spin current normal to the film. Within the accuracy of the experimental data the spin current in Fe(CsAu) decays exponentially with a decay length of 20nm. PACS: 73.50.-h, 72.25.Ba, 73.40.Jn, 73.21.C

Elliptic boundary value problems for the inhomogeneous Laplace equation on bounded domains

Elliptic estimates in Hardy classes are proved on domains with minimally smooth boundary. The methodology is different from the original methods of Chang/Krantz/Stein

Chern number in Ising models with spatially modulated real and complex fields

We study an one-dimensional transverse field Ising model with additional periodically modulated real and complex fields. It is shown that both models can be mapped on a pseudo spin system in the k space in the aid of an extended Bogoliubov transformation. This allows us to introduce the geometric quantity, the Chern number, to identify the nature of quantum phases. Based on the exact solution, we find that the spatially modulated real and complex fields rearrange the phase boundaries from that of the ordinary Ising model, which can be characterized by the Chern numbers defined in the context of Dirac and biorthonormal inner products, respectively.Comment: 5 pages, 13 figure