Classically Integrable Cosmological Models with a Scalar Field

New classes of classically integrable models in the cosmological theories with a scalar field are obtained by using freedoms of defining time and fields. In particular, some models with the sum of exponential potentials in the flat spatial metric are shown to be integrable. The model with the Sine-Gordon potential can be solved in terms of analytic continuation of the non-periodic Toda field theory.Comment: 10 pages, Late

Superconductivity in spinel oxide LiTi2O4 epitaxial thin films

LiTi2O4 is a unique material in that it is the only known oxide spinel superconductor. Although bulk studies have demonstrated that superconductivity can be generally described by the Bardeen-Cooper-Schreiffer theory, the microscopic mechanisms of superconductivity are not yet resolved fully. The sensitivity of the superconducting properties to various defects of the spinel crystal structure provides insight into such mechanisms. Epitaxial films of LiTi2O4 on single crystalline substrates of MgAl2O4, MgO, and SrTiO3 provide model systems to systematically explore the effects of lattice strain and microstructural disorder. Lattice strain that affects bandwidth gives rise to limited variations in the superconducting and normal state properties. Microstructural disorder such as antiphase boundaries that give rise to Ti network disorder can reduce the critical temperature, but Ti network disorder combined with Mg interdiffusion can affect the superconducting state much more dramatically. Thickness dependent transport studies indicate a superconductor-insulator transition as a function of film thickness regardless of lattice strain and microstructure. In addition, surface sensitive X-ray absorption spectroscopy has identified Ti to retain site symmetry and average valence of the bulk material regardless of film thickness.Comment: 25 pages, 7 figures, v2 - expanded Fig 1,2,7 with added discussion

Global-Vector Representation of the Angular Motion of Few-Particle Systems II

The angular motion of a few-body system is described with global vectors which depend on the positions of the particles. The previous study using a single global vector is extended to make it possible to describe both natural and unnatural parity states. Numerical examples include three- and four-nucleon systems interacting via nucleon-nucleon potentials of AV8 type and a 3$\alpha$ system with a nonlocal $\alpha\alpha$ potential. The results using the explicitly correlated Gaussian basis with the global vectors are shown to be in good agreement with those of other methods. A unique role of the unnatural parity component, caused by the tensor force, is clarified in the $0^-_1$ state of $^4$He. Two-particle correlation function is calculated in the coordinate and momentum spaces to show different characteristics of the interactions employed.Comment: 39 pages, 4 figure

Density of Yang-Lee zeros for the Ising ferromagnet

The densities of Yang-Lee zeros for the Ising ferromagnet on the $L\times L$ square lattice are evaluated from the exact grand partition functions ($L=3\sim16$). The properties of the density of Yang-Lee zeros are discussed as a function of temperature $T$ and system size $L$. The three different classes of phase transitions for the Ising ferromagnet, first-order phase transition, second-order phase transition, and Yang-Lee edge singularity, are clearly distinguished by estimating the magnetic scaling exponent $y_h$ from the densities of zeros for finite-size systems. The divergence of the density of zeros at Yang-Lee edge in high temperatures (Yang-Lee edge singularity), which has been detected only by the series expansion until now for the square-lattice Ising ferromagnet, is obtained from the finite-size data. The identification of the orders of phase transitions in small systems is also discussed using the density of Yang-Lee zeros.Comment: to appear in Physical Review

The Random Bit Complexity of Mobile Robots Scattering

We consider the problem of scattering $n$ robots in a two dimensional continuous space. As this problem is impossible to solve in a deterministic manner, all solutions must be probabilistic. We investigate the amount of randomness (that is, the number of random bits used by the robots) that is required to achieve scattering. We first prove that $n \log n$ random bits are necessary to scatter $n$ robots in any setting. Also, we give a sufficient condition for a scattering algorithm to be random bit optimal. As it turns out that previous solutions for scattering satisfy our condition, they are hence proved random bit optimal for the scattering problem. Then, we investigate the time complexity of scattering when strong multiplicity detection is not available. We prove that such algorithms cannot converge in constant time in the general case and in $o(\log \log n)$ rounds for random bits optimal scattering algorithms. However, we present a family of scattering algorithms that converge as fast as needed without using multiplicity detection. Also, we put forward a specific protocol of this family that is random bit optimal ($n \log n$ random bits are used) and time optimal ($\log \log n$ rounds are used). This improves the time complexity of previous results in the same setting by a $\log n$ factor. Aside from characterizing the random bit complexity of mobile robot scattering, our study also closes its time complexity gap with and without strong multiplicity detection (that is, $O(1)$ time complexity is only achievable when strong multiplicity detection is available, and it is possible to approach it as needed otherwise)

The role of magnetic anisotropy in spin filter junctions

We have fabricated oxide based spin filter junctions in which we demonstrate that magnetic anisotropy can be used to tune the transport behavior of spin filter junctions. Until recently, spin filters have been largely comprised of polycrystalline materials where the spin filter barrier layer and one of the electrodes are ferromagnetic. These spin filter junctions have relied on the weak magnetic coupling between one ferromagnetic electrode and a barrier layer or the insertion of a nonmagnetic insulating layer in between the spin filter barrier and electrode. We have demonstrated spin filtering behavior in La0.7Sr0.3MnO3/chromite/Fe3O4 junctions without nonmagnetic spacer layers where the interface anisotropy plays a significant role in determining transport behavior. Detailed studies of chemical and magnetic structure at the interfaces indicate that abrupt changes in magnetic anisotropy across the non-isostructural interface is the cause of the significant suppression of junction magnetoresistance in junctions with MnCr2O4 barrier layers.Comment: 7 pages, 7 figure

QED Corrections to the Scattering of Solar Neutrinos and Electrons

We discuss recent calculations of the O(alpha) QED corrections to the recoil electron energy spectrum in neutrino electron scattering, and to the spectrum of the combined energy of the recoil electron and a possible accompanying photon emitted in the scattering process. We then examine the role of these corrections in the interpretation of precise measurements from solar neutrino electron scattering experiments.Comment: (16 Pages, 4 Figures) Presented at the Symposium in Honor of Professor Alberto Sirlin's 70th Birthday: ``50 Years of Precision Electroweak Physics'', New York University, October 27-28, 200