Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation

In this article, we construct loop soliton solutions and mixed soliton - loop soliton solution for the Degasperis-Procesi equation. To explore these solutions we adopt the procedure given by Matsuno. By appropriately modifying the $\tau$-function given in the above paper we derive these solutions. We present the explicit form of one and two loop soliton solutions and mixed soliton - loop soliton solutions and investigate the interaction between (i) two loop soliton solutions in different parametric regimes and (ii) a loop soliton with a conventional soliton in detail.Comment: Published in Physica Scripta (2012

A direct method of solution for the Fokas-Lenells derivative nonlinear Schr\"odinger equation: I. Bright soliton solutions

We develop a direct method of solution for finding the bright $N$-soliton solution of the Fokas-Lenells derivative nonlinear Schr\"odinger equation. The construction of the solution is performed by means of a purely algebraic procedure using an elementary theory of determinants and does not rely on the inverse scattering transform method. We present two different expressions of the solution both of which are expressed as a ratio of determinants. We then investigate the properties of the solutions and find several new features. Specifically, we derive the formula for the phase shift caused by the collisions of bright solitons.Comment: To appear in J. Phys. A: Math. Theor. 45(2012) Ma

Ground State Properties and Optical Conductivity of the Transition Metal Oxide Sr2VO4{\rm Sr_{2}VO_{4}}

Combining first-principles calculations with a technique for many-body problems, we investigate properties of the transition metal oxide ${\rm Sr_{2}VO_{4}}$ from the microscopic point of view. By using the local density approximation (LDA), the high-energy band structure is obtained, while screened Coulomb interactions are derived from the constrained LDA and the GW method. The renormalization of the kinetic energy is determined from the GW method. By these downfolding procedures, an effective Hamiltonian at low energies is derived. Applying the path integral renormalization group method to this Hamiltonian, we obtain ground state properties such as the magnetic and orbital orders. Obtained results are consistent with experiments within available data. We find that ${\rm Sr_{2}VO_{4}}$ is close to the metal-insulator transition. Furthermore, because of the coexistence and competition of ferromagnetic and antiferromgnetic exchange interactions in this system, an antiferromagnetic and orbital-ordered state with a nontrivial and large unit cell structure is predicted in the ground state. The calculated optical conductivity shows characteristic shoulder structure in agreement with the experimental results. This suggests an orbital selective reduction of the Mott gap.Comment: 38pages, 22figure

Electronic structure of spinel-type LiV_2O_4

The band structure of the cubic spinel compound LiV_2O_4, which has been reported recently to show heavy Fermion behavior, has been calculated within the local-density approximation using a full-potential version of the linear augmented-plane-wave method. The results show that partially-filled V 3d bands are located about 1.9 eV above the O 2p bands and the V 3d bands are split into a lower partially-filled t_{2g} complex and an upper unoccupied e_{g} manifold. The fact that the conduction electrons originate solely from the t_{2g} bands suggests that the mechanism for the mass enhancement in this system is different from that in the 4f heavy Fermion systems, where these effects are attributed to the hybridization between the localized 4f levels and itinerant spd bands.Comment: 5 pages, revte

Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion

We explore dynamics of a density pulse induced by a local quench in a one-dimensional electron system. The spectral curvature leads to an "overturn" (population inversion) of the wave. We show that beyond this time the density profile develops strong oscillations with a period much larger than the Fermi wave length. The effect is studied first for the case of free fermions by means of direct quantum simulations and via semiclassical analysis of the evolution of Wigner function. We demonstrate then that the period of oscillations is correctly reproduced by a hydrodynamic theory with an appropriate dispersive term. Finally, we explore the effect of different types of electron-electron interaction on the phenomenon. We show that sufficiently strong interaction [$U(r)\gg 1/mr^2$ where $m$ is the fermionic mass and $r$ the relevant spatial scale] determines the dominant dispersive term in the hydrodynamic equations. Hydrodynamic theory reveals crucial dependence of the density evolution on the relative sign of the interaction and the density perturbation.Comment: 20 pages, 13 figure

Measurements of integral muon intensity at large zenith angles

High-statistics data on near-horizontal muons collected with Russian-Italian coordinate detector DECOR are analyzed. Precise measurements of muon angular distributions in zenith angle interval from 60 to 90 degrees have been performed. In total, more than 20 million muons are selected. Dependences of the absolute integral muon intensity on zenith angle for several threshold energies ranging from 1.7 GeV to 7.2 GeV are derived. Results for this region of zenith angles and threshold energies have been obtained for the first time. The dependence of integral intensity on zenith angle and threshold energy is well fitted by a simple analytical formula.Comment: 4 pages, 4 figures, 1 tabl

Darboux Transformations, Infinitesimal Symmetries and Conservation Laws for Nonlocal Two-Dimensional Toda Lattice

The technique of Darboux transformation is applied to nonlocal partner of two-dimensional periodic A_{n-1} Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear systems with quantized spectral parameter. The generalization of the Darboux transformation technique on linear equations of such a kind is given. The connections between the solutions of overdetermined linear systems and their expansions in series at singular points neighborhood are presented. The solutions of the nonlocal Toda lattice and infinite hierarchies of the infinitesimal symmetries and conservation laws are obtained.Comment: 12 pages, infinitesimal symmetries and conservation laws are adde

Electronic Structure and Heavy Fermion Behavior in LiV_2O_4

First principles density functional calculations of the electronic and magnetic properties of spinel-structure LiV$_{2}$O$_{4}$ have been performed using the full potential linearized augmented planewave method. The calculations show that the electronic structure near the Fermi energy consists of a manifold of 12 bands derived from V $t_{2g}$ states, weakly hybridized with O p states. While the total width of this active manifold is approximately 2 eV, it may be roughly decomposed into two groups: high velocity bands and flatter bands, although these mix in density functional calculations. The flat bands, which are the more atomic-like lead to a high density of states and magnetic instability of local moment character. The value of the on-site exchange energy is sensitive to the exact exchange correlation parameterization used in the calculations, but is much larger than the interaction between neighboring spins, reflecting the weak coupling of the magnetic system with the high velocity bands. A scenario for the observed heavy fermion behavior is discussed in which conduction electrons in the dispersive bands are weakly scattered by local moments associated with strongly correlated electrons in the heavy bands.This is analogous to that in conventional Kondo type heavy fermions, but is unusual in that both the local moments and conduction electrons come from the same d-manifold.Comment: 6 Revtex pages, Postscript figs embedded. Revision: figure 4 replaced with a better version, showing the band character explicitel

Case Report Sequential MR Images and Radiographs of Epiphyseal Osteomyelitis in the Distal Femur of an Infant

Magnetic resonance imaging (MRI) plays an important role in the diagnosis of osteomyelitis, especially during the early phase of the disease. The findings of sequential MRIs during the course of treatment in acute osteomyelitis in children have not yet been reported in the literature. We present a case of acute epiphyseal osteomyelitis in the distal femur of an infant. We monitored imaging changes by sequential MRIs and radiographs. MRI was more useful than radiograph for early diagnosis and evaluation of therapeutic response

Hubbard chains network on corner-sharing tetrahedra: origin of the heavy fermion state in LiV_2O_4

We investigate the Hubbard chains network model defined on corner-sharing tetrahedra (the pyrochlore lattice) which is a possible microscopic model for the heavy fermion state of LiV_2O_4. Based upon this model, we can explain transport, magnetic, and thermodynamic properties of LiV_2O_4. We calculate the spin susceptibility, and the specific heat coefficient, exploiting the Bethe ansatz exact solution of the 1D Hubbard model and bosonization method. The results are quite consistent with experimental observations. We obtain the large specific heat coefficient $\gamma\sim 222 {\rm mJ/mol K^2}$.Comment: 5 pages, 2 figures, a postscript file of Figure 1 is not included, to appear in Physical Review