Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy

We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with respect to these parameters. It is written down discrete equations which naturally generalize the first discrete Painlev\'e equation $\mathrm{dP}_{\rm I}$ in a sense that autonomous version of these equations admit the limit to the first Painlev\'e equation. It is shown that each of these equations describes B\"acklund transformations of Veselov-Shabat periodic dressing lattices with odd period known also as Noumi-Yamada systems of type $A_{2(n-1)}^{(1)}$.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Fermi liquid theory for the Anderson model out of equilibrium

We study low-energy properties of the Anderson impurity under a finite bias voltage $V$ using the perturbation theory in $U$ of Yamada and Yosida in the nonequilibrium Keldysh diagrammatic formalism, and obtain the Ward identities for the derivative of the self-energy with respect to $V$. The self-energy is calculated exactly up to terms of order $\omega^2$, $T^2$ and $V^2$, and the coefficients are defined with respect to the equilibrium ground state. From these results, the nonlinear response of the current through the impurity has been deduced up to order $V^3$.Comment: 8 pages, 1 figur

Charge and orbital ordering in underdoped La1-xSrxMnO3

We have explored spin, charge and orbitally ordered states in La1-xSrxMnO3 (0 < x < 1/2) using model Hartree-Fock calculations on d-p-type lattice models. At x=1/8, several charge and orbitally modulated states are found to be stable and almost degenerate in energy with a homogeneous ferromagnetic state. The present calculation indicates that a ferromagnetic state with a charge modulation along the c-axis which is consistent with the experiment by Yamada et al. might be responsible for the anomalous behavior around x = 1/8.Comment: 5 pages, 5 figure

Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case

In proving the Fermionic formulae, combinatorial bijection called the Kerov--Kirillov--Reshetikhin (KKR) bijection plays the central role. It is a bijection between the set of highest paths and the set of rigged configurations. In this paper, we give a proof of crystal theoretic reformulation of the KKR bijection. It is the main claim of Part I (math.QA/0601630) written by A. Kuniba, M. Okado, T. Takagi, Y. Yamada, and the author. The proof is given by introducing a structure of affine combinatorial $R$ matrices on rigged configurations.Comment: 45 pages, version for publication. Introduction revised, more explanations added to the main tex

Magnetic-field effects on the charge-spin stripe order in La-214 high-Tc cuprates

Magnetic-field effects on the charge-spin stripe order in La-214 high-Tc cuprates have been investigated from measurements of the in-plane electrical-resistivity, Rho_ab_. In La_2-x_Ba_x_CuO_4_ with x=0.10 and La_2-x_Sr_x_CuO_4_ with x=0.115 where the incommensurate charge peaks are weak and unobservable in zero field in elastic neutron-scattering measurements, respectively, the normal-state value of Rho_ab_ at low temperatures markedly increases with increasing field up to 27 T. For La_2-x_Ba_x_CuO_4_ with x=0.11 and Zn-substituted La_2-x_Sr_x_Cu_1-y_Zn_y_O_4_ with x=0.115 and y=0.02 where the charge stripe order is fairly stabilized in zero field, on the other hand, the increase in Rho_ab_ with increasing field is negligibly small. In conclusion, when the charge-spin stripe order is not fully stable in zero field, magnetic field operates to stabilize the charge-spin stripe order. The value of Rho_ab_ increases with increasing field depending on the stability of the charge stripe order.Comment: 4 pages, 2 figures, Proceedings of Yamada Conference LX on Research in High Magnetic Fields (RHMF2006) (Satellite of ICM2006