Phase Transition in a One-Dimensional Extended Peierls-Hubbard Model with a Pulse of Oscillating Electric Field: II. Linear Behavior in Neutral-to-Ionic Transition

Dynamics of charge density and lattice displacements after the neutral phase is photoexcited is studied by solving the time-dependent Schr\"odinger equation for a one-dimensional extended Peierls-Hubbard model with alternating potentials. In contrast to the ionic-to-neutral transition studied previously, the neutral-to-ionic transition proceeds in an uncooperative manner as far as the one-dimensional system is concerned. The final ionicity is a linear function of the increment of the total energy. After the electric field is turned off, the electronic state does not significantly change, roughly keeping the ionicity, even if the transition is not completed, because the ionic domains never proliferate. As a consequence, an electric field with frequency just at the linear absorption peak causes the neutral-to-ionic transition the most efficiently. These findings are consistent with the recent experiments on the mixed-stack organic charge-transfer complex, TTF-CA. We artificially modify or remove the electron-lattice coupling to discuss the origin of such differences between the two transitions.Comment: 17 pages, 9 figure

How to relate the oscillator and Coulomb systems on spheres and pseudospheres?

We show that the oscillators on a sphere and pseudosphere are related, by the so-called Bohlin transformation, with the Coulomb systems on the pseudosphere: the even states of an oscillator yields the conventional Coulomb system on pseudosphere, while the odd states yield the Coulomb system on pseudosphere in the presence of magnetic flux tube generating half spin. In the higher dimensions the oscillator and Coulomb(-like) systems are connected in the similar way. In particular, applying the Kustaanheimo-Stiefel transformation to the oscillators on sphere and pseudosphere, we obtained the preudospherical generalization of MIC-Kepler problem describing three-dimensional charge-dyon system.Comment: 12 pages, Based on talk given at XXIII Colloquium on Group Theoretical Methods in Physics (July 31-August 5, 2000, Dubna

Multi-center MICZ-Kepler systems

We present the classical solutions of the two-center MICZ-Kepler and MICZ-Kepler-Stark systems. Then we suggest the model of multi-center MICZ-Kepler system on the curved spaces equipped with $so(3)$-invariant conformal flat metrics.Comment: 7 pages, typos corrected, refs added. Contribution to the Proceedings of International Workshop on Classical and Quantum Integrable systems, 24-28.01.2007, Dubna, Russi

Exact solutions of the isoholonomic problem and the optimal control problem in holonomic quantum computation

The isoholonomic problem in a homogeneous bundle is formulated and solved exactly. The problem takes a form of a boundary value problem of a variational equation. The solution is applied to the optimal control problem in holonomic quantum computer. We provide a prescription to construct an optimal controller for an arbitrary unitary gate and apply it to a $k$-dimensional unitary gate which operates on an $N$-dimensional Hilbert space with $N \geq 2k$. Our construction is applied to several important unitary gates such as the Hadamard gate, the CNOT gate, and the two-qubit discrete Fourier transformation gate. Controllers for these gates are explicitly constructed.Comment: 19 pages, no figures, LaTeX2

Planar CuO_2 hole density estimation in multilayered high-T_c cuprates

We report that planar CuO_2 hole densities in high-T_c cuprates are consistently determined by the Cu-NMR Knight shift. In single- and bi-layered cuprates, it is demonstrated that the spin part of the Knight shift K_s(300 K) at room temperature monotonically increases with the hole density $p$ from underdoped to overdoped regions, suggesting that the relationship of K_s(300 K) vs. p is a reliable measure to determine p. The validity of this K_s(300 K)-p relationship is confirmed by the investigation of the p-dependencies of hyperfine magnetic fields and of spin susceptibility for single- and bi-layered cuprates with tetragonal symmetry. Moreover, the analyses are compared with the NMR data on three-layered Ba_2Ca_2Cu_3O_6(F,O)_2, HgBa_2Ca_2Cu_3O_{8+delta}, and five-layered HgBa_2Ca_4Cu_5O_{12+delta}, which suggests the general applicability of the K_s(300 K)-p relationship to multilayered compounds with more than three CuO_2 planes. We remark that the measurement of K_s(300 K) enables us to separately estimate p for each CuO_2 plane in multilayered compounds, where doped hole carriers are inequivalent between outer CuO_2 planes and inner CuO_2 planes.Comment: 7 pages, 5 figures, 2 Tables, to be published in Physical Review

A Generalization of the Kepler Problem

We construct and analyze a generalization of the Kepler problem. These generalized Kepler problems are parameterized by a triple $(D, \kappa, \mu)$ where the dimension $D\ge 3$ is an integer, the curvature $\kappa$ is a real number, the magnetic charge $\mu$ is a half integer if $D$ is odd and is 0 or 1/2 if $D$ is even. The key to construct these generalized Kepler problems is the observation that the Young powers of the fundamental spinors on a punctured space with cylindrical metric are the right analogues of the Dirac monopoles.Comment: The final version. To appear in J. Yadernaya fizik

Effects of high-field electrical stress on the conduction properties of ultra-thin La2O3 films

Electron transport in high-field stressed metal-insulator-silicon devices with ultrathin (<5nm) lanthanum oxide layers is investigated. We show that the leakage current flowing through the structure prior to degradation is direct and Fowler-Nordheimtunneling conduction, while that after stress exhibits diode-like behavior with series and parallel resistances. In this latter case, a closed-form expression for the current-voltage characteristic, based on the Lambert W function, is presented. Current evolution from one regime to the other during constant voltage stress takes place by means of discrete current steps of nearly identical magnitude, which would be indicative of the occurrence of multiple dielectric breakdowns across the insulating layer

Ultrafast Photoinduced Formation of Metallic State in a Perovskite-type Manganite with Short Range Charge and Orbital Order

Femtosecond reflection spectroscopy was performed on a perovskite-type manganite, Gd0.55Sr0.45MnO3, with the short-range charge and orbital order (CO/OO). Immediately after the photoirradiation, a large increase of the reflectivity was detected in the mid-infrared region. The optical conductivity spectrum under photoirradiation obtained from the Kramers-Kronig analyses of the reflectivity changes demonstrates a formation of a metallic state. This suggests that ferromagnetic spin arrangements occur within the time resolution (ca. 200 fs) through the double exchange interaction, resulting in an ultrafast CO/OO to FM switching.Comment: 4 figure

Photoinduced metallic properties of one-dimensional strongly correlated electron systems

We study photoinduced optical responses of one-dimensional strongly correlated electron systems. The optical conductivity spectra are calculated for the ground state and a photoexcited state in the one-dimensional Hubbard model at half filling by using the exact diagonalization method. It is found that, in the Mott insulator phase, the photoexcited state has large spectral weights including the Drude weight below the optical gap. As a consequence, the spectral weight above the optical gap is largely reduced. These results imply that a metallic state is induced by photoexcitation. Comparison between the photoexcited and hole-doped states shows that the photoexcitation is similar to chemical doping.Comment: 4 pages, 4 figures, submitted to J. Phys. Soc. Jp

Geometric Approach to Lyapunov Analysis in Hamiltonian Dynamics

As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of the Hamiltonian function. To separate out these two directions and to apply Lyapunov analysis effectively in directions for which Lyapunov exponents are not trivial, a geometric method is proposed for natural Hamiltonian systems, in particular. In this geometric method, Hamiltonian flows of a natural Hamiltonian system are regarded as geodesic flows on the cotangent bundle of a Riemannian manifold with a suitable metric. Stability/instability of the geodesic flows is then analyzed by linearized equations of motion which are related to the Jacobi equations on the Riemannian manifold. On some geometric setting on the cotangent bundle, it is shown that along a geodesic flow in question, there exist Lyapunov vectors such that two of them are in the two marginal directions and the others orthogonal to the marginal directions. It is also pointed out that Lyapunov vectors with such properties can not be obtained in general by the usual method which uses linearized Hamilton's equations of motion. Furthermore, it is observed from numerical calculation for a model system that Lyapunov exponents calculated in both methods, geometric and usual, coincide with each other, independently of the choice of the methods.Comment: 22 pages, 14 figures, REVTeX