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

Vibronic mixing enables ultrafast energy flow in light-harvesting complex II.

Since the discovery of quantum beats in the two-dimensional electronic spectra of photosynthetic pigment-protein complexes over a decade ago, the origin and mechanistic function of these beats in photosynthetic light-harvesting has been extensively debated. The current consensus is that these long-lived oscillatory features likely result from electronic-vibrational mixing, however, it remains uncertain if such mixing significantly influences energy transport. Here, we examine the interplay between the electronic and nuclear degrees of freedom (DoF) during the excitation energy transfer (EET) dynamics of light-harvesting complex II (LHCII) with two-dimensional electronic-vibrational spectroscopy. Particularly, we show the involvement of the nuclear DoF during EET through the participation of higher-lying vibronic chlorophyll states and assign observed oscillatory features to specific EET pathways, demonstrating a significant step in mapping evolution from energy to physical space. These frequencies correspond to known vibrational modes of chlorophyll, suggesting that electronic-vibrational mixing facilitates rapid EET over moderately size energy gaps

Reduction of quantum systems on Riemannian manifolds with symmetry and application to molecular mechanics

This paper deals with a general method for the reduction of quantum systems with symmetry. For a Riemannian manifold M admitting a compact Lie group G as an isometry group, the quotient space Q = M/G is not a smooth manifold in general but stratified into a collection of smooth manifolds of various dimensions. If the action of the compact group G is free, M is made into a principal fiber bundle with structure group G. In this case, reduced quantum systems are set up as quantum systems on the associated vector bundles over Q = M/G. This idea of reduction fails, if the action of G on M is not free. However, the Peter-Weyl theorem works well for reducing quantum systems on M. When applied to the space of wave functions on M, the Peter-Weyl theorem provides the decomposition of the space of wave functions into spaces of equivariant functions on M, which are interpreted as Hilbert spaces for reduced quantum systems on Q. The concept of connection on a principal fiber bundle is generalized to be defined well on the stratified manifold M. Then the reduced Laplacian is well defined as a self-adjoint operator with the boundary conditions on singular sets of lower dimensions. Application to quantum molecular mechanics is also discussed in detail. In fact, the reduction of quantum systems studied in this paper stems from molecular mechanics. If one wishes to consider the molecule which is allowed to lie in a line when it is in motion, the reduction method presented in this paper works well.Comment: 33 pages, no figure

Relaxation Dynamics of Photocarriers in One-Dimensional Mott Insulators Coupled to Phonons

We examine recombination processes of photocarriers in one-dimensional Mott insulators coupled to phonons. Performing density matrix renormalization group calculations, we find that, even for small electron-phonon coupling, many phonons are generated dynamically, which cause initial relaxation process after the irradiation. At the same time, spin-charge coupling coming from mixing of high- and low-energy states by the irradiation is suppressed. We discuss differences between Mott and band insulators in terms of relaxation dynamics.Comment: 5 pages, 3 figure

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

On two superintegrable nonlinear oscillators in N dimensions

We consider the classical superintegrable Hamiltonian system given by $H=T+U={p^2}/{2(1+\lambda q^2)}+{{\omega}^2 q^2}/{2(1+\lambda q^2)}$, where U is known to be the "intrinsic" oscillator potential on the Darboux spaces of nonconstant curvature determined by the kinetic energy term T and parametrized by {\lambda}. We show that H is Stackel equivalent to the free Euclidean motion, a fact that directly provides a curved Fradkin tensor of constants of motion for H. Furthermore, we analyze in terms of {\lambda} the three different underlying manifolds whose geodesic motion is provided by T. As a consequence, we find that H comprises three different nonlinear physical models that, by constructing their radial effective potentials, are shown to be two different nonlinear oscillators and an infinite barrier potential. The quantization of these two oscillators and its connection with spherical confinement models is briefly discussed.Comment: 11 pages; based on the contribution to the Manolo Gadella Fest-60 years-in-pucelandia, "Recent advances in time-asymmetric quantum mechanics, quantization and related topics" hold in Valladolid (Spain), 14-16th july 201

RELATIONSHIP BETWEEN MUSCULAR OUTPUTS AND THE HORIZONTAL PERTURBATION IN THE EARLY PHASE OF BENCH PRESS MOVEMENT UNDER STABLE AND UNSTABLE CONDITIONS

We demonstrated the relationship between the change rates of muscular outputs and horizontal perturbation under stable and unstable conditions in dynamic bench press movement. Twenty-seven male collegiate athletes attended the study. We used a tri-axis accelerometer attached to the barbell shaft to obtain the acceleration data in the bench press and computed peak force output, rate of force development (RFD), and horizontal acceleration trajectory length for 0.2 seconds after the initiation. Significant reduction was found in the peak force output and RFD under stable and unstable conditions, but not in the horizontal acceleration trajectory length. Significant correlation was found between the change rate of RFD and the horizontal acceleration trajectory length under stable and unstable conditions (r=0.55,