4,607 research outputs found
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 -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 -dimensional unitary gate
which operates on an -dimensional Hilbert space with . 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
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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 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
One-center small polarons as short-lived precursors in self-trapping processes of holes and electron-hole pairs in alkali iodides
On two superintegrable nonlinear oscillators in N dimensions
We consider the classical superintegrable Hamiltonian system given by
, 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,
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