The three-body problem and the Hannay angle

The Hannay angle has been previously studied for a celestial circular restricted three-body system by means of an adiabatic approach. In the present work, three main results are obtained. Firstly, a formal connection between perturbation theory and the Hamiltonian adiabatic approach shows that both lead to the Hannay angle; it is thus emphasised that this effect is already contained in classical celestial mechanics, although not yet defined nor evaluated separately. Secondly, a more general expression of the Hannay angle, valid for an action-dependent potential is given; such a generalised expression takes into account that the restricted three-body problem is a time-dependent, two degrees of freedom problem even when restricted to the circular motion of the test body. Consequently, (some of) the eccentricity terms cannot be neglected {\it a priori}. Thirdly, we present a new numerical estimate for the Earth adiabatically driven by Jupiter. We also point out errors in a previous derivation of the Hannay angle for the circular restricted three-body problem, with an action-independent potential.Comment: 11 pages. Accepted by Nonlinearit

^{59}Co NMR evidence for charge ordering below T_{CO}\sim 51 K in Na_{0.5}CoO_2

The CoO$_{2}$ layers in sodium-cobaltates Na$_{x}$CoO$_{2}$ may be viewed as a spin $S=1/2$ triangular-lattice doped with charge carriers. The underlying physics of the cobaltates is very similar to that of the high $T_{c}$ cuprates. We will present unequivocal $^{59}$Co NMR evidence that below $T_{CO}\sim51 K$, the insulating ground state of the itinerant antiferromagnet Na$_{0.5}$CoO$_{2}$ ($T_{N}\sim 86 K$) is induced by charge ordering.Comment: Phys. Rev. Lett. 100 (2008), in press. 4 figure

The co-chaperone p23 controls root development through the modulation of auxin distribution in the Arabidopsis root meristem.

Homologues of the p23 co-chaperone of HSP90 are present in all eukaryotes, suggesting conserved functions for this protein throughout evolution. Although p23 has been extensively studied in animal systems, little is known about its function in plants. In the present study, the functional characterization of the two isoforms of p23 in Arabidopsis thaliana is reported, suggesting a key role of p23 in the regulation of root development. Arabidopsis p23 mutants, for either form, show a short root length phenotype with a reduced meristem length. In the root meristem a low auxin level associated with a smaller auxin gradient was observed. A decrease in the expression levels of PIN FORMED PROTEIN (PIN)1, PIN3, and PIN7, contextually to an inefficient polar localization of PIN1, was detected. Collectively these results suggest that both Arabidopsis p23 isoforms are required for root growth, in particular in the maintenance of the root meristem, where the proteins are located

The Isovector Quadrupole-Quadrupole Interaction Used in Shell Model Calculations

An interaction $-\chi Q\cdot Q(1+B\vec{\tau}(1)\cdot \vec{\tau}(2))$ is used in a shell model calculation for $^{10}Be$. Whereas for $B=0$ the $2_1^+$ state is two-fold degenerate, introducing a negative $B$ causes an `isovector' $2^+$ state to come down to zero energy at $B=-0.67$ and an $S=1~L=1$ triplet ($J=0^+,~1^+,~2^+$) to come down to zero energy at $B=-0.73$. These are undesirable properties, but a large negative $B$ is apparently needed to fit the energy of the isovector giant quadrupole resonance.Comment: 12 pages, revtex, 2 figures (available on request

The co-chaperone p23 controls root development through the modulation of auxin distribution in the Arabidopsis root meristem

p23 co-chaperones play a key role in the root meristem maintenance via regulation of auxin signalling and the consequent balance between cell differentiation and division rate at the transition zon

Huffman Coding with Letter Costs: A Linear-Time Approximation Scheme

We give a polynomial-time approximation scheme for the generalization of Huffman Coding in which codeword letters have non-uniform costs (as in Morse code, where the dash is twice as long as the dot). The algorithm computes a (1+epsilon)-approximate solution in time O(n + f(epsilon) log^3 n), where n is the input size

Geometric phases and anholonomy for a class of chaotic classical systems

Berry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a particular class of chaotic systems. It is shown that this ``classical parallel transport'' is anholonomic --- transport around a closed curve in parameter space does not bring a point in phase space back to itself --- and is intimately related to the Robbins-Berry classical two-form.Comment: Revtex, 11 pages, no figures

Constructing a Large Variety of Dirac-Cone Materials in the Bi1−x{}_{1-x}Sbx{}_{x} Thin Film System

We theoretically predict that a large variety of Dirac-cone materials can be constructed in Bi${}_{1-x}$Sb${}_{x}$ thin films, and we here show how to construct single-, bi- and tri- Dirac-cone materials with various amounts of wave vector anisotropy. These different types of Dirac cones can be of special interest to electronic devices design, quantum electrodynamics and other fields

An Adiabatic Theorem without a Gap Condition

The basic adiabatic theorems of classical and quantum mechanics are over-viewed and an adiabatic theorem in quantum mechanics without a gap condition is described.Comment: Talk at QMath 7, Prague, 1998. 10 pages, 7 figure