Berry phase in a non-isolated system

We investigate the effect of the environment on a Berry phase measurement involving a spin-half. We model the spin+environment using a biased spin-boson Hamiltonian with a time-dependent magnetic field. We find that, contrary to naive expectations, the Berry phase acquired by the spin can be observed, but only on timescales which are neither too short nor very long. However this Berry phase is not the same as for the isolated spin-half. It does not have a simple geometric interpretation in terms of the adiabatic evolution of either bare spin-states or the dressed spin-resonances that remain once we have traced out the environment. This result is crucial for proposed Berry phase measurements in superconducting nanocircuits as dissipation there is known to be significant.Comment: 4 pages (revTeX4) 2 fig. This version has MAJOR changes to equation

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

Lower bounds for communication capacities of two-qudit unitary operations

We show that entangling capacities based on the Jamiolkowski isomorphism may be used to place lower bounds on the communication capacities of arbitrary bipartite unitaries. Therefore, for these definitions, the relations which have been previously shown for two-qubit unitaries also hold for arbitrary dimensions. These results are closely related to the theory of the entanglement-assisted capacity of channels. We also present more general methods for producing ensembles for communication from initial states for entanglement creation.Comment: 9 pages, 2 figures, comments welcom

Three water sites in upper mantle olivine and the role of titanium in the water weakening mechanism

Infrared spectroscopy on synthetic olivines has established that there are at least four different mechanisms by which hydrogen is incorporated into the crystal structure. Two mechanisms occur in the system MgO-SiO2-H2O associated with silicon and magnesium vacancies, respectively. A third mechanism is associated with trivalent cation substitution, commonly Fe3+ in natural olivine, while the fourth mechanism, which is the one most prevalent in natural olivines from the spinel-peridotite facies of the Earth’s upper mantle, is associated with Ti4+ [Berry et al., 2005]. Here first principles calculations based on density functional theory are used to derive the structure and relative energies of the two defects in the pure MgO-SiO2-H2O system, and possible hydrogen-bearing and hydrogen-free point defects in Ti4+-doped forsterite. Calculated structures are used to compare the predicted orientation of the O-H bonds with the experimentally determined polarization. The energies are used to discuss how different regimes of chemical environment, temperature (T), pressure (P), and both water content and water fugacity ( fH2O), impact on which of the different hydroxyl substitution mechanisms are thermodynamically stable. We find that given the presence of Ti impurities, the most stable mechanism involves the formation of silicon vacancies containing two protons charge balanced by a Ti4+ cation occupying an adjacent octahedral site. This mechanism leads to the water-mediated formation of silicon vacancies. As silicon is known to be the most slowly diffusing species in olivine, this provides a credible explanation of the observed water weakening effect in olivine

Strong Evidence of Normal Heat Conduction in a one-Dimensional Quantum System

We investigate how the normal energy transport is realized in one-dimensional quantum systems using a quantum spin system. The direct investigation of local energy distribution under thermal gradient is made using the quantum master equation, and the mixing properties and the convergence of the Green-Kubo formula are investigated when the number of spin increases. We find that the autocorrelation function in the Green-Kubo formula decays as $\sim t^{-1.5}$ to a finite value which vanishes rapidly with the increase of the system size. As a result, the Green-Kubo formula converges to a finite value in the thermodynamic limit. These facts strongly support the realization of Fourier heat law in a quantum system.Comment: 7 pages 6 figure

Transitionless quantum drivings for the harmonic oscillator

Two methods to change a quantum harmonic oscillator frequency without transitions in a finite time are described and compared. The first method, a transitionless-tracking algorithm, makes use of a generalized harmonic oscillator and a non-local potential. The second method, based on engineering an invariant of motion, only modifies the harmonic frequency in time, keeping the potential local at all times.Comment: 11 pages, 1 figure. Submitted for publicatio