Trace identities and their semiclassical implications

The compatibility of the semiclassical quantization of area-preserving maps with some exact identities which follow from the unitarity of the quantum evolution operator is discussed. The quantum identities involve relations between traces of powers of the evolution operator. For classically {\it integrable} maps, the semiclassical approximation is shown to be compatible with the trace identities. This is done by the identification of stationary phase manifolds which give the main contributions to the result. The same technique is not applicable for {\it chaotic} maps, and the compatibility of the semiclassical theory in this case remains unsettled. The compatibility of the semiclassical quantization with the trace identities demonstrates the crucial importance of non-diagonal contributions.Comment: LaTeX - IOP styl

Transport and dynamics on open quantum graphs

We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular we consider extended open graphs whose classical dynamics generate a diffusion process. The transport properties of the classical system are revealed in the scattering resonances and in the time evolution of the quantum system.Comment: 42 pages, 13 figures, submitted to PR

De Koninklijke Nederlandse Bosbouw Vereniging en het imago bij haar leden

Het bestuur van de Koninklijke Nederlandse Bosbouw Vereniging besloot in 2000 om door middel van een intern onderzoek onder de leden bouwstenen te vinden voor een nieuw verenigingsbeleid. Dit is gebeurd door middel van een enquête onder alle leden. De analyse van de antwoorden had betrekking op 44% van de leden, zijnde de respons. De functie van de KNBV wordt thans nog vooral gezien als een kennis- en informatieplatform, maar in de toekomst zou de KNBV meer als belangenorganisatie mogen fungeren. Leeftijd speelt een rol bij de mate van betrokkenheid bij en tevredenheid over de KNBV. Deze zijn groter naarmate men ouder is. Desondanks is meer aandacht voor de wensen en ideeën van de jongere leden noodzakelijk voor de ‘verjonging’ en het voortbestaan van de vereniging, zeker als 80% van de respondenten aangeeft het jammer te vinden als de KNBV zou worden opgeheven

Periodic-Orbit Theory of Anderson Localization on Graphs

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an a-periodic Kronig-Penney model in one dimension. The exact expression for the probability to return of an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, while the diagonal approximation decays diffusively. Our theory is based on the identification of families of isometric orbits. The coherent periodic-orbit sums within these families, and the summation over all families are performed analytically using advanced combinatorial methods.Comment: 4 pages, 3 figures, RevTe

QE and the Bank Lending Channel in the United Kingdom in the United Kingdom

We test whether quantitative easing (QE), in addition to boosting aggregate demand and inflation via portfolio rebalancing channels, operated through a bank lending channel (BLC) in the UK. Using Bank of England data together with an instrumental variables approach, we find no evidence of a traditional BLC associated with QE. We show, in a simple framework, that the traditional BLC is diminished if the bank receives 'flighty' deposits (deposits that are likely to quickly leave the bank). We show that QE gave rise to such flighty deposits which may explain why we nd no evidence of a BLC

Classical dynamics on graphs

We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator which generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms which decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs which converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system which undergoes a diffusion process before it escapes.Comment: 42 pages and 8 figure

Shot noise from action correlations

We consider universal shot noise in ballistic chaotic cavities from a semiclassical point of view and show that it is due to action correlations within certain groups of classical trajectories. Using quantum graphs as a model system we sum these trajectories analytically and find agreement with random-matrix theory. Unlike all action correlations which have been considered before, the correlations relevant for shot noise involve four trajectories and do not depend on the presence of any symmetry.Comment: 4 pages, 2 figures (a mistake in version 1 has been corrected

The measurement of primary productivity in a high-rate oxidation pond (HROP)

A high-rate oxidation pond is studied as a model system for comparing 14C and oxygen evolution methods as tools for measuring primary productivity in hypertrophic aquatic systems. Our results indicate that at very dense algal populations (up to 5 mg chl. a l−1) and high photosynthetic rates, 14C based results may severely underestimate primary productivity, unless a way is found to keep incubation times very short. Results obtained with our oxygen electrode were almost an order of magnitude higher than those obtained by all 14C procedures. These higher values correspond fairly well with a field-tested computer-simulation model, as well as with direct harvest data obtained at the same pond when operated under similar conditions. The examination of the size-fractionation of the photosynthetic activity underscored the important contribution of nannoplanktonic algae to the total production of the syste

Form factor for a family of quantum graphs: An expansion to third order

For certain types of quantum graphs we show that the random-matrix form factor can be recovered to at least third order in the scaled time $\tau$ from periodic-orbit theory. We consider the contributions from pairs of periodic orbits represented by diagrams with up to two self-intersections connected by up to four arcs and explain why all other diagrams are expected to give higher-order corrections only. For a large family of graphs with ergodic classical dynamics the diagrams that exist in the absence of time-reversal symmetry sum to zero. The mechanism for this cancellation is rather general which suggests that it may also apply at higher-orders in the expansion. This expectation is in full agreement with the fact that in this case the linear-$\tau$ contribution, the diagonal approximation, already reproduces the random-matrix form factor for $\tau<1$. For systems with time-reversal symmetry there are more diagrams which contribute at third order. We sum these contributions for quantum graphs with uniformly hyperbolic dynamics, obtaining $+2\tau^{3}$, in agreement with random-matrix theory. As in the previous calculation of the leading-order correction to the diagonal approximation we find that the third order contribution can be attributed to exceptional orbits representing the intersection of diagram classes.Comment: 23 pages (including 4 fig.) - numerous typos correcte