768 research outputs found
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
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
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
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 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- contribution, the diagonal
approximation, already reproduces the random-matrix form factor for .
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 , 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
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