949 research outputs found
Can Habit Formation be Reconciled with Business Cycle Facts?
Many asset pricing puzzles can be explained when habit formation is added to standard preferences. We show that utility functions with a habit then gives rise to a puzzle of consumption volatility in place of the asset pricing puzzles when agents can choose consumption and labor optimally in response to more fundamental shocks. We show that the consumption reaction to technology shocks are too small by an order of magnitude when a utility includes a habit. Alternative models with consistent and exogenous but stochastic labor input are considered. A model with persistent technology shocks and stochastic labor is shown to be potentially consistent with substantial consumption variability aswell as procyclical labor input and labor productivity even when a habit is present.
Rule of Thumb and Dynamic Programming
This paper studies the relationships between learning about rules of thumb (represented by classifier systems) and dynamic programming. Building on a result about Markovian stochastic approximation algorithms, we characterize all decision functions that can be asymptotically obtained through classifier system learning, provided the asymptotic ordering of the classifiers is strict. We demonstrate in a robust example that the learnable decision function is in general not unique, not characterized by a strict ordering of the classifiers, and may not coincide with the decision function delivered by the solution to the dynamic programming problem even if that function is attainable. As an illustration we consider the puzzle of excess sensitivity of consumption to transitory income: classifier systems can generate such behavior even if one of the available rules of thumb is the decision function solving the dynamic programming problem, since bad decisions in good times can "feel better" than good decisions in bad times.
Pitfalls in the theory of carrier dynamics in semiconductor quantum dots: the single-particle basis vs. the many-particle configuration basis
We analyze quantum dot models used in current research for misconceptions
that arise from the choice of basis states for the carriers. The examined
models originate from semiconductor quantum optics, but the illustrated
conceptional problems are not limited to this field. We demonstrate how the
choice of basis states can imply a factorization scheme that leads to an
artificial dependency between two, actually independent, quantities.
Furthermore, we consider an open quantum dot-cavity system and show how the
dephasing, generated by the dissipator in the von Neumann Lindblad equation,
depends on the choice of basis states that are used to construct the collapse
operators. We find that the Rabi oscillations of the s-shell exciton are either
dephased by the dissipative decay of the p-shell exciton or remain unaffected,
depending on the choice of basis states. In a last step we resolve this
discrepancy by taking the full system-reservoir interaction Hamiltonian into
account
Modelling formation and evolution of transverse dune fields
We model formation and evolution of transverse dune fields. In the model,
only the cross section of the dune is simulated. The only physical variable of
relevance is the dune height, from which the dune width and velocity are
determined, as well as phenomenological rules for interaction between two dunes
of different heights. We find that dune fields with no sand on the ground
between dunes are unstable, i.e. small dunes leave the higher ones behind. We
then introduce a saturation length to simulate transverse dunes on a sand bed
and show that this leads to stable dune fields with regular spacing and dune
heights. Finally, we show that our model can be used to simulate coastal dune
fields if a constant sand influx is considered, where the dune height increases
with the distance from the beach, reaching a constant value.Comment: 18 pages including 9 figure
Superthermal photon bunching in terms of simple probability distributions
We analyze the second-order photon autocorrelation function with
respect to the photon probability distribution and discuss the generic features
of a distribution that result in superthermal photon bunching ().
Superthermal photon bunching has been reported for a number of optical
microcavity systems that exhibit processes like superradiance or mode
competition. We show that a superthermal photon number distribution cannot be
constructed from the principle of maximum entropy, if only the intensity and
the second-order autocorrelation are given. However, for bimodal systems an
unbiased superthermal distribution can be constructed from second-order
correlations and the intensities alone. Our findings suggest modeling
superthermal single-mode distributions by a mixture of a thermal and a lasing
like state and thus reveal a generic mechanism in the photon probability
distribution responsible for creating superthermal photon bunching. We relate
our general considerations to a physical system, a (single-emitter) bimodal
laser, and show that its statistics can be approximated and understood within
our proposed model. Furthermore the excellent agreement of the statistics of
the bimodal laser and our model reveal that the bimodal laser is an ideal
source of bunched photons, in the sense that it can generate statistics that
contain no other features but the superthermal bunching
Jump at the onset of saltation
We reveal a discontinuous transition in the saturated flux for aeolian
saltation by simulating explicitly particle motion in turbulent flow. The
discontinuity is followed by a coexistence interval with two metastable
solutions. The modification of the wind profile due to momentum exchange
exhibits a second maximum at high shear strength. The saturated flux depends on
the strength of the wind as
The fluctuation energy balance in non-suspended fluid-mediated particle transport
Here we compare two extreme regimes of non-suspended fluid-mediated particle
transport, transport in light and heavy fluids ("saltation" and "bedload",
respectively), regarding their particle fluctuation energy balance. From direct
numerical simulations, we surprisingly find that the ratio between collisional
and fluid drag dissipation of fluctuation energy is significantly larger in
saltation than in bedload, even though the contribution of interparticle
collisions to transport of momentum and energy is much smaller in saltation due
to the low concentration of particles in the transport layer. We conclude that
the much higher frequency of high-energy particle-bed impacts ("splash") in
saltation is the cause for this counter-intuitive behavior. Moreover, from a
comparison of these simulations to Particle Tracking Velocimetry measurements
which we performed in a wind tunnel under steady transport of fine and coarse
sand, we find that turbulent fluctuations of the flow produce particle
fluctuation energy at an unexpectedly high rate in saltation even under
conditions for which the effects of turbulence are usually believed to be
small
Minimal size of a barchan dune
Barchans are dunes of high mobility which have a crescent shape and propagate
under conditions of unidirectional wind. However, sand dunes only appear above
a critical size, which scales with the saturation distance of the sand flux [P.
Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002);
B. Andreotti, P. Claudin, and S. Douady, Eur. Phys. J. B {\bf{28,}} 321 (2002);
G. Sauermann, K. Kroy, and H. J. Herrmann, Phys. Rev. E {\bf{64,}} 31305
(2001)]. It has been suggested by P. Hersen, S. Douady, and B. Andreotti, Phys.
Rev. Lett. {\bf{89,}} 264301 (2002) that this flux fetch distance is itself
constant. Indeed, this could not explain the proto size of barchan dunes, which
often occur in coastal areas of high litoral drift, and the scale of dunes on
Mars. In the present work, we show from three dimensional calculations of sand
transport that the size and the shape of the minimal barchan dune depend on the
wind friction speed and the sand flux on the area between dunes in a field. Our
results explain the common appearance of barchans a few tens of centimeter high
which are observed along coasts. Furthermore, we find that the rate at which
grains enter saltation on Mars is one order of magnitude higher than on Earth,
and is relevant to correctly obtain the minimal dune size on Mars.Comment: 11 pages, 10 figure
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