655 research outputs found
Logarithmic Gradient Transformation and Chaos Expansion of Ito Processes
Since the seminal work of Wiener, the chaos expansion has evolved to a
powerful methodology for studying a broad range of stochastic differential
equations. Yet its complexity for systems subject to the white noise remains
significant. The issue appears due to the fact that the random increments
generated by the Brownian motion, result in a growing set of random variables
with respect to which the process could be measured. In order to cope with this
high dimensionality, we present a novel transformation of stochastic processes
driven by the white noise. In particular, we show that under suitable
assumptions, the diffusion arising from white noise can be cast into a
logarithmic gradient induced by the measure of the process. Through this
transformation, the resulting equation describes a stochastic process whose
randomness depends only upon the initial condition. Therefore the stochasticity
of the transformed system lives in the initial condition and thereby it can be
treated conveniently with the chaos expansion tools
Bounds on quantum gravity parameter from the NJL effective model of QCD
Existence of a minimal measurable length, as an effective cutoff in the
ultraviolet regime, is a common feature of all approaches to the quantum
gravity proposal. It is widely believed that this length scale will be of the
order of the Planck length , where
is a dimensionless parameter that should be
fixed only by the experiments. This issue can be taken into account through the
deformed momentum spaces with compact topologies. In this paper, we consider
minimum length effects on the physical quantities related to three parameters
of the Nambu-Jona-Lasinio effective model of QCD by means of the
deformed measure which is defined on compact momentum space with topology. This measure is suggested by the doubly special relativity
theories, Snyder deformed spaces, and the deformed algebra that is obtained in
the light of the stability theory of Lie algebras. Using the current
experimental data of the particle physics collaboration, we constraint quantum
gravity parameter and we compare our results with bounds that are
arisen from the other experimental setups.Comment: 10 pages, no figure, accepted for publication in Europhysics Letter
Gravity's rainbow: a bridge between LQC and DSR
The doubly special relativity (DSR) theories are investigated in order to
take into account an observer-independent length scale in special relativity
framework. It is widely believed that any quantum theory of gravity would
reduce to a DSR model at the flat limit when purely gravitational and quantum
mechanical effects are negligible. Gravity's rainbow is a simple generalization
of DSR theories to incorporate gravity. In this paper, we show that the
effective Friedmann equations that are suggested by loop quantum cosmology
(LQC) can be exactly reobtained in rainbow cosmology setup. The deformed
geometry of LQC then completely fixes the modified dispersion relation and
results in unique DSR model. In comparison with standard LQC scenario where
only the geometry is modified, both of the geometry and matter parts get
modifications in our setup. In this respect, we find that the total number of
microstates for the universe is finite which suggests the statistical origin
for the energy and entropy density bounds. These results explicitly show that
the DSR theories are appropriate candidates for the flat limit of loop quantum
gravity.Comment: 10 pages, 4 figures, Refs. adde
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Being unsituated: Christina Rossetti's prepositions
ABSTRACT: This essay will attend to Rossettiâs poetics of place and focus on poems from different periods in her writing life, including âItalia, Io Ti Saluto!â (1865), âBy the Seaâ, âAt Homeâ, âAfter Deathâ, âDream-Landâ (1849), and âSomewhere or Otherâ (1866). Drawing on the insights of spatial criticism, I will consider not only the figuration of place but also the experience of place and the unplaceable that they present. Following on from Heather Dubrowâs work on deictics in her study of Renaissance Lyric, I propose that attention to Rossettiâs language of location, and especially to her prepositions, can help to explain the haunting sense of place expressed in her poems. I argue that a sense of dislocation was, for Rossetti, not only a psycho-spiritual condition, but also an imaginative and poetic resource
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