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 SU(2)SU(2) 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 $\lambda=\lambda_0\,l_{_{\rm Pl}}$, where $\lambda_0\sim{\mathcal O}(1)$ 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 $SU(2)$ Nambu-Jona-Lasinio effective model of QCD by means of the deformed measure which is defined on compact momentum space with ${\mathbf S}^3$ 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 $\lambda_0$ 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

Being unsituated: Christina Rossetti's prepositions

ABSTRACT: This essay will attend to Rossetti’s poetics of place and focus on poems from different periods in her writing life, including “Italia, Io Ti Saluto!” (1865), “By the Sea”, “At Home”, “After Death”, “Dream-Land” (1849), and “Somewhere or Other” (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 Dubrow’s work on deictics in her study of Renaissance Lyric, I propose that attention to Rossetti’s 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