Path Integral for non-relativistic Generalized Uncertainty Principle corrected Hamiltonian

Generalized Uncertainty Principle (GUP) has brought the idea of existence of minimum measurable length in Quantum physics. Depending on this GUP, non-relativistic Hamiltonian at the Planck scale is modified. In this article, we construct the kernel for this GUP corrected Hamiltonian for free particle by applying the Hamiltonian path integral approach and check the validity conditions for this kernel thoroughly. Interestingly, the probabilistic interpretation of this kernel induces a momentum upper bound in the theory which is comparable with GUP induced maximum momentum uncertainty.Comment: 11 pages, no figures, some new result added, accepted to be published in Physical Review

Weak limits for exploratory plots in the analysis of extremes

Exploratory data analysis is often used to test the goodness-of-fit of sample observations to specific target distributions. A few such graphical tools have been extensively used to detect subexponential or heavy-tailed behavior in observed data. In this paper we discuss asymptotic limit behavior of two such plotting tools: the quantile-quantile plot and the mean excess plot. The weak consistency of these plots to fixed limit sets in an appropriate topology of $\mathbb{R}^2$ has been shown in Das and Resnick (Stoch. Models 24 (2008) 103-132) and Ghosh and Resnick (Stochastic Process. Appl. 120 (2010) 1492-1517). In this paper we find asymptotic distributional limits for these plots when the underlying distributions have regularly varying right-tails. As an application we construct confidence bounds around the plots which enable us to statistically test whether the underlying distribution is heavy-tailed or not.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ401 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Status and performance of the Compact Muon Solenoid pixel detector

The Compact Muon Solenoid (CMS) experiment at the LHC incorporates a 66 million channel silicon pixel detector at its center for track seeding and precise vertexing. The hardware and data acquisition software of the pixel detector are briefly introduced in this paper. Experience with installation is succinctly recounted and some of the calibrations performed during the commissioning period are described. Preliminary performance numbers like charge collection and hit residuals from cosmic ray tracks are presented

Noncommutative Extension of AdS-CFT and Holographic Superconductors

In this Letter, we consider a Non-Commutative (NC) extension of AdS-CFT correspondence and its effects on holographic superconductors. NC corrections are incorporated via the NC generalization of Schwarzschild black hole metric in AdS with the probe limit. We study NC effects on the relations connecting the charge density and the critical temperature of the Holographic Superconductors. Furthermore, condensation operator of the superconductor has been analyzed. Our results suggest that generically, NC effects increase the critical temperature of the holographic superconductor.Comment: One figure is added, modification in formalism and noncommutative effects emergent from star product has been removed. Results altered but main conclusions remain unchanged. To appear in Phys.Lett.

Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral

In this article, we discuss some well-known theoretical models where an observer-independent energy scale or a length scale is present. The presence of this invariant scale necessarily deforms the Lorentz symmetry. We study different aspects and features of such theories about how modifications arise due to this cutoff scale. First we study the formulation of energy-momentum tensor for a perfect fluid in doubly special relativity (DSR), where an energy scale is present. Then we go on to study modifications in thermodynamic properties of photon gas in DSR. Finally we discuss some models with generalized uncertainty principle (GUP).Comment: This is a review article based on our works arXiv:1002.0192, arXiv:0908.0413, arXiv:1205.3919; v2: text overlap with gr-qc/0207085 remove