Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem

In this letter we study the Aharonov-Bohm problem for a spin-1/2 particle in the quantum deformed framework generated by the $\kappa$-Poincar\'{e}-Hopf algebra. We consider the nonrelativistic limit of the $\kappa$-deformed Dirac equation and use the spin-dependent term to impose an upper bound on the magnitude of the deformation parameter $\varepsilon$. By using the self-adjoint extension approach, we examine the scattering and bound state scenarios. After obtaining the scattering phase shift and the $S$-matrix, the bound states energies are obtained by analyzing the pole structure of the latter. Using a recently developed general regularization prescription [Phys. Rev. D. \textbf{85}, 041701(R) (2012)], the self-adjoint extension parameter is determined in terms of the physics of the problem. For last, we analyze the problem of helicity conservation.Comment: 12 pages, no figures, submitted for publicatio

Remarks on the Aharonov-Casher dynamics in a CPT-odd Lorentz-violating background

The Aharonov-Casher problem in the presence of a Lorentz-violating background nonminimally coupled to a spinor and a gauge field is examined. Using an approach based on the self-adjoint extension method, an expression for the bound state energies is obtained in terms of the physics of the problem by determining the self-adjoint extension parameter.Comment: Matches published versio

On the κ\kappa-Dirac Oscillator revisited

This Letter is based on the $\kappa$-Dirac equation, derived from the $\kappa$-Poincar\'{e}-Hopf algebra. It is shown that the $\kappa$-Dirac equation preserves parity while breaks charge conjugation and time reversal symmetries. Introducing the Dirac oscillator prescription, $\mathbf{p}\to\mathbf{p}-im\omega\beta\mathbf{r}$, in the $\kappa$-Dirac equation, one obtains the $\kappa$-Dirac oscillator. Using a decomposition in terms of spin angular functions, one achieves the deformed radial equations, with the associated deformed energy eigenvalues and eigenfunctions. The deformation parameter breaks the infinite degeneracy of the Dirac oscillator. In the case where $\varepsilon=0$, one recovers the energy eigenvalues and eigenfunctions of the Dirac oscillator.Comment: 5 pages, no figures, accepted for publication in Physics Letters

Thermodynamic Formalism for Topological Markov Chains on Borel Standard Spaces

We develop a Thermodynamic Formalism for bounded continuous potentials defined on the sequence space $X\equiv E^{\mathbb{N}}$, where $E$ is a general Borel standard space. In particular, we introduce meaningful concepts of entropy and pressure for shifts acting on $X$ and obtain the existence of equilibrium states as additive probability measures for any bounded continuous potential. Furthermore, we establish convexity and other structural properties of the set of equilibrium states, prove a version of the Perron-Frobenius-Ruelle theorem under additional assumptions on the regularity of the potential and show that the Yosida-Hewitt decomposition of these equilibrium states do not have a purely additive part. We then apply our results to the construction of invariant measures of time-homogeneous Markov chains taking values on a general Borel standard space and obtain exponential asymptotic stability for a class of Markov operators. We also construct conformal measures for an infinite collection of interacting random paths which are associated to a potential depending on infinitely many coordinates. Under an additional differentiability hypothesis, we show how this process is related after a proper scaling limit to a certain infinite dimensional diffusion.Comment: Accepted for publication in Discrete and Continuous Dynamical Systems. 23 page

Controlling Network Latency in Mixed Hadoop Clusters: Do We Need Active Queue Management?

With the advent of big data, data center applications are processing vast amounts of unstructured and semi-structured data, in parallel on large clusters, across hundreds to thousands of nodes. The highest performance for these batch big data workloads is achieved using expensive network equipment with large buffers, which accommodate bursts in network traffic and allocate bandwidth fairly even when the network is congested. Throughput-sensitive big data applications are, however, often executed in the same data center as latency-sensitive workloads. For both workloads to be supported well, the network must provide both maximum throughput and low latency. Progress has been made in this direction, as modern network switches support Active Queue Management (AQM) and Explicit Congestion Notifications (ECN), both mechanisms to control the level of queue occupancy, reducing the total network latency. This paper is the first study of the effect of Active Queue Management on both throughput and latency, in the context of Hadoop and the MapReduce programming model. We give a quantitative comparison of four different approaches for controlling buffer occupancy and latency: RED and CoDel, both standalone and also combined with ECN and DCTCP network protocol, and identify the AQM configurations that maintain Hadoop execution time gains from larger buffers within 5%, while reducing network packet latency caused by bufferbloat by up to 85%. Finally, we provide recommendations to administrators of Hadoop clusters as to how to improve latency without degrading the throughput of batch big data workloads.The research leading to these results has received funding from the European Unions Seventh Framework Programme (FP7/2007–2013) under grant agreement number 610456 (Euroserver). The research was also supported by the Ministry of Economy and Competitiveness of Spain under the contracts TIN2012-34557 and TIN2015-65316-P, Generalitat de Catalunya (contracts 2014-SGR-1051 and 2014-SGR-1272), HiPEAC-3 Network of Excellence (ICT- 287759), and the Severo Ochoa Program (SEV-2011-00067) of the Spanish Government.Peer ReviewedPostprint (author's final draft

Interconnect Energy Savings and Lower Latency Networks in Hadoop Clusters: The Missing Link

An important challenge of modern data centres running Hadoop workloads is to minimise energy consumption, a significant proportion of which is due to the network. Significant network savings are already possible using Energy Efficient Ethernet, supported by a large number of NICs and switches, but recent work has demonstrated that the packet coalescing settings must be carefully configured to avoid a substantial loss in performance. Meanwhile, Hadoop is evolving from its original batch concept to become a more iterative type of framework. Other recent work attempts to reduce Hadoop's network latency using Explicit Congestion Notifications. Linking these studies reveals that, surprisingly, even when packet coalescing does not hurt performance, it can degrade network latency much more than previously thought. This paper is the first to analyze the impact of packet coalescing in the context of network latency. We investigate how to design and configure interconnects to provide the maximum energy savings without degrading cluster throughput performance or network latency.The research leading to these results has received funding from the European Unions Seventh Framework Programme (FP7/2007–2013) under grant agreement number 610456 (Euroserver). The research was also supported by the Ministry of Economy and Competitiveness of Spain under the contracts TIN2012-34557 and TIN2015-65316-P, Generalitat de Catalunya (contracts 2014-SGR-1051 and 2014-SGR-1272), HiPEAC-3 Network of Excellence (ICT- 287759), and the Severo Ochoa Program (SEV-2011-00067) of the Spanish Government.Peer ReviewedPostprint (author's final draft