Full Counting Statistics of Cooper Pair Shuttling

The Cooper pair shuttle is a simple model system that combines features of coherent and incoherent transport. We evaluate the full counting statistics (FCS) of charge transfer via the shuttle in the incoherent regime. We describe two limiting cases when the FCS allows for classical interpretation. Generally, the classical interpretation fails yielding negative and imaginary "probabilities". This signals that superconducting coherence survives even in incoherent regime. We evaluate the current noise in some detail.Comment: 4 pages, 3 figures; v2 (published version) corrected misprint

Linear Quantum Entropy and Non-Hermitian Hamiltonians

We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians.~Within such a framework, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian Hamiltonian (which is typically useful within a mixed quantum-classical representation). Both the case of a system represented by a pure non-Hermitian Hamiltonian as well as that of the case of non-Hermitian dynamics in a classical bath are explicitly considered.Comment: Entropy, Special Issue "Entropy in Quantum Systems and Quantum Field Theory (QFT)

Rigorous construction of ground state correlations in graphene: renormalization of the velocities and Ward Identities

We consider the 2D Hubbard model on the honeycomb lattice, as a model for single layer graphene with screened Coulomb interactions; at half filling and weak coupling, we construct its ground state correlations by a convergent multiscale expansion, rigorously excluding the presence of magnetic or superconducting instabilities or the formation of a mass gap. The Fermi velocity, which can be written in terms of a convergent series expansion, remains close to its non-interacting value and turns out to be isotropic. On the contrary, the interaction produces an asymmetry between the two components of the charge velocity, in contrast with the predictions based on relativistic or continuum approximations.Comment: 4 pages, 1 figure; version published on Phys. Rev. B; erratum adde

Multi-parametric R-matrix for the sl(2|1) Yangian

We study the Yangian of the sl(2|1) Lie superalgebra in a multi-parametric four-dimensional representation. We use Drinfeld's second realization to independently rederive the R-matrix, and to obtain the antiparticle representation, the crossing and the unitarity condition. We consistently apply the Yangian antipode and its inverse to the individual particles involved in the scattering. We explicitly find a scalar factor solving the crossing and unitarity conditions, and study the analytic structure of the resulting dressed R-matrix. The formulas we obtain bear some similarities with those familiar from the study of integrable structures in the AdS/CFT correspondence, although they present obvious crucial differences.Comment: 25 pages, LaTeX, no figures; v2: typos corrected, minor changes, added pole analysis of the dressed R-matrix; v3: clarifications added, typos corrected, references added; v4: typos corrected, minor changes, version to appear in J. Math. Phy

Real-Time Containers: A Survey

Container-based virtualization has gained a significant importance in a deployment of software applications in cloud-based environments. The technology fully relies on operating system features and does not require a virtualization layer (hypervisor) that introduces a performance degradation. Container-based virtualization allows to co-locate multiple isolated containers on a single computation node as well as to decompose an application into multiple containers distributed among several hosts (e.g., in fog computing layer). Such a technology seems very promising in other domains as well, e.g., in industrial automation, automotive, and aviation industry where mixed criticality containerized applications from various vendors can be co-located on shared resources. However, such industrial domains often require real-time behavior (i.e, a capability to meet predefined deadlines). These capabilities are not fully supported by the container-based virtualization yet. In this work, we provide a systematic literature survey study that summarizes the effort of the research community on bringing real-time properties in container-based virtualization. We categorize existing work into main research areas and identify possible immature points of the technology

The Italian primary school-size distribution and the city-size: a complex nexus

We characterize the statistical law according to which Italian primary school-size distributes. We find that the school-size can be approximated by a log-normal distribution, with a fat lower tail that collects a large number of very small schools. The upper tail of the school-size distribution decreases exponentially and the growth rates are distributed with a Laplace PDF. These distributions are similar to those observed for firms and are consistent with a Bose-Einstein preferential attachment process. The body of the distribution features a bimodal shape suggesting some source of heterogeneity in the school organization that we uncover by an in-depth analysis of the relation between schools-size and city-size. We propose a novel cluster methodology and a new spatial interaction approach among schools which outline the variety of policies implemented in Italy. Different regional policies are also discussed shedding lights on the relation between policy and geographical features.Comment: 16 pages, 10 figure

Optimal Online Selection of a Monotone Subsequence: a Central Limit Theorem

Consider a sequence of $n$ independent random variables with a common continuous distribution $F$, and consider the task of choosing an increasing subsequence where the observations are revealed sequentially and where an observation must be accepted or rejected when it is first revealed. There is a unique selection policy $\pi_n^*$ that is optimal in the sense that it maximizes the expected value of $L_n(\pi_n^*)$, the number of selected observations. We investigate the distribution of $L_n(\pi_n^*)$; in particular, we obtain a central limit theorem for $L_n(\pi_n^*)$ and a detailed understanding of its mean and variance for large $n$. Our results and methods are complementary to the work of Bruss and Delbaen (2004) where an analogous central limit theorem is found for monotone increasing selections from a finite sequence with cardinality $N$ where $N$ is a Poisson random variable that is independent of the sequence.Comment: 26 page

Three-quark potentials in an SU(3)SU(3) effective Polyakov loop model

Three-quark potentials are studied in great details in the three-dimensional $SU(3)$ pure gauge theory at finite temperature, for the cases of static sources in the fundamental and adjoint representations. For this purpose, the corresponding Polyakov loop model in its simplest version is adopted. The potentials in question, as well as the conventional quark--anti-quark potentials, are calculated numerically both in the confinement and deconfinement phases. Results are compared to available analytical predictions at strong coupling and in the limit of large number of colors $N$. The three-quark potential is tested against the expected $\Delta$ and $Y$ laws and the $3q$ string tension entering these laws is compared to the conventional $q\bar{q}$ string tension. As a byproduct of this investigation, essential features of the critical behaviour across the deconfinement transition are elucidated.Comment: 28 pages, 18 figures, 4 tables; some text and a few references added; version accepted for publication on Nucl. Phys.