The Razumov-Stroganov conjecture: Stochastic processes, loops and combinatorics

A fascinating conjectural connection between statistical mechanics and combinatorics has in the past five years led to the publication of a number of papers in various areas, including stochastic processes, solvable lattice models and supersymmetry. This connection, known as the Razumov-Stroganov conjecture, expresses eigenstates of physical systems in terms of objects known from combinatorics, which is the mathematical theory of counting. This note intends to explain this connection in light of the recent papers by Zinn-Justin and Di Francesco.Comment: 6 pages, 4 figures, JSTAT News & Perspective

Gravitational waves from hyperbolic encounters

The emission of gravitational waves from a system of massive objects interacting on hyperbolic orbits is studied in the quadrupole approximation. Analytic expressions are derived for the gravitational radiation luminosity, the total energy output and the gravitational radiation amplitude. An estimation of the expected number of events towards different targets (i.e. globular clusters and the center of the Galaxy) is also given. In particular, for a dense stellar cluster at the galactic center, a rate up to one event per year is obtained.Comment: 6 pages, 2 figure

Viscoelasticity and Stokes-Einstein relation in repulsive and attractive colloidal glasses

We report a numerical investigation of the visco-elastic behavior in models for steric repulsive and short-range attractive colloidal suspensions, along different paths in the attraction-strength vs packing fraction plane. More specifically, we study the behavior of the viscosity (and its frequency dependence) on approaching the repulsive glass, the attractive glass and in the re-entrant region where viscosity shows a non monotonic behavior on increasing attraction strength. On approaching the glass lines, the increase of the viscosity is consistent with a power-law divergence with the same exponent and critical packing fraction previously obtained for the divergence of the density fluctuations. Based on mode-coupling calculations, we associate the increase of the viscosity with specific contributions from different length scales. We also show that the results are independent on the microscopic dynamics by comparing newtonian and brownian simulations for the same model. Finally we evaluate the Stokes-Einstein relation approaching both glass transitions, finding a clear breakdown which is particularly strong for the case of the attractive glass.Comment: 12 pages; sent to J. Chem. Phy

Stochastic macromodeling for hierarchical uncertainty quantification of nonlinear electronic systems

A hierarchical stochastic macromodeling approach is proposed for the efficient variability analysis of complex nonlinear electronic systems. A combination of the Transfer Function Trajectory and Polynomial Chaos methods is used to generate stochastic macromodels. In order to reduce the computational complexity of the model generation when the number of stochastic variables increases, a hierarchical system decomposition is used. Pertinent numerical results validate the proposed methodology

Experimental reversion of the optimal quantum cloning and flipping processes

The quantum cloner machine maps an unknown arbitrary input qubit into two optimal clones and one optimal flipped qubit. By combining linear and non-linear optical methods we experimentally implement a scheme that, after the cloning transformation, restores the original input qubit in one of the output channels, by using local measurements, classical communication and feedforward. This significant teleportation-like method demonstrates how the information is preserved during the cloning process. The realization of the reversion process is expected to find useful applications in the field of modern multi-partite quantum cryptography.Comment: 10 pages, 3 figure

Anomalous resilient to decoherence macroscopic quantum superpositions generated by universally covariant optimal quantum cloning

We show that the quantum states generated by universal optimal quantum cloning of a single photon represent an universal set of quantum superpositions resilient to decoherence. We adopt Bures distance as a tool to investigate the persistence ofquantum coherence of these quantum states. According to this analysis, the process of universal cloning realizes a class of quantum superpositions that exhibits a covariance property in lossy configuration over the complete set of polarization states in the Bloch sphere.Comment: 8 pages, 6 figure

Visualizing probabilistic models: Intensive Principal Component Analysis

Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in high-dimensions. Inspired by replica theory from statistical mechanics, we consider replicas of the system to tune the dimensionality and take the limit as the number of replicas goes to zero. The result is the intensive embedding, which is not only isometric (preserving local distances) but allows global structure to be more transparently visualized. We develop the Intensive Principal Component Analysis (InPCA) and demonstrate clear improvements in visualizations of the Ising model of magnetic spins, a neural network, and the dark energy cold dark matter ({\Lambda}CDM) model as applied to the Cosmic Microwave Background.Comment: 6 pages, 5 figure

Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics

We consider the level 1 solution of quantum Knizhnik-Zamolodchikov equation with reflecting boundary conditions which is relevant to the Temperley--Lieb model of loops on a strip. By use of integral formulae we prove conjectures relating it to the weighted enumeration of Cyclically Symmetric Transpose Complement Plane Partitions and related combinatorial objects

Possible polarisation and spin dependent aspects of quantum gravity

We argue that quantum gravity theories that carry a Lie algebraic modification of the Poincare' and Heisenberg algebras inevitably provide inhomogeneities that may serve as seeds for cosmological structure formation. Furthermore, in this class of theories one must expect a strong polarisation and spin dependence of various quantum-gravity effects.Comment: Awarded an "honourable mention" in the 2007 Gravity Research Foundation Essay Competitio