11,632 research outputs found
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
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
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
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
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