1,217 research outputs found
Distribution of resonances for open quantum maps
We analyze simple models of classical chaotic open systems and of their
quantizations (open quantum maps on the torus). Our models are similar to
models recently studied in atomic and mesoscopic physics. They provide a
numerical confirmation of the fractal Weyl law for the density of quantum
resonances of such systems. The exponent in that law is related to the
dimension of the classical repeller (or trapped set) of the system. In a
simplified model, a rigorous argument gives the full resonance spectrum, which
satisfies the fractal Weyl law. For this model, we can also compute a quantity
characterizing the fluctuations of conductance through the system, namely the
shot noise power: the value we obtain is close to the prediction of random
matrix theory.Comment: 60 pages, no figures (numerical results are shown in other
references
Artin's primitive root conjecture -a survey -
This is an expanded version of a write-up of a talk given in the fall of 2000
in Oberwolfach. A large part of it is intended to be understandable by
non-number theorists with a mathematical background. The talk covered some of
the history, results and ideas connected with Artin's celebrated primitive root
conjecture dating from 1927. In the update several new results established
after 2000 are also discussed.Comment: 87 pages, 512 references, to appear in Integer
Probability around the Quantum Gravity. Part 1: Pure Planar Gravity
In this paper we study stochastic dynamics which leaves quantum gravity
equilibrium distribution invariant. We start theoretical study of this dynamics
(earlier it was only used for Monte-Carlo simulation). Main new results concern
the existence and properties of local correlation functions in the
thermodynamic limit. The study of dynamics constitutes a third part of the
series of papers where more general class of processes were studied (but it is
self-contained), those processes have some universal significance in
probability and they cover most concrete processes, also they have many
examples in computer science and biology. At the same time the paper can serve
an introduction to quantum gravity for a probabilist: we give a rigorous
exposition of quantum gravity in the planar pure gravity case. Mostly we use
combinatorial techniques, instead of more popular in physics random matrix
models, the central point is the famous exponent.Comment: 40 pages, 11 figure
Bilinear semi-classical moment functionals and their integral representation
We introduce the notion of bilinear moment functional and study their general
properties. The analogue of Favard's theorem for moment functionals is proven.
The notion of semi-classical bilinear functionals is introduced as a
generalization of the corresponding notion for moment functionals and motivated
by the applications to multi-matrix random models. Integral representations of
such functionals are derived and shown to be linearly independent.Comment: 25 pages, 3 figures, minor correction and change to Figure
Jet substructure and probes of CP violation in Vh production
We analyse the hVV (V = W, Z) vertex in a model independent way using Vh
production. To that end, we consider possible corrections to the Standard Model
Higgs Lagrangian, in the form of higher dimensional operators which parametrise
the effects of new physics. In our analysis, we pay special attention to linear
observables that can be used to probe CP violation in the same. By considering
the associated production of a Higgs boson with a vector boson (W or Z), we use
jet substructure methods to define angular observables which are sensitive to
new physics effects, including an asymmetry which is linearly sensitive to the
presence of CP odd effects. We demonstrate how to use these observables to
place bounds on the presence of higher dimensional operators, and quantify
these statements using a log likelihood analysis. Our approach allows one to
probe separately the hZZ and hWW vertices, involving arbitrary combinations of
BSM operators, at the Large Hadron Collider.Comment: 37 pages, 17 figures; v3 matches published versio
Dyson-Schwinger Equations and the Application to Hadronic Physics
We review the current status of nonperturbative studies of gauge field theory
using the Dyson-Schwinger equation formalism and its application to hadronic
physics. We begin with an introduction to the formalism and a discussion of
renormalisation in this approach. We then review the current status of studies
of Abelian gauge theories [e.g., strong coupling quantum electrodynamics]
before turning our attention to the non-Abelian gauge theory of the strong
interaction, quantum chromodynamics. We discuss confinement, dynamical chiral
symmetry breaking and the application and contribution of these techniques to
our understanding of the strong interactions.Comment: 110 pages, LaTeX. Replaced only to facilitate retrieval. Also
available at /u/ftp/pub/Review.uu via anonymnous-ft
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