314,621 research outputs found
Quantum Hall Transition in the Classical Limit
We study the quantum Hall transition using the density-density correlation
function. We show that in the limit h->0 the electron density moves along the
percolating trajectories, undergoing normal diffusion. The localization
exponent coincides with its percolation value \nu=4/3. The framework provides a
natural way to study the renormalization group flow from percolation to quantum
Hall transition. We also confirm numerically that the critical conductivity of
a classical limit of quantum Hall transition is \sigma_{xx} = \sqrt{3}/4.Comment: 8 pages, 4 figures; substantial changes include the critical
conductivity calculatio
Path integrals and symmetry breaking for optimal control theory
This paper considers linear-quadratic control of a non-linear dynamical
system subject to arbitrary cost. I show that for this class of stochastic
control problems the non-linear Hamilton-Jacobi-Bellman equation can be
transformed into a linear equation. The transformation is similar to the
transformation used to relate the classical Hamilton-Jacobi equation to the
Schr\"odinger equation. As a result of the linearity, the usual backward
computation can be replaced by a forward diffusion process, that can be
computed by stochastic integration or by the evaluation of a path integral. It
is shown, how in the deterministic limit the PMP formalism is recovered. The
significance of the path integral approach is that it forms the basis for a
number of efficient computational methods, such as MC sampling, the Laplace
approximation and the variational approximation. We show the effectiveness of
the first two methods in number of examples. Examples are given that show the
qualitative difference between stochastic and deterministic control and the
occurrence of symmetry breaking as a function of the noise.Comment: 21 pages, 6 figures, submitted to JSTA
Explicit generation of the branching tree of states in spin glasses
We present a numerical method to generate explicit realizations of the tree
of states in mean-field spin glasses. The resulting study illuminates the
physical meaning of the full replica symmetry breaking solution and provides
detailed information on the structure of the spin-glass phase. A cavity
approach ensures that the method is self-consistent and permits the evaluation
of sophisticated observables, such as correlation functions. We include an
example application to the study of finite-size effects in single-sample
overlap probability distributions, a topic that has attracted considerable
interest recently.Comment: Version accepted for publication in JSTA
Gravity as an emergent phenomenon: a GFT perspective
While the idea of gravity as an emergent phenomenon is an intriguing one,
little is known about concrete implementations that could lead to viable
phenomenology, most of the obstructions being related to the intrinsic
difficulties of formulating genuinely pregeometric theories. In this paper we
present a preliminary discussion of the impact of critical behavior of certain
microscopic models for gravity, based on group field theories, on the dynamics
of the macroscopic regime. The continuum limit is examined in light of some
scaling assumption, and the relevant consequences for low energy effective
theories are discussed, the role of universality, the corrections to scaling,
the emergence of gravitational theories and the nature of their thermodynamical
behavior.Comment: 1+26 page
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