27,548 research outputs found
Structure of the broken phase of the sine-Gordon model using functional renormalization
We study in this paper the sine-Gordon model using functional Renormalization
Group (fRG) at Local Potential Approximation (LPA) using different RG schemes.
In , using Wegner-Houghton RG we demonstrate that the location of the
phase boundary is entirely driven by the relative position to the Coleman fixed
point even for strongly coupled bare theories. We show the existence of a set
of IR fixed points in the broken phase that are reached independently of the
bare coupling. The bad convergence of the Fourier series in the broken phase is
discussed and we demonstrate that these fixed-points can be found only using a
global resolution of the effective potential. We then introduce the methodology
for the use of Average action method where the regulator breaks periodicity and
show that it provides the same conclusions for various regulators. The behavior
of the model is then discussed in and the absence of the previous
fixed points is interpreted.Comment: 43 pages, 32 figures, accepted versio
The non-perturbative renormalization group in the ordered phase
We study some analytical properties of the solutions of the non perturbative
renormalization group flow equations for a scalar field theory with
symmetry in the ordered phase, i.e. at temperatures below the critical
temperature. The study is made in the framework of the local potential
approximation. We show that the required physical discontinuity of the magnetic
susceptibility at ( spontaneous magnetization) is
reproduced only if the cut-off function which separates high and low energy
modes satisfies to some restrictive explicit mathematical conditions; we stress
that these conditions are not satisfied by a sharp cut-off in dimensions of
space .Comment: 27 pages, 14 figures, 7 table
Decay rate estimations for linear quadratic optimal regulators
Let be the optimal control of the open-loop system
in a linear quadratic optimization problem. By using
different complex variable arguments, we give several lower and upper estimates
of the exponential decay rate of the closed-loop system .
Main attention is given to the case of a skew-Hermitian matrix .
Given an operator , for a class of cases, we find a matrix that
provides an almost optimal decay rate.
We show how our results can be applied to the problem of optimizing the decay
rate for a large finite collection of control systems , , and illustrate this on an example of a concrete mechanical system. At the
end of the article, we pose several questions concerning the decay rates in the
context of linear quadratic optimization and in a more general context of the
pole placement problem.Comment: 25 pages, 1 figur
Is Hilbert space discrete?
We show that discretization of spacetime naturally suggests discretization of
Hilbert space itself. Specifically, in a universe with a minimal length (for
example, due to quantum gravity), no experiment can exclude the possibility
that Hilbert space is discrete. We give some simple examples involving qubits
and the Schrodinger wavefunction, and discuss implications for quantum
information and quantum gravity.Comment: 4 pages, revtex, 1 figur
Robust â„‹2 Performance: Guaranteeing Margins for LQG Regulators
This paper shows that ℋ2 (LQG) performance specifications can be combined with structured uncertainty in the system, yielding robustness analysis conditions of the same nature and computational complexity as the corresponding conditions for ℋ∞ performance. These conditions are convex feasibility tests in terms of Linear Matrix Inequalities, and can be proven to be necessary and sufficient under the same conditions as in the ℋ∞ case.
With these results, the tools of robust control can be viewed as coming full circle to treat the problem where it all began: guaranteeing margins for LQG regulators
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