Search results for "OPTIMIZATION"
showing 10 items of 2824 documents
Chattering phenomenon in quantum optimal control
2022
We present a quantum optimal control problem which exhibits a chattering phenomenon. This is the first instance of such a process in quantum control. Using the Pontryagin Maximum Principle and a general procedure due to V. F. Borisov and M. I. Zelikin, we characterize the local optimal synthesis, which is then globalized by a suitable numerical algorithm. We illustrate the importance of detecting chattering phenomena because of their impact on the efficiency of numerical optimization procedures.
Toward Prediction of Financial Crashes with a D-Wave Quantum Annealer
2019
The prediction of financial crashes in a complex financial network is known to be an NP-hard problem, which means that no known algorithm can efficiently find optimal solutions. We experimentally explore a novel approach to this problem by using a D-Wave quantum annealer, benchmarking its performance for attaining a financial equilibrium. To be specific, the equilibrium condition of a nonlinear financial model is embedded into a higher-order unconstrained binary optimization (HUBO) problem, which is then transformed into a spin-1/2 Hamiltonian with at most, two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be app…
Determination of resonance parameters in QCD by functional analysis methods
1988
A mathematically rigorous method based on functional analysis is used to determine resonance parameters of an amplitude from its given asymptotic expression in the space-like region. This method is checked on a model amplitude where both the asymptotic expression and the exact function are known. This method is then applied to the determination of the mass and the width of the ρ-meson from the corresponding space-like asymptotic QCD expression.
Chiral sum rules and vacuum condensates from tau-lepton decay data
2015
QCD finite energy sum rules, together with the latest updated ALEPH data on hadronic decays of the tau-lepton are used in order to determine the vacuum condensates of dimension $d=2$ and $d=4$. These data are also used to check the validity of the Weinberg sum rules, and to determine the chiral condensates of dimension $d=6$ and $d=8$, as well as the chiral correlator at zero momentum, proportional to the counter term of the ${\cal{O}}(p^4)$ Lagrangian of chiral perturbation theory, $\bar{L}_{10}$. Suitable (pinched) integration kernels are introduced in the sum rules in order to suppress potential quark-hadron duality violations. We find no compelling indications of duality violations in t…
Violation of quark-hadron duality and spectral chiral moments in QCD
2010
We analyze the spectral moments of the V - A two-point correlation function. Using all known short-distance constraints and the most recent experimental data from tau decays, we determine the lowest spectral moments, trying to assess the uncertainties associated with the so-called violations of quark-hadron duality. We have generated a large number of acceptable spectral functions, satisfying all conditions, and have used them to extract the wanted hadronic parameters through a careful statistical analysis. We obtain accurate values for the chi PT couplings L-10 and C-87, and a realistic determination of the dimension six and eight contributions in the operator product expansion, O-6 = (-5.…
Pinched weights and duality violation in QCD sum rules: A critical analysis
2010
We analyze the so-called pinched weights, that are generally thought to reduce the violation of quarkhadron duality in finite-energy sum rules. After showing how this is not true in general, we explain how to address this question for the left-right correlator and any particular pinched weight, taking advantage of our previous work [1], where the possible high-energy behavior of the left-right spectral function was studied. In particular, we show that the use of pinched weights allows to determine with high accuracy the dimension six and eight contributions in the operator-product expansion, O-6 = (-4.3(-0.7)(+0.9)) x 10(-3) GeV6 and O-8 = (-7.2(-5.3)(+4.2)) x 10(-3) GeV8.
Comparison between two strictly local QCD sum rules
1989
Two strictly local QCD sum rules, analytic extrapolation by conformal mapping and analytic continuation by duality, are developed and presented in full detail. They allow the extrapolation of the QCD amplitude to a single point near zero in the complex {ital q}{sup 2} plane. Being orthogonal to the usual QCD sum rules, they present a drastic enlargement of phenomenological applications. In addition, the stability of both methods is shown explicitly, a fact which makes them particularly reliable. The difference between the two methods is illustrated in connection with the determination of the hadronic ({ital g}{minus}2) factor of the muon. Their effectiveness is demonstrated in the calculati…
B and B(S) decay constants from moments of finite energy sum rules in QCD
2004
We use an appropriate combination of moments of finite energy sum rules in QCD in order to compute the B_q-meson decays constants f_B and f_{B_s}.We perform the calculation using a two-loop computation of the imaginary part of the pseudoscalar two point function in terms of the running bottom quark mass. The results are stable with the so called QCD duality threshold and they are in agreement with the estimates obtained from Borel transform QCD sum rules and lattice computations.
TheA 1-and the ϕ-meson in QCD
1993
Recently we used a method of stable analytic extrapolation to test whether strictly local duality between the asymptotic and the resonance region, which is believed to be valid in QCD, appears already at the present stage of QCD calculations. Probing the QCD ϱ-amplitude, we found a prominent bump structure in the resonance region, i.e. a rather direct evidence for the validity of local duality. In the present paper we confirm and extend this result by giving two further applications, theA1-meson and the ϕ-meson. While we do not meet theA1, as was to be expected since other sum rules can not separate it from the continuum, too, the extrapolation of the ϕ-amplitude leads to an enormous bump. …
Duality in semileptonicτdecay
1984
The branching ratios for all channels of tau decay are reconsidered within the framework of perturbative and nonperturbative QCD. The predictions agree with experiment.