Search results for "Statistical"
showing 10 items of 4960 documents
Indeterminacy relations in random dynamics
2007
We analyze various uncertainty measures for spatial diffusion processes. In this manifestly non-quantum setting, we focus on the existence issue of complementary pairs whose joint dispersion measure has strictly positive lower bound.
Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well
2014
This paper is a direct offspring of Ref. [J. Math. Phys. 54, 072103, (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of mentions was maid with respect to various inconsistencies and faulty statements omnipresent in the literature devoted to so-called fractional quantum mechanics spectral problems. Presently, we give a decisive computer-assisted proof, for an exemplary finite and ultimately infinite Cauchy well problem, that spectral solutions proposed so far were plainly wrong. As a constructive input, we provide an explicit spectral solution of the finite Cauchy well. The infinite well emerges as a limiting case in a sequence of deep…
General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles
2017
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, which is the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. H…
Toward Pricing Financial Derivatives with an IBM Quantum Computer
2021
Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either the instantaneous interest rate or the instantaneous forward rate. A successful approach to model the latter is the celebrated Heath-Jarrow-Morton framework, in which its dynamics is entirely specified by volatility factors. In its multifactor version, this model considers several noisy components to capture at best the dynamics of several time-maturing forward rates. However, as no general analytical solution is available, there is a trade-off between t…
Kac-Moody group representations and generalization of the Sugawara construction of the Virasoro algebra
1988
We discuss the dynamical structure of the semidirect product of the Virasoro and affine Kac-Moody groups within the framework of a group quantization formalism. This formalism provides a realization of the Virasoro algebra acting on Kac-Moody Fock states which generalizes the Sugawara construction. We also give an explicit construction of the standard Kac-Moody group representations associated with strings on SU(2) and recover, in particular, the ‘renormalization’ β factor of L(z)
Accuracy of Rotational Parameters Predicted by High-Level Quantum-Chemical Calculations: Case Study of Sulfur-Containing Molecules of Astrochemical I…
2018
The accuracy of rotational parameters obtained from high-level quantum-chemical calculations is discussed for molecules containing second-row atoms. The main focus is on computed rotational constants for which two statistical analyses have been carried out. A first benchmark study concerns sulfur-bearing species and involves 15 molecules (for a total of 74 isotopologues). By comparing 15 different computational approaches, all of them based on the coupled-cluster singles and doubles approach (CCSD) augmented by a perturbative treatment of triple excitations, CCSD(T), we have analyzed the effects on computed rotational constants due to (i) extrapolation to the complete basis-set limit, (ii) …
Measuring KS0K± interactions using Pb–Pb collisions at sNN=2.76 TeV
2019
We present the first measurements of femtoscopic correlations between the KS0 and K± particles in pp collisions at s=7 TeV measured by the ALICE experiment. The observed femtoscopic correlations are consistent with final-state interactions proceeding solely via the a0(980) resonance. The extracted kaon source radius and correlation strength parameters for KS0K− are found to be equal within the experimental uncertainties to those for KS0K+ . Results of the present study are compared with those from identical-kaon femtoscopic studies also performed with pp collisions at s=7 TeV by ALICE and with a KS0K± measurement in Pb–Pb collisions at sNN=2.76 TeV. Combined with the Pb–Pb results, our pp a…
QCD matching conditions at thresholds
1993
The use of MS-like renormalization schemes in QCD requires an implementation of nontrivial matching conditions across thresholds, a fact often overlooked in the literature. We shortly review the use of these matching conditions in QCD and check explicitly that the prediction for $\alpha_s(M_Z)$, obtained by running the strong coupling constant from the $M_\tau$ scale, does not substantially depend on the exact value of the matching point chosen in crossing the $b$-quark threshold when the appropriate matching conditions are taken into account.
Multiparton NLO corrections by numerical methods
2013
In this talk we discuss an algorithm for the numerical calculation of one-loop QCD amplitudes and present results at next-to-leading order for jet observables in electron-positron annihilation calculated with the above-mentioned method. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of QCD one-loop amplitudes, as well as a method to deform the integration contour for the loop integration into the complex plane to match Feynman's i delta rule. The algorithm is formulated at the amplitude level and does not rely on Feynman graphs. Therefore all ingredients of the algorithm can be calculated efficiently using recurrence relations. The…
Recent results within Lipatov's high energy effective action
2013
We review Lipatov’s high energy effective action and show that it is a useful computational tool to calculate QCD scattering amplitudes in the high energy limit. We explain in some detail our recent work where a novel regularization and subtraction procedure has been proposed that allows to extend the use of this effective action beyond tree level. As explicit results we discuss the derivation of forward jet vertices, for jet events with and without rapidity gaps.