Search results for " formula"
showing 10 items of 629 documents
Gluon mass generation in the presence of dynamical quarks
2013
We study in detail the impact of dynamical quarks on the gluon mass generation mechanism, in the Landau gauge, for the case of a small number of quark families. As in earlier considerations, we assume that the main bulk of the unquenching corrections to the gluon propagator originates from the fully dressed quark-loop diagram. The nonperturbative evaluation of this diagram provides the key relation that expresses the unquenched gluon propagator as a deviation from its quenched counterpart. This relation is subsequently coupled to the integral equation that controls the momentum evolution of the effective gluon mass, which contains a single adjustable parameter; this constitutes a major impr…
Precision Measurement of the First Ionization Potential of Nobelium
2018
One of the most important atomic properties governing an element's chemical behavior is the energy required to remove its least-bound electron, referred to as the first ionization potential. For the heaviest elements, this fundamental quantity is strongly influenced by relativistic effects which lead to unique chemical properties. Laser spectroscopy on an atom-at-a-time scale was developed and applied to probe the optical spectrum of neutral nobelium near the ionization threshold. The first ionization potential of nobelium is determined here with a very high precision from the convergence of measured Rydberg series to be 6.626 21±0.000 05 eV. This work provides a stringent benchmark for st…
Pricing of forwards and other derivatives in cointegrated commodity markets
2015
Abstract We analyze cointegration in commodity markets, and propose a parametric class of pricing measures which preserves cointegration for forward prices with fixed time to maturity. We present explicit expressions for the term structure of volatility and correlation in the context of our spot price models based on continuous-time autoregressive moving average dynamics for the stationary components. The term structures have many interesting shapes, and we provide some empirical evidence from refined oil future prices at NYMEX defending our modeling idea. Motivated from these results, we present a cointegrated forward price dynamics using the Heath–Jarrow–Morton approach. In this setting, …
Exact solution of generalized Tavis - Cummings models in quantum optics
1996
Quantum inverse methods are developed for the exact solution of models which describe N two-level atoms interacting with one mode of the quantized electromagnetic field containing an arbitrary number of excitations M. Either a Kerr-type nonlinearity or a Stark-shift term can be included in the model, and it is shown that these two cases can be mapped from one to the other. The method of solution provides a general framework within which many related problems can similarly be solved. Explicit formulae are given for the Rabi splitting of the models for some N and M, on- and off-resonance. It is also shown that the solution of the pure Tavis - Cummings model can be reduced to solving a homogen…
A weakly-interacting many-body system of Rydberg polaritons based on electromagnetically induced transparency
2020
We proposed utilizing a medium with a high optical depth (OD) and a Rydberg state of low principal quantum number, $n$, to create a weakly-interacting many-body system of Rydberg polaritons, based on the effect of electromagnetically induced transparency (EIT). We experimentally verified the mean field approach to weakly-interacting Rydberg polaritons, and observed the phase shift and attenuation induced by the dipole-dipole interaction (DDI). The DDI-induced phase shift or attenuation can be viewed as a consequence of the elastic or inelastic collisions among the Rydberg polaritons. Using a weakly-interacting system, we further observed that a larger DDI strength caused a width of the mome…
Dimensionless analysis of RC rectangular sections under axial load and biaxial bending
2012
This paper proposes a numerical procedure able to provide ultimate curvature and moment domains of rectangular RC sections subjected to combined axial load and biaxial bending. The formulation is carried out in dimensionless terms in order to give results that are valid for classes of sections characterized by the same values of the geometric and mechanical parameters governing the section response. The role of some of these parameters is investigated here. The results show possible correlations linking the actual values of moment and curvature to the values corresponding to two cases of uniaxial bending to be considered separately. © 2012 Elsevier Ltd.
Towards an accurate molecular orbital theory for excited states : Ethene, butadiene, and hexatriene
1993
A newly proposed quantum chemical approach for ab initio calculations of electronic spectra of molecular systems is applied to the molecules ethene, trans‐1,3‐butadiene, and trans‐trans‐1,3,5‐hexatriene. The method has the aim of being accurate to better than 0.5 eV for excitation energies and is expected to provide structural and physical data for the excited states with good reliability. The approach is based on the complete active space (CAS) SCF method, which gives a proper description of the major features in the electronic structure of the excited state, independent of its complexity, accounts for all near degeneracy effects, and includes full orbital relaxation. Remaining dynamic ele…
Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral
2014
A novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators endowed with fractional derivatives elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes which rely on a discrete version of the…
Enumeration and Structure of Trapezoidal Words
2013
Trapezoidal words are words having at most $n+1$ distinct factors of length $n$ for every $n\ge 0$. They therefore encompass finite Sturmian words. We give combinatorial characterizations of trapezoidal words and exhibit a formula for their enumeration. We then separate trapezoidal words into two disjoint classes: open and closed. A trapezoidal word is closed if it has a factor that occurs only as a prefix and as a suffix; otherwise it is open. We investigate open and closed trapezoidal words, in relation with their special factors. We prove that Sturmian palindromes are closed trapezoidal words and that a closed trapezoidal word is a Sturmian palindrome if and only if its longest repeated …
On the Structure of Bispecial Sturmian Words
2013
A balanced word is one in which any two factors of the same length contain the same number of each letter of the alphabet up to one. Finite binary balanced words are called Sturmian words. A Sturmian word is bispecial if it can be extended to the left and to the right with both letters remaining a Sturmian word. There is a deep relation between bispecial Sturmian words and Christoffel words, that are the digital approximations of Euclidean segments in the plane. In 1997, J. Berstel and A. de Luca proved that \emph{palindromic} bispecial Sturmian words are precisely the maximal internal factors of \emph{primitive} Christoffel words. We extend this result by showing that bispecial Sturmian wo…