Search results for "Approx"

Correspondence between generalized binomial field states and coherent atomic states

2008

We show that the N-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of N two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the N-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.

Comparison of Microscopic Interacting Boson Model and Quasiparticle Random Phase Approximation 0νββ Decay Nuclear Matrix Elements

2021

The fundamental nature of the neutrino is presently a subject of great interest. A way to access the absolute mass scale and the fundamental nature of the neutrino is to utilize the atomic nuclei through their rare decays, the neutrinoless double beta (0νββ) decay in particular. The experimentally measurable observable is the half-life of the decay, which can be factorized to consist of phase space factor, axial vector coupling constant, nuclear matrix element, and function containing physics beyond the standard model. Thus reliable description of nuclear matrix element is of crucial importance in order to extract information governed by the function containing physics beyond the standard m…

Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems

2020

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind,…

Can the adaptive Metropolis algorithm collapse without the covariance lower bound?

2011

The Adaptive Metropolis (AM) algorithm is based on the symmetric random-walk Metropolis algorithm. The proposal distribution has the following time-dependent covariance matrix at step $n+1$ \[ S_n = Cov(X_1,...,X_n) + \epsilon I, \] that is, the sample covariance matrix of the history of the chain plus a (small) constant $\epsilon>0$ multiple of the identity matrix $I$. The lower bound on the eigenvalues of $S_n$ induced by the factor $\epsilon I$ is theoretically convenient, but practically cumbersome, as a good value for the parameter $\epsilon$ may not always be easy to choose. This article considers variants of the AM algorithm that do not explicitly bound the eigenvalues of $S_n$ away …

Representing compact sets of compact operators and of compact range vector measures

1987

The Complex WKB Method

2019

In this chapter we shall study the exponential growth and asymptotic expansions of exact solutions of second-order differential equations in the semi-classical limit. As an application, we establish a Bohr-Sommerfeld quantization condition for Schrodinger operators with real-analytic complex-valued potentials.

Computing the Trace

2001

So far we have been interested in the general expression for the WKB-propagation function. Now we turn our attention to the trace of that propagator, since we want to exhibit the energy eigenvalues of a given potential. From earlier discussions we know that the energy levels of a given Hamiltonian are provided by the poles of the Green’s function:

Synchronous R-NSGA-II: An Extended Preference-Based Evolutionary Algorithm for Multi-Objective Optimization

2015

Classical evolutionary multi-objective optimization algorithms aim at finding an approx- imation of the entire set of Pareto optimal solutions. By considering the preferences of a decision maker within evolutionary multi-objective optimization algorithms, it is possible to focus the search only on those parts of the Pareto front that satisfy his/her preferences. In this paper, an extended preference-based evolutionary algorithm has been proposed for solving multi-objective optimiza- tion problems. Here, concepts from an interactive synchronous NIMBUS method are borrowed and combined with the R-NSGA-II algorithm. The proposed synchronous R-NSGA-II algorithm uses preference information provid…

Strictly correlated electrons approach to excitation energies of dissociating molecules

2019

In this work we consider a numerically solvable model of a two-electron diatomic molecule to study a recently proposed approximation based on the density functional theory of so-called strictly correlated electrons (SCE). We map out the full two-particle wave function for a wide range of bond distances and interaction strengths and obtain analytic results for the two-particle states and eigenenergies in various limits of strong and weak interactions, and in the limit of large bond distance. We then study the so-called Hartree-exchange-correlation (Hxc) kernel of time-dependent density functional theory which is a key ingredient in calculating excitation energies. We study an approximation b…

Few-body insights of multiquark exotic hadrons

2018

In this contribution we discuss the adequate treatment of the $4-$ and $5-$body dynamics within a constituent quark framework. We stress that the variational and Born-Oppenheimer approximations give energies rather close to the exact ones, while the diquark approximation might be rather misleading. Hall-Post inequalities provide very useful lower bounds that exclude possible stable states for some mass ratios and color wave functions.