Search results for "Exact results"
showing 10 items of 12 documents
Exact Canonical Dressing of Two-Level Atoms by Two-Photon Processes
1984
The aim of this paper is to present new exact results on the subject of dressing of a two-level atom by an electromagnetic field.
Quasiparticle Mean Field: BCS and Beyond
2007
In the previous two chapters we have laid the foundation for the BCS theory to describe open-shell nuclei. The properties of BCS solutions were compared with exact results from schematic solvable models. In this chapter we go into the details of numerical solution of the BCS equations. The implications of these solutions are discussed through applications to ds- and pf-shell nuclei.
INTERFACE TENSION AND CORRELATION LENGTH OF 2D POTTS MODELS: NUMERICAL VERSUS EXACT RESULTS
1994
I briefly review new analytical formulas for the correlation length and interface tension of two-dimensional q-state Potts models and compare them with numerical results from recent Monte Carlo simulation studies.
Exact results for accepting probabilities of quantum automata
2001
One of the properties of Kondacs-Watrous model of quantum finite automata (QFA) is that the probability of the correct answer for a QFA cannot be amplified arbitrarily. In this paper, we determine the maximum probabilities achieved by QFAs for several languages. In particular, we show that any language that is not recognized by an RFA (reversible finite automaton) can be recognized by a QFA with probability at most 0.7726...
A Wigner molecule at extremely low densities: a numerically exact study
2019
In this work we investigate Wigner localization at very low densities by means of the exact diagonalization of the Hamiltonian. This yields numerically exact results. In particular, we study a quasi-one-dimensional system of two electrons that are confined to a ring by three-dimensional gaussians placed along the ring perimeter. To characterize the Wigner localization we study several appropriate observables, namely the two-body reduced density matrix, the localization tensor and the particle-hole entropy. We show that the localization tensor is the most promising quantity to study Wigner localization since it accurately captures the transition from the delocalized to the localized state an…
Scattering coefficients and gray-body factor for 1D BEC acoustic black holes: exact results
2015
A complete set of exact analytic solutions to the mode equation is found in the region exterior to the acoustic horizon for a class of 1D Bose-Einstein condensate (BEC) acoustic black holes. From these, analytic expressions for the scattering coefficients and gray-body factor are obtained. The results are used to verify previous predictions regarding the behaviors of the scattering coefficients and gray-body factor in the low frequency limit.
Variational Cluster Methods in Coordinate Space for Small Systems: Center of Mass Corrections Made Easy
1991
A reexamination of the center of mass problem for light systems in the context of coupled cluster theory has produced a new variational version of the method which is developed entirely in coordinate space. It involves independent cluster functions which depend only on the relative coordinates of the subclusters of the system. In applications to the 4He nucleus described via a number of phenomenological and quasirealistic microscopic Wigner potentials, the method is shown to be quantitatively rather accurate, producing in all cases almost exact results for the ground-state energies at the SUB(3) level of approximation.
Time characteristics of Lévy flights in a steep potential well
2013
Using the method previously developed for ordinary Brownian diffusion, we derive a new formula to calculate the correlation time of stationary Lévy flights in a steep potential well. For the symmetric quartic potential, we obtain the exact expression of the correlation time of steady-state Lévy flights with index α = 1. The correlation time of stationary Lévy flights decreases with an increasing noise intensity and steepness of potential well.
Corrigendum to “On magnetic guidance of charged particles” [Phys. Lett. B 755 (2016) 409–413]
2016
The quantities α′ n and α′ n f are the positions where R(α) in Eqs. (7) and (9) have their maxima, respectively. In Fig. 1(a) the approximation based on these equations is compared with exact results obtained on the basis of Ref. [3]. The position of the spikes are now exactly reproduced. However, for small R ’s there remain some deviations. In particular, for the lowest orbit the expression (α2 + − α2 0) of [2, Eq. (13)] gets imaginary for R/r0 < 0.246 and causes a little kink, see Fig. 1(a). This fact prompted Dubbers [2] replacing for R ≤ 0.34 the quantity α+(R) by the approximation which reads corrected [4] α0[1 + (R/r0)/(8 sin2 α0/2)]. In addition, the statement in Ref. [2] that normal…
Fragmentation of fractal random structures.
2014
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model allows us to discuss a wide range of systems with fractal properties including trees as well as dense clusters. We present exact results for the densities of fragmenting edges and the distribution of fragment sizes for critical clusters in two dimensions. Dynamical fragmentation with a size cutoff leads to broad distributions of fragment sizes. The resulting power laws are shown to encode characteristic fingerprints of the fragmented objects.