23 research outputs found
Two-boson Correlations in Various One-dimensional Traps
A one-dimensional system of two trapped bosons which interact through a
contact potential is studied using the optimized configuration interaction
method. The rapid convergence of the method is demonstrated for trapping
potentials of convex and non-convex shapes. The energy spectra, as well as
natural orbitals and their occupation numbers are determined in function of the
inter-boson interaction strength. Entanglement characteristics are discussed in
dependence on the shape of the confining potential.Comment: 5 pages, 3 figure
Quasi-exact solutions for two interacting electrons in two-dimensional anisotropic dots
We present an analysis of the two-dimensional Schrodinger equation for two
electrons interacting via Coulombic force and confined in an anizotropic
harmonic potential. The separable case of wy = 2wx is studied particularly
carefully. The closed-form expressions for bound-state energies and the
corresponding eigenfunctions are found at some particular values of wx. For
highly-accurate determination of energy levels at other values of wx, we apply
an efficient scheme based on the Frobenius expansion.Comment: 11 pages, 4 figure
Three strongly correlated charged bosons in a one-dimensional harmonic trap: natural orbital occupancies
We study a one-dimensional system composed of three charged bosons confined
in an external harmonic potential. More precisely, we investigate the
ground-state correlation properties of the system, paying particular attention
to the strong-interaction limit. We explain for the first time the nature of
the degeneracies appearing in this limit in the spectrum of the reduced density
matrix. An explicit representation of the asymptotic natural orbitals and their
occupancies is given in terms of some integral equations.Comment: 6 pages, 4 figures, To appear in European Physical Journal
The optimized Rayleigh-Ritz scheme for determining the quantum-mechanical spectrum
The convergence of the Rayleigh-Ritz method with nonlinear parameters
optimized through minimization of the trace of the truncated matrix is
demonstrated by a comparison with analytically known eigenstates of various
quasi-solvable systems. We show that the basis of the harmonic oscillator
eigenfunctions with optimized frequency ? enables determination of boundstate
energies of one-dimensional oscillators to an arbitrary accuracy, even in the
case of highly anharmonic multi-well potentials. The same is true in the
spherically symmetric case of V (r) = {\omega}2r2 2 + {\lambda}rk, if k > 0.
For spiked oscillators with k < -1, the basis of the pseudoharmonic oscillator
eigenfunctions with two parameters ? and {\gamma} is more suitable, and
optimization of the latter appears crucial for a precise determination of the
spectrum.Comment: 22 pages,8 figure
Ground-state correlation properties of charged bosons trapped in strongly anisotropic harmonic potentials
We study systems of a few charged bosons contained within a strongly
anisotropic harmonic trap. A detailed examination of the ground-state
correlation properties of two-, three-, and four-particle systems is carried
out within the framework of the single-mode approximation of the transverse
components. The linear correlation entropy of the quasi-1D systems is discussed
in dependence on the confinement anisotropy and compared with a strictly 1D
limit. Only at weak interaction the correlation properties depend strongly on
the anisotropy parameter.Comment: 5 pages, 6 figure
Application of the Frobenius method to the Schrodinger equation for a spherically symmetric potential: anharmonic oscillator
The power series method has been adapted to compute the spectrum of the
Schrodinger equation for central potential of the form . The bound-state energies
are given as zeros of a calculable function, if the potential is confined in a
spherical box. For an unconfined potential the interval bounding the energy
eigenvalues can be determined in a similar way with an arbitrarily chosen
precision. The very accurate results for various spherically symmetric
anharmonic potentials are presented.Comment: 16 pages, 5 figures, published in J. Phys
Variational collocation for systems of coupled anharmonic oscillators
We have applied a collocation approach to obtain the numerical solution to
the stationary Schr\"odinger equation for systems of coupled oscillators. The
dependence of the discretized Hamiltonian on scale and angle parameters is
exploited to obtain optimal convergence to the exact results. A careful
comparison with results taken from the literature is performed, showing the
advantages of the present approach.Comment: 14 pages, 10 table
Analysis of possibilities of application of reliability engineering in monitoring vertical displacements
Reliability engineering is widely applied in many technical areas. It is always used when we deal with utilisation of materials, constructed elements, subsystems, being parts of systems or entire objects. In geodesy issues related to reliability engineering have been introduced recently. They are connected with city vertical control networks. Those networks, considered as a "material" product, undergo the process of ageing. Researchers dealing with those issues apply reliability engineering to forecast the level of degradation of those networks. Such forecasts allow to commence certain efforts in order to maintain the quality of a network at the level which ensures it correct operations performed for economic purposes. Monitoring of vertical networks is important in order to ensure the safety of many building constructions. The basis for determination of displacements is to ensure the continuation of operation of the reference base in the designed control network. The paper will present analysis and proposals concerning utilisation of elements of reliability engineering for estimations of durability of reference bases and their comparison for utilisation in the process of forecasting the durability of city vertical control networks