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Przemyslaw Koscik

Publications and source records attributed to Przemyslaw Koscik.

15 recordsLinked to original sources
arXiv2016

Bipartite correlations in quantum resonance states

We discuss a diagonal representation of a reduced density matrix determined within the framework of the complex scaling method. We also discuss a possible measure of bipartite correlations in quantum resonance states. As an example, we consider a one-dimensional system of two bosons with a contact interaction subjected to an open potential well. The correlation properties of the lowest-energy resonance state of the system are explored over a wide range of the inter-boson interaction strength, including the Tonks-Girardeau regime.

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arXiv2015

Entanglement in helium atom confined in an impenetrable cavity

We explore ground-state entanglement properties of helium atom confined at the center of an impenetrable spherical cavity of varying radius by using explicitly correlated Hylleraas-type basis set. Results for the dependencies of the von Neumann and linear entanglement entropic measures on the cavity radius are discussed in details. Some highly accurate numerical results for the von Neumann and linear entropy are reported for the first time. It is found that the transition to the strong confinement regime is manifested by the entropies as an appearance of the inflection points on their variations.

quant-ph↗
arXiv2015

The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

We study one-dimensional systems of $N$ particles in a one-dimensional harmonic trap with an inverse power law interaction $\sim|x|^{-d}$. Within the framework of the harmonic approximation we derive, in the strong interaction limit, the Schmidt decomposition of the one-particle reduced density matrix and investigate the nature of the degeneracy appearing in its spectrum. Furthermore, the ground-state asymptotic occupancies and their natural orbitals are derived in closed analytic form, which enables their easy determination for a wide range of values of $N$. A closed form asymptotic expression for the von Neumann entanglement entropy is also provided and its dependence on $N$ is discussed for the systems with $d=1$ (charged particles) and with $d=3$ (dipolar particles).

quant-ph↗
arXiv2014

Quantum entanglement of two harmonically trapped dipolar particles

We study systems of two identical dipolar particles confined in quasi one-dimensional harmonic traps. Numerical results for the dependencies of the entanglement on the control parameters of the systems are provided and discussed in detail. In the limit of a strong interaction between the particles, the occupancies and the von Neumann entropies of the bosonic and fermionic ground states are derived in closed analytic forms by applying the harmonic approximation. The strong correlation regimes of the system with the dipolar bosons and the system with the charged ones are compared with each other in regard to aspects of their entanglement.

quant-ph↗
arXiv2014

Entanglement entropies in the ground states of helium-like atoms

We examine the entanglement in the ground states of helium and helium-like ions using an original Hylleraas expansion. The von Neumann and linear entropies of the reduced density matrix are accurately computed by performing the Schmidt decomposition of the S singlet spatial wavefunctions. The results presented are more accurate than currently available in published literature.

quant-ph↗
arXiv2013

Entanglement in S states of two-electron quantum dots with Coulomb impurities at the center

We study a system of two Coulombically interacting electrons in an external harmonic potential in the presence of an on-centre Coulomb impurity. Detailed results for the dependencies of the reduced von Neumann entropy on the control parameters of the system are provided for both the ground state and the triplet S states with the lowest energy. Among other features, it is found that in the weak confinement regime the entanglement is strongly affected by the presence of an acceptor impurity.

quant-ph↗
arXiv2012

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.

quant-ph↗
arXiv2012

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.

quant-ph↗
arXiv2010

Two-electron entanglement in a two-dimensional isotropic harmonic trap: Radial correlation effects in the low density limit

We study a two-dimensional system of two Coulombically interacting electrons in an external harmonic confining potential. More precisely, we present calculations for the singlet ground-state of the system. We explain the nature of the degeneracy in the spectrum of the reduced density matrix and provide detailed results for the dependencies of the entanglement on the interaction strength. Among other features, it is indicated that in the limit of an infinitely strong interaction, the angular and radial correlations are asymptotically independent of each other. Appearing in this limit, the pure radial correlation effects are quantitatively investigated for the first time.

quant-ph↗
arXiv2010

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.

quant-ph↗
arXiv2010

Two-electron entanglement in elliptically deformed quantum dots

Entropic entanglement measures of a two-dimensional system of two Coulombically interacting particles confined in an anisotropic harmonic potential are discussed in dependence on the anisotropy and the interaction strength. The harmonic approximation appears exact in the strong interaction limit, allowing determination of the asymptotic expression for the linear entropy. Entanglement properties are dramatically influenced by the anisotropy of the confining potential in the strong-correlation regime.

quant-ph↗
arXiv2010

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) = ω2r2 2 + λrk, if k > 0. For spiked oscillators with k < -1, the basis of the pseudoharmonic oscillator eigenfunctions with two parameters ? and γ is more suitable, and optimization of the latter appears crucial for a precise determination of the spectrum.

quant-ph↗
arXiv2007

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.

quant-ph↗
arXiv2005

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 $V(r)={d_{-2}\over r^2}+{d_{-1}\over r}+\sum_{i=0}^{\infty} d_{i}r^i$. 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.

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