scholarly journals Spatial Entanglement of Fermions in One-Dimensional Quantum Dots

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 868
Author(s):  
Ivan P. Christov
Keyword(s):  
Quantum Dots ◽  
Quantum Monte Carlo ◽  
Wave Functions ◽  
Quantum Nonlocality ◽  
One Dimensional ◽  
Hartree Fock ◽  
Spin Polarized ◽  
Quantum Monte Carlo Method ◽  
The Rich ◽  
Reduced Density

The time-dependent quantum Monte Carlo method for fermions is introduced and applied in the calculation of the entanglement of electrons in one-dimensional quantum dots with several spin-polarized and spin-compensated electron configurations. The rich statistics of wave functions provided by this method allow one to build reduced density matrices for each electron, and to quantify the spatial entanglement using measures such as quantum entropy by treating the electrons as identical or distinguishable particles. Our results indicate that the spatial entanglement in parallel-spin configurations is rather small, and is determined mostly by the spatial quantum nonlocality introduced by the ground state. By contrast, in the spin-compensated case, the outermost opposite-spin electrons interact like bosons, which prevails their entanglement, while the inner-shell electrons remain largely at their Hartree–Fock geometry. Our findings are in close correspondence with the numerically exact results, wherever such comparison is possible.

Particle-hole pair and beelectron states in ZnO/(Zn,Mg)O quantum wells and Dirac materials.

2015 ◽  
Vol 10 (1) ◽  
pp. 2583-2604
Author(s):  
Lyubov E. Lokot
Keyword(s):  
Quantum Well ◽  
Charge Density ◽  
Heavy Hole ◽  
Wave Functions ◽  
One Dimensional ◽  
Exchange Correlation ◽  
Hartree Fock ◽  
Exchange Correlation Potential ◽  
Correlation Potential ◽  
The One

In this paper a theoretical studies of the space separation of electron and hole wave functions in the quantum well ZnO/Mg(0.27)Zn(0.73)O are presented. For this aim the self-consistent solution of the Schrödinger equations for electrons and holes and the Poisson equations at the presence of spatially varying quantum well potential due to the piezoelectric effect and local exchange-correlation potential is found. The one-dimensional Poisson equation contains the Hartree potential which includes the one-dimensional charge density for electrons and holes along the polarization field distribution. The three-dimensional Poisson equation contains besides the one-dimensional charge density for electrons and holes the exchange-correlation potential which is built on convolutions of a plane-wave part of wave functions in addition. The shifts of the Hartree valence band spectrums and the conduction band spectrum with respect to the flat band spectrums as well as the Hartree-Fock band spectrums with respect to the Hartree ones are found. An overlap integrals of the wave functions of holes and electron with taking into account besides the piezoelectric effects the exchange-correlation effects in addition is greater than an overlap integral of Hartree ones. The Hartree particles distribute greater on edges of quantum well than Hartree-Fock particles. It is found that an effective mass of heavy hole of Mg(0.27)Zn(0.73)O under biaxial strain is greater than an effective-mass of heavy hole of ZnO. It is calculated that an electron mass is less than a hole mass. It is found that the Bohr radius is grater than the localization range particle-hole pair, and the excitons may be spontaneously created.Schrödinger equation for pair of two massless Dirac particles when magnetic field is applied in Landau gauge is solved exactly. In this case the separation of center of mass and relative motion is obtained. Landau quantization $\epsilon=\pm\,B\sqrt{l}$ for pair of two Majorana fermions coupled via a Coulomb potential from massless chiral Dirac equation in cylindric coordinate is found. The root ambiguity in energy spectrum leads into Landau quantization for beelectron, when the states in which the one simultaneously exists are allowed. The tachyon solution with imaginary energy in Cooper problem ($\epsilon^{2}<0$) is found.

THE DIFFUSION QUANTUM MONTE CARLO METHOD: DESIGNING TRIAL WAVE FUNCTIONS FOR NiO

2003 ◽  
Vol 17 (28) ◽  
pp. 5425-5434 ◽  
Author(s):  
R. J. NEEDS ◽  
M. D. TOWLER
Keyword(s):  
Monte Carlo ◽  
Wave Function ◽  
Monte Carlo Method ◽  
Transition Metal ◽  
Quantum Monte Carlo ◽  
Monte Carlo Study ◽  
Trial Wave Function ◽  
Wave Functions ◽  
Quantum Monte Carlo Method

A brief overview of the diffusion quantum Monte Carlo method is given. The importance of the trial wave function is emphasised and we discuss how to design satisfactory forms for transition metal monoxides. Some results of a diffusion quantum Monte Carlo study of NiO are reported.

DIFFUSION MONTE CARLO STUDY OF GROUND STATE PROPERTIES OF QUANTUM DOTS

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1443-1446 ◽  
Author(s):  
FRANCESCO PEDERIVA
Keyword(s):  
Quantum Dots ◽  
Monte Carlo ◽  
Ground State ◽  
Monte Carlo Study ◽  
Wave Functions ◽  
Local Spin Density Approximation ◽  
Density Approximation ◽  
Diffusion Monte Carlo ◽  
Hartree Fock ◽  
Parabolic Quantum Dot

We present the results of Diffusion Monte Carlo (DMC) calculations based on accurate multiconfiguration wave functions for N electrons (N≤13) confined to a parabolic quantum dot. The density and correlation energies have been computed and compared with the predictions of local spin density approximation theory (LSDA). We also computed the addition energy a function of the number of electrons in the dot, and compared them with the results of LSDA and Hartree Fock calculations. DMC results show a behavior qualitatively closer to the result of recent capacitance experiments.

VARIATIONAL COMPUTATIONS FOR EXCITONS IN QUANTUM DOTS: A QUANTUM MONTE CARLO STUDY

2011 ◽  
Vol 25 (01) ◽  
pp. 119-130
Author(s):  
A. YILDIZ ◽  
S. ŞAKİROĞLU ◽  
Ü. DOĞAN ◽  
K. AKGÜNGÖR ◽  
H. EPİK ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Monte Carlo ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Three Dimensional ◽  
Monte Carlo Study ◽  
Wave Functions ◽  
Monte Carlo Techniques ◽  
Oscillator Basis ◽  
Ground State Energies

A study of variational wave functions for calculation of the ground-state energies of excitons confined in a two-dimensional (2D) disc-like and three-dimensional (3D) spherical parabolic GaAs quantum dots (QDs) is presented. We have used four variational trial wave functions constructed as the harmonic-oscillator basis multiplied by different correlation functions. The proposed correlation function formed by including linear expansion in terms of Hylleraas-like coordinates to the Jastrow factor is able to capture nearly exactly the ground-state energies of 3D excitons, and it properly account for the results of 2D excitons. Quantum Monte Carlo techniques combined with the proposed wave function are a powerful tool for studying excitons in parabolic QDs.

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