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Analytical Solutions for States of the 3D Hooke's Atom in an External B Field

Samuel B. Trickey, Wuming Zhu

Bulletin of the American Physical SocietyMar 24, 20050 citations

Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke’s atom

Ilkka Ruokosenmäki, Hossein Gholizade, Ilkka Kylänpää +1 more

arXiv:1510.02230Computer Physics CommunicationsOct 8, 20163 citations

Hooke's Atom in an Arbitrary External Electric Field: Analytical Solutions of Two-Electron Problem by Path Integral Approach

Liang Cai, Ping Zhang, Tao Yang +1 more

By using the path integral approach, we investigate the problem of Hooke's atom (two electrons interacting with Coulomb potential in an external harmonic-oscillator potential) in an arbitrary time-dependent electric field. For a certain infinite set of discrete oscillator frequencies, we obtain the analytical solutions. The ground state polarization of the atom is then calculated. The same result is also obtained through linear response theory.

Communications in Theoretical PhysicsApr 1, 20114 citations

Eigenstates and dynamics of Hooke’s atom: Exact results and path integral simulations

Hossein Gholizadehkalkhoran, Ilkka Ruokosenmäki, Tapio T. Rantala

The system of two interacting electrons in one-dimensional harmonic potential or Hooke’s atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the “space splitting” arising from the one-dimensional Coulomb potential. Here, we complete the numerous previous studies of the ground state of Hooke’s atom by including the excited states and dynamics, not considered earlier. With the perturbation theory, we reach essentially exact eigenstate energies and wave functions for the strong confinement regime as novel results. We also consider external perturbation induced quantum dynamics in a simple separable case. Finally, we test our novel numerical approach based on real-time path integrals (RTPIs) in reproducing the above. The RTPI turns out to be a straightforward approach with exact account of electronic correlations for solving the eigenstates and dynamics without the conventional restrictions of electronic structure methods.The system of two interacting electrons in one-dimensional harmonic potential or Hooke’s atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the “space splitting” arising from the one-dimensional Coulomb potential. Here, we complete the numerous previous studies of the ground state of Hooke’s atom by including the excited states and dynamics, not considered earlier. With the perturbation theory, we reach essentially exact eigenstate energies and wave functions for the strong confinement regime as novel results. We also consider external perturbation induced quantum dynamics in a simple separable case. Finally, we test our novel numerical approach based on real-time path integrals (RTPIs) in reproducing the above. The RTPI turns out to be a straightforward approach with exact account of electronic correlations for solving the eigenstates and dynamics without the conventional restrictions of electronic structure methods.

Journal of Mathematical PhysicsMay 1, 20185 citations

Interacting electrons in one dimension: a path integral Monte Carlo study

Alexander P. Lyubartsev

Path integral Monte Carlo simulations have been carried out for a system of interacting fermionic particles in one dimension. Due to the fact that the sign problem can be completely eliminated for one-dimensional systems, such simulations allow one to obtain accurate energies and particle densities in arbitrary external potentials. Two cases were considered: electrons in the field of a uniform neutralizing background and in an effective field of atoms on a lattice. In the latter case, a clear asymmetry of the charge density distribution of conducting electrons and holes has been observed.Path integral Monte Carlo simulations have been carried out for a system of interacting fermionic particles in one dimension. Due to the fact that the sign problem can be completely eliminated for one-dimensional systems, such simulations allow one to obtain accurate energies and particle densities in arbitrary external potentials. Two cases were considered: electrons in the field of a uniform neutralizing background and in an effective field of atoms on a lattice. In the latter case, a clear asymmetry of the charge density distribution of conducting electrons and holes has been observed.

Journal of Physics A Mathematical and TheoreticalJun 12, 20076 citations

On the Interaction Between a Time-Dependent Field and a Two-Level Atom: Path Integral Treatment

Hilal Benkhelil, Mekki Aouachria

International Journal of Theoretical PhysicsNov 2, 20200 citations

Hooke＇s Atom in an Arbitrary External Electric Field： Analytical Solutions of Two-Electron Problem by Path Integral Approach

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Hooke＇s Atom in an Arbitrary External Electric Field： Analytical Solutions of Two-Electron Problem by Path Integral Approach

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