Role of exchange interaction in self-consistent calculations of endohedral fullerenes

Results of the self-consistent calculation of electronic structure of endohedral fullerene Ar@C$_{60}$ within the Hartree-Fock and the local density approximations are presented. Hartree-Fock approximation is used for the self-consistent description for the first time. It is shown that the accurate account of the exchange interaction between all electrons of the compound leads to the significant modification of the atomic valent shell which causes the noticeable charge redistribution inside the endohedral compound.Comment: 5 figures, Proceedings of the 5th Conference on Elementary Processes in Atomic Systems (CEPAS 2011), submitted to Nuclear Instruments and Methods in Physics Research Section

Spatial and spin symmetry breaking in semidefinite-programming-based Hartree-Fock theory

The Hartree-Fock problem was recently recast as a semidefinite optimization over the space of rank-constrained two-body reduced-density matrices (RDMs) [Phys. Rev. A 89, 010502(R) (2014)]. This formulation of the problem transfers the non-convexity of the Hartree-Fock energy functional to the rank constraint on the two-body RDM. We consider an equivalent optimization over the space of positive semidefinite one-electron RDMs (1-RDMs) that retains the non-convexity of the Hartree-Fock energy expression. The optimized 1-RDM satisfies ensemble $N$-representability conditions, and ensemble spin-state conditions may be imposed as well. The spin-state conditions place additional linear and nonlinear constraints on the 1-RDM. We apply this RDM-based approach to several molecular systems and explore its spatial (point group) and spin ($S^2$ and $S_3$) symmetry breaking properties. When imposing $S^2$ and $S_3$ symmetry but relaxing point group symmetry, the procedure often locates spatial-symmetry-broken solutions that are difficult to identify using standard algorithms. For example, the RDM-based approach yields a smooth, spatial-symmetry-broken potential energy curve for the well-known Be--H$_2$ insertion pathway. We also demonstrate numerically that, upon relaxation of $S^2$ and $S_3$ symmetry constraints, the RDM-based approach is equivalent to real-valued generalized Hartree-Fock theory.Comment: 9 pages, 6 figure

A New Method and a New Scaling For Deriving Fermionic Mean-field Dynamics

We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schroedinger equation for fermionic many-particle systems in quantum mechanics. The method is an adaption of the method used in [Pickl, Lett. Math. Phys., 97(2):151-164, 2011] for bosonic systems to fermionic systems. It is based on a Gronwall type estimate for a suitable measure of distance between the microscopic solution and an antisymmetrized product state. We use this method to treat a new mean-field limit for fermions with long-range interactions in a large volume. Some of our results hold for singular attractive or repulsive interactions. We can also treat Coulomb interaction assuming either a mild singularity cutoff or certain regularity conditions on the solutions to the Hartree(-Fock) equations. In the considered limit, the kinetic and interaction energy are of the same order, while the average force is subleading. For some interactions, we prove that the Hartree(-Fock) dynamics is a more accurate approximation than a simpler dynamics that one would expect from the subleading force. With our method we also treat the mean-field limit coupled to a semiclassical limit, which was discussed in the literature before, and we recover some of the previous results. All results hold for initial data close (but not necessarily equal) to antisymmetrized product states and we always provide explicit rates of convergence.Comment: 42 pages, LaTex; v2: introduction expanded, presentation of main results improved, several minor improvements and references adde

Spontaneous coherence and the quantum Hall Effect in triple-layer electron systems

We investigate spontaneous interlayer phase coherence and the occurrence of the quantum Hall effect in triple-layer electron systems. Our work is based on a simple tight-binding model that greatly facilitates calculations and whose accuracy is verified by comparison with recent experiments. By calculating the ground state in an unrestricted Hartree-Fock approximation and the collective-mode spectrum in a time-dependent Hartree-Fock approximation, we construct a phase diagram delimiting regions in the parameter space of the model where the integer quantum Hall effect occurs in the absence of interlayer tunneling.Comment: To appear in Phys. Rev. B, 20 pages, 5 PostScript figures uuencoded with TeX fil

Spontaneous Coherence and Collective Modes in Double-Layer Quantum Dot Systems

We study the ground state and the collective excitations of parabolically-confined double-layer quantum dot systems in a strong magnetic field. We identify parameter regimes where electrons form maximum density droplet states, quantum-dot analogs of the incompressible states of the bulk integer quantum Hall effect. In these regimes the Hartree-Fock approximation and the time-dependent Hartree-Fock approximations can be used to describe the ground state and collective excitations respectively. We comment on the relationship between edge excitations of dots and edge magneto-plasmon excitations of bulk double-layer systems.Comment: 20 pages (figures included) and also available at http://fangio.magnet.fsu.edu/~jhu/Paper/qdot_cond.ps, replaced to fix figure

Effect of Pauli repulsion and transfer on fusion

The effect of the Pauli exclusion principle on the nucleus-nucleus bare potential is studied using a new density-constrained extension of the Frozen-Hartree-Fock (DCFHF) technique. The resulting potentials exhibit a repulsion at short distance. The charge product dependence of this Pauli repulsion is investigated. Dynamical effects are then included in the potential with the density-constrained time-dependent Hartree-Fock (DCTDHF) method. In particular, isovector contributions to this potential are used to investigate the role of transfer on fusion, resulting in a lowering of the inner part of the potential for systems with positive Q-value transfer channels.Comment: Proceedings of an invited talk given at FUSION17, Hobart, Tasmania, AU (20-24 February, 2017