In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes the solution of the computational problem. These algorithms have generally been studied in the case where the “straight line” path from initial to final Hamilt...

In this paper, a mass (or normalization) and magnetization conservative and energydiminishing numerical method is presented for computing the ground state of spin-1 (or F = 1 spinor) Bose–Einstein condensates (BECs). We begin with the coupled Gross–Pitaevskii equations, and the ground state is defined as the minimizer of the energy functional under two constraints on the mass and magnetization....

In the present work, the exact diagonalization method had been implemented to calculate the ground state energy of shallow donor impurity located at finite distance along the growth axis in GaAs/AlGaAs heterostructure in the presence of a magnetic field taken to be along z direction. The impurity binding energy of the ground state had been calculated as a function of confining frequency and mag...

We construct a set of exact ground states with a localized ferromagnetic domain wall and an extended spiral structure in a quasi-one-dimensional deformed flatband Hubbard model. In the case of quarter filling, we show the uniqueness of the ground state with a fixed magnetization. The ground states with these structures are degenerate with the all-spin-up and all-spin-down states. This property ...

In this paper, we consider the Lx solution u to mass critical NLS iut + ∆u = ±|u| 4 d u. We prove that in dimensions d ≥ 4, if the solution is spherically symmetric and is almost periodic modulo scaling, then it must lie in H x for some ε > 0. Moreover, the kinetic energy of the solution is localized uniformly in time. One important application of the theorem is a simplified proof of the scatte...