For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and V (x) = g/x with the coefficient g in a certain range (x being a space coordinate in one or more dimensions), the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physica...

The simplest iterative complement (SIC) calculations starting from Hartree-Fock and giving full configuration interaction (CI) at convergence were performed using regular and inverse Hamiltonians. Each iteration step is variational and involves only one variable. The convergence was slow when we used the regular Hamiltonian, but became very fast when we used the inverse Hamiltonian. This differ...

The condensation of closed string tachyons localized at the fixed point of a C/Γ orbifold can be studied in the framework of renormalization group flow in a gauged linear sigma model. The evolution of the Higgs branch along the flow describes a resolution of singularities via the process of tachyon condensation. The study of the fate of D-branes in this process has lead to a notion of a “quantu...

Some Bravais lattices have a particular geometry that can slow down the motion of Bloch electrons by pre-localization due to the band-structure properties. Another known source of electronic localization in solids is the Coulomb repulsion in partially filled d or f orbitals, which leads to the formation of local magnetic moments. The combination of these two effects is usually considered of lit...

The generalised Madelung problem, that of finding the spatial electric potential within a crystal lattice, is often approached via analytic function theory. But new results can be achieved through careful application of standard theorems from classical electro-statics. In this way we show that the celebrated Madelung constant for the NaCl crystal can be rigorously bounded through symmetry argum...

We study the large-order asymptotic behavior of the perturbation series for short-distance coefficients in the NRQCD factorization formulas for the decays J/ψ → e+e− and ηc → γγ. The short-distance coefficients of the leading matrix elements are calculated to all orders in the large-Nf limit. We find that there is a universal Borel resummable renormalon associated with the cancellation of the C...

this article addresses an efficient and novel method for singularity-free path planning and obstacle avoidance of parallel manipulator based on neural networks. a modified 4-5-6-7 interpolating polynomial is used to plan a trajectory for a spherical parallel manipulator. the polynomial function which is smooth and continuous in displacement, velocity, acceleration and jerk is used to find a pat...

The disclosure of basic nonlinear optical properties graphene-like nanostructures with correlated electron-hole dynamics over a wide range frequencies and pump field intensities is great importance for both graphene fundamental physics the expected novel applications two-dimensional (2D) hexagonal in extreme optics. In current paper, interaction 2D bichromatic infrared driving taking into accou...