Related papers: Wavefunctions for large electronic systems
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
This paper intends to provide a theoretical basis for the unification of the integer and the fractional quantum Hall effects. Guided by concepts and theories of quantum mechanics and with the solution of the Pauli equation in a magnetic…
We introduce a novel energy functional for ground-state electronic-structure calculations. Its fundamental variables are the natural spin-orbitals of the implied singlet many-body wave function and their joint occupation probabilities. The…
An eikonal expansion is developed in order to provide systematic corrections to the eikonal approximation through order 1/k^2, where k is the wave number. The expansion is applied to wave functions for the Klein-Gordon equation and for the…
An differential equation for wave functions is proposed, which is equivalent to Schr\"{o}dinger's wave equation and can be used to determine energy-level gaps of quantum systems. Contrary to Schr\"{o}dinger's wave equation, this equation is…
We demonstrate numerically that non-Abelian quasihole excitations of the $\nu = 5/2$ fractional quantum Hall state have some of the key properties necessary to support quantum computation. We find that as the quasihole spacing is increased,…
We present a simple formalism for the calculation of the derivatives of the electronic density matrix at any order, within density functional theory. Our approach, contrary to previous ones, is not based on the perturbative expansion of the…
Several methods are constructed for large-scale electronic structure calculations. Test calculations are carried out with up to 10^7 atoms. As an application, cleavage process of silicon is investigated by molecular dynamics simulation with…
Solving for the many-body wavefunction represents a significant challenge on both classical and quantum devices because of the exponential scaling of the Hilbert space with system size. While the complexity of the wavefunction can be…
We have investigated the organization and dynamics of the large turbulent structures that develop in the logarithmic and outer layers of high-Reynolds-number wall flows. These structures have sizes comparable to the flow thickness and…
Multipole moments are the first order responses of the energy to spatial derivatives of the electric field strength. The quality of density functional theory (DFT) prediction of molecular multipole moments thus characterizes errors in…
This study theoretically considers the motion of N identical inelastic particles between two oscillating walls. The particles' average energy increases abruptly at certain critical filling fractions, wherein the system changes into a…
Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms…
Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize, thereby reducing the magnitude of the interaction. Exchange integrals of…
The form of the wave function at three-electron coalescence points is examined for several spin states using an alternative method to the usual Fock expansion. We find that, in two- and three-dimensional systems, the non-analytical nature…
There are many ways to numerically represent of chemical systems in order to compute their electronic structure. Basis functions may be localized in real-space (atomic orbitals), in momentum-space (plane waves), or in both components of…
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…
One attractive interpretation of quantum mechanics is the ensemble interpretation, where Quantum Mechanics merely describes a statistical ensemble of objects and not individual objects. But this interpretation does not address why the…
Many-fermion Hilbert space has the algebraic structure of a free module generated by a finite number of antisymmetric functions called shapes. Physically, each shape is a many-body vacuum, whose excitations are described by symmetric…
Conceiving a molecule as composed of smaller molecular fragments, or subunits, is one of the pillars of the chemical and physical sciences, and leads to productive methods in quantum chemistry. Using a fragmentation scheme, efficient…