Set Of Single-particle States Research Articles

Construction and Universal Application of Entanglement-Erasing Partner States.

We investigate the subadditivity of the bipartite entanglement entropy (EE) of many-particle states, represented by Slater determinants, with respect to single particle excitations. In this setting, subadditivity can be phrased as erasure of EE, i.e., as a relative decrease in EE when adding excitations to the quantum state. We identify sets of single particle states that yield zero EE if jointly excited. Such states we dub entanglement erasing partner states (EEPS). These EEPS reveal a mechanism that describes how to disentangle two subspaces of a Hilbert space by exciting additional states. We demonstrate this general finding in Anderson and many-body localized models. The studied concept of entanglement erasure further enables us to derive the EE of Slater determinants in the free tight binding model. Here, our analytical findings show surprisingly good agreement with numerical results of the interacting XXX chain. The described EEPS further impose a universal, i.e., model independent, erasure of EE for randomly excited Slater determinants. This feature allows us to compute many-particle EE by means of the associated single particle states and the filling ratio. This novel finding can be employed to drastically reduce the computational effort in free models.

QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

QmeQ is an open-source Python package for numerical modeling of transport through quantum dot devices with strong electron–electron interactions using various approximate master equation approaches. The package provides a framework for calculating stationary particle or energy currents driven by differences in chemical potentials or temperatures between the leads which are tunnel coupled to the quantum dots. The electronic structures of the quantum dots are described by their single-particle states and the Coulomb matrix elements between the states. When transport is treated perturbatively to lowest order in the tunneling couplings, the possible approaches are Pauli (classical), first-order Redfield, and first-order von Neumann master equations, and a particular form of the Lindblad equation. When all processes involving two-particle excitations in the leads are of interest, the second-order von Neumann approach can be applied. All these approaches are implemented in QmeQ. We here give an overview of the basic structure of the package, give examples of transport calculations, and outline the range of applicability of the different approximate approaches. Program summaryProgram Title:QmeQProgram Files doi:http://dx.doi.org/10.17632/8687mrhgg9.1Licensing provisions: BSD 2-ClauseProgramming language:PythonExternal libraries:NumPy, SciPy, CythonNature of problem: Calculation of stationary state currents through quantum dots tunnel coupled to leads.Solution method: Exact diagonalization of the quantum dot Hamiltonian for a given set of single particle states and Coulomb matrix elements. Numerical solution of the stationary-state master equation for a given approximate approach.Restrictions: Depending on the approximate approach the temperature needs to be sufficiently large compared to the coupling strength for the approach to be valid.

Photoelectron spectra from full time dependent self-interaction correction

In the framework of time dependent density functional theory at the level of the local density approximation, we discuss the applicability of a self-interaction correction to the description of realistic irradiation scenarios of small clusters and molecules. The practical implementation of the static and dynamic self-interaction correction is formulated in terms of two complementing sets of single particle states. We show that an efficient numerical implementation of the two-set approach allows such calculations at a reasonable numerical expense and that scaling with system size imposes no hindrance for calculations in larger systems. As an example of a particular application, we discuss the computation of photoelectron spectra, addressing also its relation to the single particle energies of the occupied states in the two-set approach.

Gamow-Hartree-Fock-Bogoliubov method: Representation of quasiparticles with Berggren sets of wave functions

Single-particle resonant states, also called Gamow states, as well as bound and scattering states of complex energy form a complete set, the Berggren completeness relation. It is the building block of the recently introduced Gamow shell model, where weakly bound and resonant nuclear wave functions are expanded with a many-body basis of Slater determinants generated by this set of single-particle states. However, Gamow states have never been studied in the context of Hartree-Fock-Bogoliubov theory, except in the Bardeen-Cooper-Schriefer (BCS) approximation, where both the upper and lower components of a quasiparticle wave function are assumed to possess the same radial dependence with that of a Gamow state associated with the Hartree-Fock potential. Hence, an extension of the notion of Gamow state has to be effected in the domain of quasiparticles. It is shown theoretically and numerically that bound, resonant and scattering quasiparticles are well defined and form a complete set, by which bound Hartree-Fock-Bogoliubov ground states can be constructed. It is also shown that the Gamow-Hartree-Fock single-particle basis can be used to solve the Gamow-Hartree-Fock-Bogoliubov problem. As an illustration, the proposed method is applied to neutron-rich nickel isotopes close to the neutron drip-line.

Study of resonant structures in a deformed mean field by the contour deformation method in momentum space

Solution of the momentum space Schr\"odinger equation in the case of deformed fields is being addressed. In particular it is shown that a complete set of single particle states which includes bound, resonant and complex continuum states may be obtained by the Contour Deformation Method. This generalized basis in the complex energy plane is known as a Berggren basis. The momentum space Schr\"odinger equation is an integral equation which is easily solved by matrix diagonalization routines even for the case of deformed fields. The method is demonstrated for axial symmetry and a fictitious "deformed $^5$He", but may be extended to more general deformation and applied to truly deformed halo nuclei.

Multiband theory of multi-exciton complexes in self-assembled quantum dots

We report on a multiband microscopic theory of many-exciton complexes in self-assembled quantum dots. The single particle states are obtained by three methods: single-band effective-mass approximation, the multiband $\mathbf{k}∙\mathbf{p}$ method, and the tight-binding method. The electronic structure calculations are coupled with strain calculations via Bir-Pikus Hamiltonian. The many-body wave functions of $N$ electrons and $N$ valence holes are expanded in the basis of Slater determinants. The Coulomb matrix elements are evaluated using statically screened interaction for the three different sets of single particle states and the correlated $N$-exciton states are obtained by the configuration interaction method. The theory is applied to the excitonic recombination spectrum in InAs/GaAs self-assembled quantum dots. The results of the single-band effective-mass approximation are successfully compared with those obtained by using the of $\mathbf{k}∙\mathbf{p}$ and tight-binding methods.

Toward a global exciton model: the equilibrium component

The shell corrections to the equilibrium state densities in the exciton model code PRECO-E have been revised by adding a correction to the level density parameter and by modifying the energy shift based on the set of single particle states from the pre-equilibrium calculations. The range of mass numbers over which shell structure washes out was increased in both parts of the calculations. Additionally, the proton total reaction cross sections below the Coulomb barrier have been extended to lower energies, and a global function has been applied to reduce their intensity. Finally a method of compensating for the lack of gamma-ray competition with secondary particle evaporation in the calculations has been added.

Shell-corrected particle-hole state densities for pre-equilibrium reaction calculations

Calculated particle-hole state densities in the shell-shifted equi-spacing model (s2-ESM) potentially provide a fast and simple way to consistently include shell structure effects in pre-equilibrium reaction calculations. Results from the existing state density formalism were compared with results from the exact counting of states, and the methodology for evaluating the effective single particle state densities in the s2-ESM state density formula was completely revised. Calculated state densities were then compared with literature results obtained from more realistic sets of single particle states, indicating the model's utility. Finally, model-independent estimates of the sizes of the shell gaps were obtained from a set of nuclear mass tables so that the s2-ESM can be used in reaction calculations without the introduction of any new free parameters.

Pairing Corrections and Spin Cutoff Factors in Exciton Level Densities for Two Kinds of Fermions

Pairing corrections in particle-hole (exciton) state-density formulas used in precompound nuclear reaction theories are, strictly speaking, dependent on the nuclear excitation energy U and the exciton number n. A general formula for (U, n)-dependent pairing corrections was derived earlier for the exciton state-density formula for a system of one kind of fermion. A similar derivation is made for a system of two kinds of fermions, a system in which neutrons and protons occupy different sets of single-particle states. In this paper it is shown that the constant-pairing- energy correction used in standard state-density formulas, such as U{sub 0} in Gilbert and Cameron, is a limiting case of the present general (U,n)-dependent results. Spin cutoff factors are calculated using the same pairing theory and parameterized into an explicit (U,n)-dependent function, thereby defining the exciton level-density formula for two kinds of fermions. The results show that the ratios in the exciton level densities in the one-and two-fermion approaches vary with both U and n, thus, most likely leading to differences in calculated compound-to-precompound ratios. However, the differences in the spin cutoff factors in the two cases are found to be rather small.

Nonlocal screening in metal surfaces.

Due to the effect of the nonuniform environment on the static screening of the Coulomb potential, the local-density approximation for the particle-hole interaction is found to be inadequate to determine the surface energy of simple metals. Use of the same set of single-particle states, and thus the same one-body density and the same work function, has eliminated the single-electron states in favor of the structure of the short-ranged correlations as the basis of this effect. A posteriori simplifications of the Fermi hypernetted-chain theory may be found to allow the same calculational accuracy with simpler computational tools.

A relativistic structure model for heavy atoms

An ansatz for the calculation of the structure of heavy atoms using a relativistic model is described and developed. After using a series of Dirac-Fock calculations to define a suitable set of single-particle states, the set of orbitals is Schmidt orthogonalised and the one- and two-body Hamiltonian matrix elements calculated. This list of matrix elements is then processed and redefined to eliminate any reference to the inner electrons which are assumed to constitute a fixed core. These matrix elements are then utilised for large-dimension configuration-interaction calculations using Slater determinants as the basis functions. As an example, the ansatz is applied to the calculation of the low-lying states of Pb I and demonstrate the importance of configuration mixings within the ground-state manifold.

Single particle effects in precompound reactions

Double differential cross sections have been measured with time of flight techniques at 16 angles between 3.5/sup 0/ and 159/sup 0/ (lab) for the inclusive production of neutrons from reactions of 25 MeV protons with /sup 50,52,53/Cr, /sup 54,56,58/Fe, /sup 59/Co, /sup 60/Ni, /sup 63/Cu, /sup 89/Y, /sup 90,91,92,94/Zr, /sup 92,94,95,96,97,98,100/Mo, /sup 110/Pd, and /sup 159/Tb and of 18 MeV protons with /sup 90,91,92,94/Zr. The spectra from /sup 90,91,92,94/Zr targets are compared with qualitative and quantitative predictions based on proton-particle--neutron-hole state densities generated from different sets of single particle states using the recursion method of Williams et al. An end point gap of nearly 4 MeV in the /sup 91/Zr(p,n) spectrum may be understood quantitatively in terms of such an extreme single particle model argument. The experimental peak structure shows reasonably good agreement with the calculated results. It is shown that precompound spectra exhibit pronounced structure which is dependent upon nuclear structure effects for near closed shell nuclei, and that these effects should and do disappear rapidly with nuclear deformation, as predicted earlier by Williams et al.

Realistic calculations of parity distributions and densities of exciton states at high excitation energy

The density of states with fixed number of excitons and parity distribution in even-even nuclei has been studied as a function of excitation energy. In the calculations the properties of thermodynamic systems of even-even nuclei with realistic sets of single particle states and pairing constants has been used. The transformation of properties of even-even into odd thermodynamic system is also discussed.